a linear regression model using triangular fuzzy number coefficients fuzzy regression analysis using fuzzy linear models with symmetric triangular fuzzy number coefficients has been formulated earlier the goal of this regression is to find the coefficients of a proposed model for all given input output data sets in this paper we extend the results of a fuzzy linear regression model that uses symmetric triangular coefficient to one with non symmetric fuzzy triangular coefficients this work eradicates the inflexibility of existing fuzzy linear regression models

on the uniqueness of possibilistic measure of uncertainty and information abstract it is demonstrated through a series of theorems that the u uncertainty introduced by higashi and klir in 1982 is the only possibilistic measure of uncertainty and information that satisfies possibilistic counterparts of axioms of the well established shannon and hartley measures of uncertainty and information two complementary forms of the possibilistic counterparts of the probabilistic branching or grouping axiom which is usually used in proofs of the uniqueness of the shannon measure are introduced in this paper for the first time a one to one correspondence between possibility distributions and basic probabilistic assignments introduced by shafer in his mathematical theory of evidence is instrumental in most proofs in this paper the uniqueness proof is based on possibilistic formulations of axioms of symmetry expansibility additivity branching monotonicity and normalization

lq suboptimal decentralised controllers with disturbance rejection property for hierarchical systems this article is concerned with decentralised output regulation of hierarchical systems subject to input and output disturbances it is assumed that the disturbance can be represented as the output of an autonomous linear time invariant lti system with an unknown initial state the primary objective is to design a decentralised controller with the property that not only does it reject the degrading effect of the disturbance on the output to achieve a satisfactory steady state performance it also results in a small linear quadratic lq cost function implying a good transient behaviour to this end the underlying problem is treated in two phases in the first step a number of modified systems are defined in terms of the original system the problem of designing an lq centralised controller which stabilises all the modified systems and rejects the disturbance in the original system is considered and it is shown that this centralised controller can be found efficiently by solving a linear matrix ine

optimal unidirectional error detecting correcting codes in this correspondence a class of t error correcting and multiple unidirectional error detecting systematic codes is presented these codes are significantly more efficient than the earlier codes the efficiency of these codes approaches the efficiency of the bch codes asymptotically furthermore it is shown that these codes can be easily decoded also in this correspondence we have presented a generalization of berger codes over zq these new codes are also shown to be optimal

interconnection based performance analysis for a class of decentralized controllers this paper is concerned with decentralized controller design for large scale interconnected systems of pseudo hierarchical structure given such a system one can use existing techniques to design a decentralized controller for the reference hierarchical model obtained by eliminating certain weak interconnections of the original system although this indirect controller design is appealing as far as the computational complexity is concerned it does not necessarily result in satisfactory performance for the original pseudo hierarchical system an lq cost function is defined in order to evaluate the performance discrepancy between the pseudo hierarchical system and its reference hierarchical model under the designed decentralized controller a discrete lyapunov equation is then solved to compute this performance index however due to the large scale nature of the system this equation cannot be handled efficiently in many real world systems thus attaining an upper bound on this cost function can be more desirable than finding its exact value in practice for this purpose a novel technique is proposed which only requires solving a simple lmi optimization problem with three variables the problem is then reduced to a scalar optimization problem for which an explicit solution is provided it is also shown that when the original model is exactly hierarchical then the upper bounds obtained from the lmi and scalar optimization problems will both be equal to zero

a new class of symmetric error correcting unidirectional error detecting codes abstract a new class of symmetric error correcting unidirectional error detecting codes are developed they provide protection against both transient and permanent faults the codes are systematic in nature and hence the information bits are easy to retrieve the encoding decoding methods for these codes are discussed

maximum entropy membership functions for discrete fuzzy variables due to the deficiency of information the membership function of a fuzzy variable cannot be obtained explicitly it is a challenging work to find an appropriate membership function when certain partial information about a fuzzy variable is given such as expected value or moments this paper solves such problems for discrete fuzzy variables via maximum entropy principle and proves some maximum entropy theorems with certain constraints a genetic algorithm is designed to solve the general maximum entropy model for discrete fuzzy variables which is illustrated by some numerical experiments

sampling fuzzy discretization and signal reconstruction abstract the sampling theorem provides the condition under which a continuous time signal can be precisely represented and completely recovered from its instantaneous values equally spaced in time it gives a condition for the signal reconstruction problem the importance of this theorem pertains to the necessity of knowing when a continuous time signal is uniquely represented by its discrete version so that continuous time signals can be properly converted and handled by sampled data systems like digital computers the problem of the equivalence between either continuous time or discrete time signals and their fuzzy descriptions is analyzed here this encompasses the analysis of signal reconstruction when fuzzy systems are used as sampled data systems such as fuzzy filters fuzzy models or fuzzy controllers a necessary and sufficient condition is given for ensuring that the fuzzy system processes the legitimate representations of the signal presented at its interfaces furthermore a sufficient condition suitable for automatic tuning of membership functions is proposed and discussed the discussion encompasses the outline of some requirements that membership functions at fuzzy system interfaces should meet to allow humans to assess their semantic meaning

systematic t error correcting all unidirectional error detecting codes in this paper we give methods for the construction of systematic t random error correcting and all unidirectional error detecting codes also we give the encoding decoding algorithms and discuss their implementation

structural modification of systems using discretization and generalized sampled data hold functions this paper investigates the decentralized control of lti continuous time plants using generalized sampled data hold functions gshf gshfs can be used to modify the structure of the digraph of the resultant discrete plant by removing certain interconnections in the discrete time equivalent model to form a hierarchical system model of the plant this is a new application of discretization and has as its motivation the design of decentralized controllers using centralized methods

constructions and properties of block codes for partial response channels we report on block coding techniques for partial response channels with transfer function 1 spl mnplus d sup m m 1 2 we consider various constructions of block codes with prescribed minimum euclidean distance upper and lower bounds to the size of a code with minimum squared euclidean distance greater than unity are furnished a table is presented of cardinalities of codes of small length with prescribed minimum squared euclidean distance

efficiencies of two stage systems with fuzzy data two stage dea data envelopment analysis models show the performance of individual processes and thus are more informative than the conventional one stage models for making decisions this paper extends this approach from deterministic to uncertain situations where the observations are represented by fuzzy numbers the extension principle is utilized to develop a pair of two level mathematical programs to calculate the lower and upper bounds of the a cut of the fuzzy efficiency by enumerating various values of a the membership functions of fuzzy efficiencies are constructed numerically it is found that the property of the system efficiency being equal to the product of the two process efficiencies which holds for the deterministic case also holds for the fuzzy case this property can be generalized to series systems with more than two processes an example of non life insurance companies in taiwan is used to explain how to calculate the system and process efficiencies and how to derive their relationship when the data is fuzzy

an improvement on constructions of t ec aued codes a common method of constructing t error correcting all unidirectional error detecting t ec aued codes is to choose a t ec code and then to append a tail such that the new code can detect all unidirectional errors the tail is a function of the weight of the codeword we present a technique to reduce the weight distribution of the t ec code so that the tail needed will be shorter in some cases the weight distribution span of the code is reduced by eliminating the all zero codeword and replacing it with a codeword of weight greater than 2t 1

possibilistic kalman filtering for radar 2d tracking abstract standard kalman filter skf introduced by kalman in the 60s has gained a non estimated importance in control as well as in robotics community its importance arises from the obtained optimal result in the sense of variance minimization under stochastic gaussian and unbiased perturbations and when the state model as well as the measurement model are precisely known however when the last requirement is relaxed such that one or more parameters governing the models are ill defined and rather given in terms of interval evaluations chen et al ieee trans aerospace electr syst 33 1 1997 251 259 have proposed interval kalman filter ikf by extending the arithmetic operations to interval calculus in this paper we rather assume that the uncertainty pervading some parameters of the models are given in terms of possibility distributions 21 this leads to a formulation of possibilistic kalman filtering pkf which agrees with ikf the same example of 2d radar tracking is tackled comparisons with ikf are investigated as well the influence of the modelling process on the performance of the filter besides the proposal permits to capture certainty qualified information which cannot be obtained from ikf

possibility and necessity in optimization abstract we employ possibility and necessity in fuzzy programming and in other optimization problems that traditionally use random variables the possibility approach to multiobjective programming produces the same results as fuzzy programming a detailed example is presented to illustrate the use of possibility and necessity in optimization problems that usually employ random variables to describe uncertainty

image segmentation using fuzzy homogeneity criterion abstract the approach proposed here is using fuzzy homogeneity vectors and the fuzzy cooccurrence matrix to segment images homogeneity vectors could be used to represent the homogeneous feature between a pixel and its neighbors and the degree of homogeneity could be determined by using a fuzzy membership function combining the homogeneity vectors and the fuzzy membership function we could extract the feature of an image which determines the fuzzy region width with the fuzzy region width we could use the fuzzy cooccurrence matrix to measure the fuzzy geometry properties of an image which is the fuzzy entropy values that can be employed for determinine the thresholds to segment images the advantages of this approach are as follows first homogeneity vectors take account of the spatial gray tone dependence thus using homogeneity vectors has a better noise tolerance second from the extracted feature the fuzzy region width could be determined automatically third because the fuzzy region width is decided by the feature of the image it could be adjusted according to the nature of the image fourth the dimension of the fuzzy cooccurrence matrix representing the image is significantly decreased but the properties of images are faithfully preserved a large number of experiments have been carried out on different kinds of images and good results have been achieved by the proposed method this method will have wide application in image processing

fuzzy integrals on l fuzzy sets abstract the fuzzy measures and fuzzy integrals for zadeh s fuzzy sets were studied by qiao and wang 5 6 7 12 in this paper we consider the real valued fuzzy measures and fuzzy integrals for l fuzzy sets where l is a pseudocomplemented infinitely distributive complete lattice on a fuzzy algebra of l fuzzy sets the concepts of fuzzy measure and fuzzy integral are introduced some equivalent forms of fuzzy integrals on l fuzzy sets are given moreover we discuss several properties of fuzzy integrals on l fuzzy sets and prove some convergence theorems for a sequence of fuzzy integrals on l fuzzy sets

a possibilistic argument for irreversibility abstract our aim is to explicate the idea of irreversibility by a mathematical representation of irreversible processes occurring in possibilistic dynamical systems with this in mind solutions of the cauchy problem in the space of fuzzy points are examined to meet the correspondence argument solutions of the cauchy problem in the space of concentrated points are examined too

the expected value of a fuzzy number abstract the notions of expected interval and expected value of fuzzy number are introduced the expected interval is defined as the expected value of an interval random set generated by the fuzzy number and the expected value of this number is defined as the centre of the expected interval the linearity of the expected interval is studied

the evidential reasoning approach for mada under both probabilistic and fuzzy uncertainties abstract many multiple attribute decision analysis mada problems are characterised by both quantitative and qualitative attributes with various types of uncertainties incompleteness or ignorance and vagueness or fuzziness are among the most common uncertainties in decision analysis the evidential reasoning er approach has been developed in the 1990s and in the recent years to support the solution of mada problems with ignorance a kind of probabilistic uncertainty in this paper the er approach is further developed to deal with mada problems with both probabilistic and fuzzy uncertainties in this newly developed er approach precise data ignorance and fuzziness are all modelled under the unified framework of a distributed fuzzy belief structure leading to a fuzzy belief decision matrix a utility based grade match method is proposed to transform both numerical data and qualitative fuzzy assessment information of various formats into the fuzzy belief structure a new fuzzy er algorithm is developed to aggregate multiple attributes using the information contained in the fuzzy belief matrix resulting in an aggregated fuzzy distributed assessment for each alternative different from the existing er algorithm that is of a recursive nature the new fuzzy er algorithm provides an analytical means for combining all attributes without iteration thus providing scope and flexibility for sensitivity analysis and optimisation a numerical example is provided to illustrate the detailed implementation process of the new er approach and its validity and wide applicability

discrete time control of continuous systems with approximate decentralized fixed modes in this paper the discrete time control of decentralized continuous time systems which have approximate decentralized fixed modes is studied it is shown that under certain conditions discrete time controllers can improve the overall performance of the decentralized control system when a linear time invariant continuous time controller is ineffective in order to obtain these conditions a quantitative measure for different types of approximate fixed modes in a decentralized system is given in this case it is shown that discrete time zero order hold zoh controllers and in particular that generalized sampled data hold functions gshf can significantly improve the overall performance of the resultant closed loop system the proposed sampled data controller is in fact a linear time varying controller for the continuous time system

adaptation of the mactaggart and jack complex multiplication algorithm for floating point operators with a suitable treatment of the exponents in the input operands a hardware implementation of the mactaggart and jack fixed point complex multiplication algorithm can also calculate a floating point product with no loss in accuracy from the greater dynamic range of the floating point inputs this floating point technique can be extended to any sum to two products operation such as encountered in matrix multiplication and vector cross products

on fuzzy codes for asymmetric unidirectional errors abstract in this paper we investigate whether the distance between fuzzy code words fuzzy subsets of n tuples over a set f is dependent upon the dimension of the space as well as the distance between the non fuzzy code words on which they are based this is done for both asymmetric errors and unidirectional errors the results are compared and contrasted with the work of von kaenel 3 on fuzzy codes for symmetric errors

test pattern generation based on reed muller coefficients reed muller coefficients are used to generate a test pattern selection procedure for detecting single stuck at faults this procedure is based on the heuristics deduced from the way in which the spectral coefficients are affected by such faults the changes that the spectral coefficients undergo are also compared with the fault models used most frequently to model defects in combinational circuits the proposed pattern generating procedure does not need a simulation of the circuit for each of the possible stuck at faults and its complexity is proportional to the number of gates in the circuit the proportionality constant increases exponentially as the number of inputs in the circuit increases to evaluate the performance of the proposed method its application to some benchmark circuits including the alu 74181 is presented

on unordered codes by extending the results obtained by d e knuth 1986 a parallel unordered coding scheme with 2 sup r information bits is described balanced codes in which each codeword contains equal amounts of zeros and ones with r check bits and up to 2 sup r 1 r 2 information bits are constructed unordered codes with r check bits and up to 2 sup r 2 sup r 1 1 information bits are designed codes capable of detecting 2 sup r 1 2 sup r 2 1 unidirectional errors using r check bits are also described a review of previous work is presented

on the determination of strength of belief for decision support under uncertainty part ii fusing strengths of belief the problem of decision making under uncertainty is described and the difficulty of comparing actions with uncertain outcomes is noted we discuss the role of valuation functions which convert an uncertain outcome into a single representative value and hence aid in the comparison of uncertain alternatives the need for information about the strength of belief that a given outcome will occur is pointed out we then look at various methods for obtaining this information we consider in particular detail the situation in which the strength of belief is dependent on the outcome payoff

representation similarity measures and aggregation methods using fuzzy sets for content based recommender systems representation of features of items and user feedback and reasoning about their relationships are major problems in recommender systems this is because item features and user feedback are subjective imprecise and vague the paper presents a fuzzy set theoretic method ftm for recommender systems that handles the non stochastic uncertainty induced from subjectivity vagueness and imprecision in the data and the domain knowledge and the task under consideration the research further advances the application of fuzzy modeling for content based recommender systems initially presented by ronald yager the paper defines a representation method similarity measures and aggregation methods as well as empirically evaluates the methods performance through simulation using a benchmark movie data ftm consist of a representation method for items features and user feedback using fuzzy sets and a content based algorithm based on various fuzzy set theoretic similarity measures the fuzzy set extensions of the jaccard index cosine proximity or correlation similarity measures and aggregation methods for computing recommendation confidence scores the maximum minimum or weighted sum fuzzy set theoretic aggregation methods compared to the baseline crisp set based method csm presented the empirical evaluation of the ftm using the movie data and simulation shows an improvement in precision without loss of recall moreover the paper provides a guideline for recommender systems designers that will help in choosing from a combination of one of the fuzzy set theoretic aggregation methods and similarity measures

a note on similarity based definitions of possibility and probability probability theory is a rigorous theorywhich rests on a firm foundation the brilliant successes of probability theory are visible to all what is problematical relates to the basic question what is probability there are many answers but no unanimity what is suggested in this note are definitions of possibility and probability which are based on fuzzy logic more concretely the definitions are based on the concept of similarity similarity based definition of probability reduces to the traditional frequency based definition of probability when similarity is exact

combining uncertainty and imprecision in models of medical diagnosis the paper presents a unified fuzzy probabilistic framework for modeling processes of medical diagnosis the two basic concepts of the dempster shafer theory i e focal elements and a basic probability assignment correspond to disease symptoms and the significance of an individual symptom in the diagnosis respectively the belief computation is related to diagnostic inference the final conclusion of the inference is the diagnosis with the greatest belief value fuzzy sets are used to describe focal elements it is shown how their membership functions and basic probability assignments are estimated on the basis of experimental data the interpretation of focal elements as fuzzy sets along with individual consideration of evidence imprecision and uncertainty of diagnosis are the essential new aspects of the presented method experimental studies have demonstrated the superiority of the proposed approach over some other modeling alternatives

brief paper generalized sampled data hold functions with asymptotic zero order hold behavior and polynomic reconstruction we present a generalized sampled data hold function that combines arbitrary z domain zero placement ability with zero order hold behavior under constant input thus exhibiting minimal intersample ripple by design our hold can be regarded as a generalization of the fractional order hold with a polynomial instead of a simple linear pattern and therefore with as many tuning parameters as desired moreover the polynomial approach turns out to provide a simple mechanism of control energy minimization among other benefits all these features help to achieve qualitatively better perfect model referencing because problematic sampling z zeros or the intersample issues of the conventional generalized holds need no longer be endured

another method for constructing t ec aued codes an improved method to construct t ec aued t error correcting and all unidirectional error detecting codes is presented in some cases the new method improves the best known t ec aued codes furthermore the construction does not require complementation of codewords except the all zero and the all ones words

applications of fuzzy chaos to fuzzy simulation in this paper we wish to use fuzzy chaos to generate fuzzy simulation we first discuss how fuzzy chaos can produce a chaotic sequence of fuzzy numbers we apply this technique to fuzzily simulate a solution to a simple fuzzy optimization problem other applications of fuzzy simulation to fuzzy mathematical programming fuzzy max flow fuzzy regression and tuning a fuzzy controller are also presented

constant weight codes for correcting symmetric errors and detecting unidirectional errors proposes two classes of constant weight codes which can be used for correcting t symmetric errors and simultaneously detecting all unidirectional errors codes in the first class are in quasi systematic form and codes in the second class are in systematic form since each codeword of codes in both classes can be divided into a data part and a parity check part the proposed codes have the merit of easily mapping messages into codewords

a note on the conditional probability of fuzzy subsets of a continuous domain abstract the notion of a mass assignment corresponding to a discrete fuzzy set is generalised to include all fuzzy sets the definition is motivated by considering a possible mechanism by which an intelligent agent could extend set theoretic operations to fuzzy sets this same mechanism also suggests an alternative definition for the conditional probability of fuzzy sets it is noted that this definition is probability possibility consistent and it is shown that in the case where the probability distribution on the domain has a density function then the conditional probability of f given g can be expressed as the probability of f calculated relative to a conditional density function dependent on g this result is used to develop an analytical method for calculating conditional probabilities of fuzzy subsets of the reals where the membership functions of f and g and the density function are continuous piecewise linear functions such a method has applications to the development of a general semantic unification in fril

a hierarchical neural model of matching abstract the issue of matching two fuzzy sets emerges as an essential design aspect in many algorithms of processing fuzzy information including fuzzy controllers pattern classifiers knowledge based systems etc this paper introduces a new model of matching the primordial features of the proposed model involve 1 i matching being carried out with respect to the grades of membership of the discussed fuzzy sets as well as some of their functionals like energy entropy transom 2 ii the concepts of hierarchies of matching in the model leading directly to a straightforward distinction between local and global levels of matching and 3 iii a distributed character of the model that is realized as a logic based neural network with enhanced learning capabilities

new lower bounds for asymmetric and unidirectional codes new lower bounds on the sizes of asymmetric codes and unidirectional codes are presented various methods are used three of them of special interest the first is a partitioning method that is a modification of a method used to construct constant weight codes the second is a combining codes method that is used to obtain a new code from a few others the third method is shortening by weights that is applied on symmetric codes or on codes generated by the combining codes method tables for the sizes of codes of length n

fuzzy set connectives as combinations of belief structures abstract consonant belief structures provide a representation for fuzzy sets owing to the fact that their plausibility measures are essentially possibility measures we note that two belief structures are equivalent if their plausibility and belief functions are equal this observation leads us to provide a multiple number of equivalent representations for any belief structure commensurate representations can be induced for two different belief structures by forcing the same number of focal elements with the same weights we show that if we represent two consonant belief structures in a commensurate manner then their aggregations are closed with respect to consonance provided that the additional requirement that the underlying probability distributions satisfy a condition of correlation is imposed the results of this work allow us to use belief structure representations for the manipulation of fuzzy subsets under various logical combinations all basic fuzzy set connectives can thus be interpreted in the framework of the theory of evidence

aggregating constraint satisfaction degrees expressed by possibilistic truth values in information systems one often has to deal with constraints in order to compel the semantics and integrity of the stored information or to express some querying criteria hereby different constraints can be of different importance a method to aggregate the information about the satisfaction of a finite number of constraints for a given data instance is presented central to the proposed method is the use of extended possibilistic truth values to express the degree of satisfaction of a constraint and the use of residual implicators and residual coimplicators to model the impact and relevance of a constraint the proposed method can be applied to any constraint based system a database application is discussed and illustrated

single value simulation of fuzzy variable some further results abstract the problem of a proper choice from the class of random sets equivalent to a fuzzy set under one point coverages is considered the selected random variable is used for construction of a random variable probability distribution serving as a random generator of a value of the fuzzy variable with values restricted by the fuzzy set the problem is determined for two selection criteria i maximum probability possibility consistency and ii maximum entropy in the case of the entropy criterion the problem has been solved first by goodman and here only another proof of the result is presented

on symmetric error correcting and all unidirectional error detecting codes the design of binary block codes that are capable of correcting up to t symmetric errors and detecting all unidirectional errors is discussed a class of systematic t symmetric error correcting all unidirectional error detecting t syec aued codes are proposed when t 0 the proposed codes become berger codes for t 1 the proposed codes are shown to be of asymptotically optimal order methods to construct nonsystematic t syec aued codes for t 2 and 3 are also presented

uncertainty modelling for vague concepts a prototype theory approach an epistemic model of the uncertainty associated with vague concepts is introduced label semantics theory is proposed as a framework for quantifying an agent s uncertainty concerning what labels are appropriate to describe a given example an interpretation of label semantics is then proposed which incorporates prototype theory by introducing uncertain thresholds on the distance between elements and prototypes for description labels this interpretation naturally generates a functional calculus for appropriateness measures a more general model with distinct threshold variables for different labels is discussed and we show how different kinds of semantic dependence can be captured in this model

uncertain robot environment modelling using fuzzy numbers abstract in this paper we present a fuzzy oriented methodology to model an uncertain geometric robot environment and to manipulate geometric uncertainties between robot coordinate frames we describe any geometric primitive of robot environment as a parameter vector in parameter space not only ill known values of the parameterized geometric primitives but the uncertain quantities of coordinate transformations are represented by means of fuzzy numbers restricted to appropriate membership functions for consistent interpretation about geometric primitives between different coordinate frames we manipulate these uncertain quantities using fuzzy arithmetic as an application we deal with a 2 dimensional straight line correspondence problem of a mobile robot vision system this example shows the usefulness of the proposed methodology

some new results concerning random sets and fuzzy sets abstract this paper is a continuation of past work showing direct connections between fuzzy set theory and classical probability theory through the use of random sets this includes characterizations of random intervals one point coverage equivalent to fuzzy sets determination of all nested random sets equivalent to fuzzy sets the solution of the one and multiple point coverage problems for random sets in finite spaces and the use of entropy for ordering random sets within the class of one point coverage equivalent ones for any given fuzzy set finally a connection between random variables random sets and fuzzy sets is pointed out

rough approximation of a preference relation by a multi attribute dominance for deterministic stochastic and fuzzy decision problems abstract the case of mixed data in which attributes have a different nature is not well known in current literature although it is essential from a practical point of view this situation is particularly frequent in risk management modelling which incorporates various degrees of precision of the variables measured and can also be noted in a planning context for project evaluation problems taking into account information of a mixed qualitative and quantitative type for a set of alternatives evaluated by a set of attributes three kinds of evaluations are considered in this paper deterministic stochastic or fuzzy with relation to each attribute the mixed data multi attribute dominance for a reduced number of attributes mmd r is proposed to model the preferences in this kind of problem the approach is based on the dominance based rough set approach proposed by greco matarazzo and slowinski

network of probabilities associated with a capacity of order 2 abstract this paper studies capacities of order 2 from a geometric point of view that is from convex polytope of probabilities defined by them this convex polytope is characterized by means of a network of probabilities representing relationships among vertices defined by the edges interesting properties may be obtained about the capacities from this network

lym type inequalities for tec aued codes some lym type inequalities are introduced to obtain a relationship between the parameters of t error correcting all unidirectional error detecting codes of length n as an application of these inequalities new lower bounds on the redundancies of systematic tec aued codes are derived and an extensive table is given

a new table of constant weight codes a table of binary constant weight codes of length nl28 is presented explicit constructions are given for most of the 600 codes in the table the majority of these codes are new the known techniques for constructing constant weight codes are surveyed and a table of unrestricted binary codes of length nl28 is given

the possibilistic moments of fuzzy numbers and their applications this paper introduces the nearest weighted interval and point approximations of a fuzzy number and then suggests weighted possibilistic moments about these points of fuzzy numbers the possibilistic moments play an important role in fuzzy sets and systems specifically in physics mathematics and statistics we provide the definition of the moments of fuzzy numbers as well as the definition of moments in probability theory some of their applications are mentioned

bounds on the capacity of the unidirectional channels in the usual binary symmetric channel both 1 spl rarr 0 and 0 spl rarr 1 types of errors can occur in the binary asymmetric channel only 1 spl rarr 0 type of errors can occur whereas in the unidirectional channel both 1 spl rarr 0 and 0 spl rarr 1 types of errors can occur but unlike the binary symmetric channel for any particular transmitted word of length n all the errors are of the same type in general a symmetric unidirectional channel is a channel which shows the behavior of both the symmetric and unidirectional channel many practical systems such as semiconductor memories and circuits can be modeled as a unidirectional and or symmetric unidirectional channels this paper gives the formal definition of these last two channels and shows some interesting simple bounds on their information capacities

two batch search with lie cost we consider the problem of searching for an unknown number in the search space u 0 m 1 q ary questions can be asked and some of the answers may be wrong an arbitrary integer weighted bipartite graph gamma is given stipulating the cost gamma i j of each answer jnei when the correct answer is i i e the cost of a wrong answer correct answers are supposed to be cost less it is assumed that a maximum cost e for the sum of the cost of all wrong answers can be afforded by the responder during the whole search we provide tight upper and lower bounds for the largest size m m q e gamma n for which it is possible to find an unknown number x isinu with n q ary questions and maximum lie cost e our results improve the bounds of cicalese et al 2004 and ahlswede et al 2008 the questions in our strategies can be asked in two batches of nonadaptive questions finally we remark that our results can be further generalized to a wider class of error models including also unidirectional errors

variable length unordered codes in an unordered code no code word is contained in any other code word unordered codes are all unidirectional error detecting aued codes in the binary case it is well known that among all systematic codes with k information bits berger codes are optimal unordered codes with r log2 k 1 log2k check bits this paper gives some new theory on variable length unordered codes and introduces a new class of systematic instantaneous unordered codes with variable length check symbols the average redundancy of the new codes presented here is r 1 2 log2k c where c 1 0470 1 1332 ir and k in is the number of information bits when k is large it is shown that such redundancy is at most 0 6069 bits off the redundancy of an optimal systematic unordered code design with fixed length information symbols and variable length check symbols and at most 2 8075 bits off the redundancy of an optimal variable length unordered code design the generalization is also given for the nonbinary case and it is shown that similar results hold true

on viewing fuzzy measures as fuzzy subsets we introduce the concept of a fuzzy measure discuss some of their basic properties and look at some notable examples we introduce a correspondence between a fuzzy measure on x and a fuzzy subset over the power set of x these fuzzy subsets are required to have special properties on the space 2x and we refer to these as measure type fuzzy sets we take advantage of this correspondence between a fuzzy measure and a fuzzy set to suggest the formulation of various set operations on fuzzy measures

new techniques for constructing t ecd edaued and t ecd eds ued codes abstract this paper presents procedures for constructing systematic t error correcting d error detecting all unidirectional error detecting t ed d ed aued codes as well as t error correcting d error detecting and s unidirectional error detecting t ec d ed aued codes the technique proposed are similar to those recently reported to construct t ec aued codes a t ec d ed code is chosen and then a tail is appended in such a way that the new code can detect all or s errors when they are unidirectional interesting tail sequences are included in this paper the efficiency of the t ec d ed aued and t ec d ed s ued codes reported in this paper compares favorably to the existing methods in addition these procedures enable simple and fast encoding and decoding algorithms many useful codes are tabulated

optimal q ary error correcting all unidirectional error detecting codes codes that can correct up to t symmetric errors and detect all unidirectional errors known as t ec aued codes are studied in this paper given positive integers q a and t let n q a t 1 denote the length of the shortest q ary t ec aued code of size a we introduce combinatorial constructions for q ary t ec aued codes via one factorizations of complete graphs and concatenation of mds codes and codes from resolvable set systems consequently we determine the exact values of n q a t 1 for several new infinite families of q a and t

on the undetected error probability of nonlinear binary constant weight codes the undetected error probability uep of binary n 2 spl delta m nonlinear constant weight codes over the binary symmetric channel bsc is investigated where n is the blocklength m is the weight of codeword and 2 spl delta is the minimum distance of the codes the distance distribution of the n 2 m nonlinear constant weight codes is evaluated it is proven in this paper that the 5 2 2 code 5 2 3 code 6 2 3 code 7 2 4 code 7 2 3 code and 8 2 4 code are the only proper error detecting codes in the n 2 m nonlinear constant weight codes for n spl ges 5 in the sense that their uep is increased monotonically with the channel error rate p of course all these proper codes are m out of n codes furthermore it is conjectured that except for the cases of n spl les 4 spl delta there are no proper error detecting binary n 2 spl delta m nonlinear constant weight codes for n 8 and spl deltaspl ges 1

on differential equations with interactive fuzzy parameter via t norms abstract in this paper we study fuzzy differential equations with uncertain parameters modeled by interactive fuzzy numbers the interactivity is formalized with the help of upper semicontinuous t norms to obtain solutions to fuzzy differential equations we use two different approaches the first uses a family of differential inclusions while the second is the fuzzification of the deterministic problem using the zadeh extension principle we show that the solutions obtained by the two methods are equal interactivity among the parameters and variable of the problem are studies with respect two methods we show that a hierarchy in uncertainties of the solutions arises when we chose one of the basic t norm the minimum the t norm of the product the t norm of lukasiewicz and t norm of the drastic product to model the interaction between parameters finally to illustrate the concepts introduced in the paper we study the malthusian model with interactive parameters

interval random sets and entropy abstract the problem of proper choice from the class of interval random sets generated by some fuzzy set is considered this problem is determined for the maximum entropy criterion the class of interval random sets is studied

fuzzy hypotheses testing in the framework of fuzzy logic abstract testing hypotheses about the probability distribution underlying the available empirical data is one of the fundamental data analytic tasks in any application domain basically it consists in checking the null hypothesis that the probability distribution a priori assumed to belong to a certain set of distributions actually belongs to some its narrow subset which must be precisely delimited in advance however sometimes there are not enough clues for such a precise delimitation especially if the purpose of the data analysis is explorative a situation encountered increasingly often due to the growing amount of routinely collected data and the increasing importance of data mining that is why generalizations of statistical hypotheses testing to vague hypotheses have been investigated for more than a decade so far based on the most straightforward approach to replace the set defining the null hypothesis by a fuzzy set in this paper a principally different approach is presented motivated by the observational logic and its success in automated knowledge discovery its key idea is to view statistical testing of a fuzzy hypothesis as the application of an appropriate generalized quantifier of a fuzzy predicate calculus to predicates describing the data the theoretical principles of the approach are explained and its first implementations are briefly sketched

reliability estimation and design with insufficient data based on possibility theory early in the engineering design cycle it is difficult to quantify product reliability or compliance to performance targets because of insufficient data or information for modeling the uncertainties design decisions are therefore based on fuzzy information that is vague imprecise qualitative linguistic or incomplete the uncertain information is usually available as intervals with lower and upper limits in this work the possibility theory is used to assess design reliability with incomplete information the possibility theory can be viewed as a variant of fuzzy set theory the formal theories to handle uncertainty are first introduced using the theoretical fundamentals of fuzzy measures a computationally efficient and accurate hybrid global local optimization approach is subsequently described for calculating the confidence level of fuzzy response the method combines the advantages of the commonly used vertex and discretization methods subsequently the possibility theory is used in design a possibility based design optimization method is proposed where all design constraints are expressed in a possibilistic way it is shown that the method gives a conservative solution compared with all conventional reliability based designs obtained with different probability distributions finally a general possibility based design optimization method which handles a combination of random and possibilistic design variables is presented several numerical examples demonstrate the application of possibility theory in design

some optimal binary and ternary t ec aued codes codes that can correct up to t symmetric errors and detect all unidirectional errors are studied boumlinck and van tilborg gave a bound on the length of binary such codes a generalization of this bound to arbitrary alphabet size is given this generalized boumlinck van tilborg bound combined with constructions is used to determine some optimal binary and ternary codes for correcting t symmetric errors and detecting all unidirectional errors

constructions and bounds for systematic tec aued codes several methods of constructing systematic t error correcting all unidirectional error detecting codes are described these codes can be constructed by adding a tail to a linear t error correcting code but other constructions presented are more of an ad hoc nature these codes will often be found as suitably chosen subsets of nonsystematic tec aued codes further bounds on the word length of systematic tec aued codes are derived and extensive tables are given

generalized bose lin codes a class of codes detecting asymmetric errors bose and lin introduced a class of systematic codes for detection of binary asymmetric errors in this note we describe a generalization to q ary asymmetric error detecting codes for these codes the possible undetectable errors are characterized and the undetectable errors of minimum weight are determined

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

non pathological sampling for generalized sampled data hold functions abstract given a generalized sampled data hold function gshf we define a frequency dependent response function having many properties analogous to those of a transfer function in particular the zeros of the response function have transmission blocking properties we then study the problem of non pathological sampling with a gshf sampling is said to be pathological if the discretized version of a stabilizable detectable continuous time plant is not itself stabilizable and detectable sufficient conditions for nonpathological sampling with a zero order hold have long been known we extend these to the case of a gshf and describe the role in non pathological sampling played by right half plane zeros of the response function the results are presented for square multivariable linear systems and include a generalization to allow for a time delay

a probabilistic approach to the arithmetics of fuzzy numbers an alternative look on fuzzy numbers based on two random variables and their summation and multiplication is introduced this approach to summation covers the standard zadeh s extension principle and triangular norm based approach however it is more general we illustrate it on some examples moreover copula based summation preserving the class of triangular trapezoidal fuzzy numbers is discussed

fuzzy integral in multicriteria decision making abstract this paper presents a synthesis on the use of fuzzy integral as an aggregation operator in multicriteria decision making definitions essential properties are given and compared to those of usual aggregation operators a quick survey on applications is given

on some optimization problems under uncertainty abstract the last ten years show a diversification of the approaches for handling uncertainties in optimization problems by certain relaxations or on the contrary seeking a more conservative solution in this paper we present some new results and points of view in nonlinear inexact and fuzzy mathematical programming possible applications to capital budgeting of interrelated projects and to production planning are also discussed

characterization and comparison of sugeno and choquet integrals abstract starting from the concept of equiordered functions we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure sugeno and choquet integrals the characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals pointing out their formal similarities and their conceptual differences

efficient encoding algorithm for second order spectral null codes using cyclic bit shift some efficient second order spectral null codes encoded an index of the random walk function recursively and ended with the short base second order spectral null codes all of these codes used the tallini bose random walk function that exchanges two consecutive bits in this paper we propose a new random walk function based on cyclic bit shift on which the redundancy can be improved moreover the bit shift can be implemented efficiently by either software or hardware

single value simulation of fuzzy variables abstract the basic ideas of the present paper arise from relations between random sets and fuzzy ones the suggested approach which may be called fuzzy numerical simulation allows for ascribing a precise numerical value to a fuzzy variable by generating a value of a random variable related in some way to the fuzzy variable the so called generative characteristics of a fuzzy variable being the expected value and variance of the generating random variable are introduced the problem of simultaneous generating values of two fuzzy variables is also discussed finally methods of generating when a fuzzy variable is described with a complex body of evidence are presented

theory of unidirectional error correcting detecting codes in this paper we present some basic theory on unidirectional error correcting detecting codes we define symmetric asymmetric and unidirectional error classes and proceed to derive the necessary and sufficient conditions for a binary code to be unidirectional error correcting detecting

advanced fuzzy inference engines in situation aware computing we focus on the very important family of context aware applications context aware computing relies on tasks like capturing sensing environmental parameters e g lightness location classifying context and inferring further knowledge about that context determine the situation the user is currently in however the relevant applications have to deal with the inherent imperfection of context sensing for decision making we propose an extension of context representation and inference for situation aware applications our model relies on fuzzy set theory to accommodate the imperfection of sensed context based on this model we have developed three fuzzy inference engines which rely on advanced semantics specialization mereological and compatibility relations we have evaluated the proposed engines through a series of experiments involving real users our findings indicate the strong points of the proposed context classification and inference processes

user preferences discovery using fuzzy models user preferences discovery aims to learn the patterns of user preferences for various services or items such as movies preferences discovery is essential to the development of intelligent personalization applications based on decision and utility theories traditional approaches to preferences discovery explicitly query users about the behavior of value function or utility of every outcome with respect to each decision criterion consequently these approaches are generally error prone and labor intensive although implicit elicitation approaches have been proposed to address the above limitations extent approaches largely ignore multi valued nature of item features and uncertainty associated with item features and user preferences to address uncertainty due to vagueness and imprecision this research proposed a general framework for preferences discovery based on fuzzy set theories in addition new fuzzy models were created for preferences discovery and representation further an algorithm was developed to predict user preferences with uncertainty and visualization of item features user feedback and the discovered preferences helped improve the interpretation of the discovered knowledge the results of the simulation evaluation using a benchmark movie dataset revealed that the proposed preference discovery method 1 doubled the accuracy of preference discovery as compared to random prediction and 2 outperformed conventional techniques in making movie recommendation these findings suggest that fuzzy models are effective for preferences patterns discovery and personalized recommendation application

distributed control design for spatially interconnected systems this paper deals with analysis synthesis and implementation of distributed controllers designed for spatially interconnected systems we develop a state space framework for posing problems of this type and focus on systems whose model is spatially discrete in this paper analysis and synthesis results are developed for this class of systems using the l sub 2 induced norm as the performance criterion the results are stated in terms of linear matrix inequalities and are thus readily amenable to computation a special implementation of the resulting controllers is presented which is particularly attractive for distributed operation of the controller several examples are provided to further illustrate the application of the results

a set of practical experiments to validate the fuzzy kalman filter abstract the fuzzy kalman filter fkf was recently reformulated with a number of basic examples included in order to demonstrate its applicability we now look ahead to its practical implementation introducing deep analysis which includes very detailed simulations and complete real applications this will allow us to not only validate the fkf but also to draw important conclusions which will help users in the adjustment of the fuzzy filter parameters and the choosing of possibilistic distributions

ranking fuzzy interval numbers in the setting of random sets abstract a new approach to the problem of extending interval order relations to the case of fuzzy interval numbers is presented in the approach the connectedness between fuzzy sets and random sets is used finally eight different fuzzy order relations are given some formal properties of these relations are investigated and the problem of computing the values of their membership functions discussed for trapezoidal fuzzy interval numbers the formulae depend on the parameters from which these numbers are derived

fuzzy inference relation based on the theory of falling shadows abstract in this paper we establish a theoretical approach to define a fuzzy inference relation based on the theory of falling shadows the main characteristic of our definition of fuzzy inference relation is that it is semantically dependent in the sense that the formula of our definition will vary according to the correlation of the antecedent and the consequence of the given implication we shall show that the formulae of fuzzy inference relation given by ukasiewicz zadeh and the probability formula are consequences of our definition under three different correlations of the propositions