adaptive fuzzy rule based classification systems this paper proposes an adaptive method to construct a fuzzy rule based classification system with high performance for pattern classification problems the proposed method consists of two procedures an error correction based learning procedure and an additional learning procedure the error correction based learning procedure adjusts the grade of certainty of each fuzzy rule by its classification performance that is when a pattern is misclassified by a particular fuzzy rule the grade of certainty of that rule is decreased on the contrary when a pattern is correctly classified the grade of certainty is increased because the error correction based learning procedure is not meaningful after all the given patterns are correctly classified we cannot adjust a classification boundary in such a case to acquire a more intuitively acceptable boundary we propose an additional learning procedure we also propose a method for selecting significant fuzzy rules by pruning unnecessary fuzzy rules which consists of the error correction based learning procedure and the concept of forgetting we can construct a compact fuzzy rule based classification system with high performance

minimum probability of error for asynchronous gaussian multiple access channels consider a gaussian multiple access channel shared by k users who transmit asynchronously independent data streams by modulating a set of assigned signal waveforms the uncoded probability of error achievable by optimum multiuser detectors is investigated it is shown that the k user maximum likelihood sequence detector consists of a bank of single user matched filters followed by a viterbi algorithm whose complexity per binary decision is o 2 k the upper bound analysis of this detector follows an approach based on the decomposition of error sequences the issues of convergence and tightness of the bounds are examined and it is shown that the minimum multiuser error probability is equivalent in the iow noise region to that of a single user system with reduced power these results show that the proposed multiuser detectors afford important performance gains over conventional single user systems in which the signal constellation carries the entire burden of complexity required to achieve a given performance level

characterizations of discrete sugeno integrals as polynomial functions over distributive lattices we give several characterizations of discrete sugeno integrals over bounded distributive lattices as particular cases of lattice polynomial functions that is functions which can be represented in the language of bounded lattices using variables and constants we also consider the subclass of term functions as well as the classes of symmetric polynomial functions and weighted infimum and supremum functions and present their characterizations accordingly moreover we discuss normal form representations of these functions

quantitative weights and aggregation based on the strong idempotency of aggregation operators quantitative weights are incorporated into the fusion process our general method is compared with some previous specific cases more details about weighted aggregation based on some penalty function is given further weighted integral based aggregation linked to quantifier based fuzzy measures is investigated especially weighted owa operators several examples are included

reciprocal transitive matrices over abelian linearly ordered groups we consider reciprocal matrices over an abelian linearly ordered group in this way we provide a general framework including multiplicative additive and fuzzy matrices in a multi criteria decision making context a pairwise comparison matrix a a i j is a reciprocal matrix that represents a useful tool for determining a weighting vector w for a set x of decision elements but when a is inconsistent the weighting vector usually proposed in literature may provide a ranking on x that does not agree with the expressed preference intensities a i j thus it is unreliable we analyze a condition of transitivity for a reciprocal matrix a a i j over an abelian linearly ordered group that whenever a is a pairwise comparison matrix allows us to state a qualitative dominance ranking on x and obtain ordinal evaluation vectors in this way we get a first tool for checking the reliability of a weighting vector we also provide tools to check the transitivity

optimum sequence multisets for synchronous code division multiple access channels it is shown that the sum capacity of the symbol synchronous code division multiple access channel with equal average input energy constraints is maximized precisely by those spreading sequence multisets that meet welch s lower bound on total squared correlation it is further shown that the symmetric capacity of the channel determined by these same sequence multisets is equal to the sum capacity

new families of binary sequences with optimal three level autocorrelation in this correspondence we give several new families of binary sequences of period n with optimal three level autocorrelation where n spl equiv 2 mod 4 these sequences are either balanced or almost balanced our construction is based on cyclotomy

new bounds on the total squared correlation and optimum design of ds cdma binary signature sets the welch lower bound see welch r l ieee trans inform theory vol it 20 p 397 9 1974 on the total squared correlation tsc of signature sets is known to be tight for real valued signatures and loose for binary signatures whose number is not a multiple of four we derive new bounds on the tsc of binary signature sets for any number of signatures k and any signature length l then for almost all k l in 1 2 256 we design optimum binary signature sets that achieve the new bounds the design procedure is based on simple transformations of hadamard matrices

multi attribute search framework for optimizing extended belief rule based systems the advantages and applications of rule based systems have caused them to be widely recognized as one of the most popular systems in human decision making due to their accuracy and efficiency to improve the performance of rule based systems there are several issues proposed to be focused first it is unnecessary to take the entire rule base into consideration during each decision making process second there is no need to visit the entire rule base to search for the key rules last the key rules for each decision making process should be different this paper focuses on an advanced extended belief rule base ebrb system and proposes a multi attribute search framework masf to reconstruct the relationship between rules in the ebrb to form the masf based ebrb masfs can be divided into k dimensional tree kdt based masfs and burkhard keller bkt based masfs the former is targeted at decision making problems with small scale attribute datasets while the latter is for those with large scale attribute datasets based on the masf based ebrb the k neighbor search and the best activated rule set algorithms are further proposed to find both the unique and the desired rules for each decision making process without visiting the entire ebrb especially when handling classification problems with large attribute datasets two sets of experiments based on benchmark datasets with different numbers of attributes are performed to analyze the difference between kdt based masfs and bkt based masfs and to demonstrate how to use masfs to improve the accuracy and efficiency of ebrb systems masfs and their corresponding algorithms are also regarded as a general optimization framework that can be used with other rule based systems

optimal odd length binary z complementary pairs a pair of sequences is called a golay complementary pair gcp if their aperiodic auto correlation sums are zero for all out of phase time shifts existing known binary gcps only have even lengths in the form of 21026 where are non negative integers to fill the gap left by the odd lengths we investigate the optimal oddlength binary pairs which display the closest correlation property to that of gcps our criteria of closeness is that each pair has the maximum possible zero correlation zone zcz width and minimum possible out of zone aperiodic auto correlation sums such optimal pairs are called optimal odd length binary z complementary pairs ob zcp in this paper we show that each optimal ob zcp has maximum zcz width of n 1 2 and minimum out of zone aperiodic sum magnitude of 2 where n denotes the sequence length odd systematic constructions of such optimal op zcps are proposed by insertion and deletion of certain binary gcps which settle the 2011 li fan tang tu open problem positively the proposed optimal ob zcps may serve as a replacement for gcps in many engineering applications where odd sequence lengths are preferred in addition they give rise to a new family of base two almost difference families adf which are useful in studying partially balanced incomplete block design bibd index terms aperiodic correlation almost difference set ads almost difference families adf golay complementary pair gcp zero correlation zone zcz z complementary pair zcp

a semiring based study of judgment matrices properties and models in decision making and group decision making multiplicative reciprocal judgment matrices and additive reciprocal judgment matrices are used as two kinds of important preference information in this paper semirings are applied to the discussion of judgment matrix properties first two special semirings are constructed second the properties of the consistent judgment matrices are given as a set of equations all in the semiring sense which include idempotency equations and fixed point equations we find that there exists one and only one specially constrained fixed point as the priority vector of a consistent judgment matrix third optimization models for inconsistent judgment matrices are presented finally we offer some simple illustrative examples

the maximum squared correlation sum capacity and total asymptotic efficiency of minimum total squared correlation binary signature sets the total squared correlation tsc maximum squared correlation msc sum capacity c sub sum and total asymptotic efficiency tae of underloaded signature sets as well as the tsc and c sub sum of overloaded signature sets are metrics that are optimized simultaneously over the real complex field in this present work closed form expressions are derived for the msc c sub sum and tae of minimum tsc binary signature sets the expressions disprove the general equivalence of these performance metrics over the binary field and establish conditions on the number of signatures and signature length under which simultaneous optimization can or cannot be possible the sum capacity loss of the recently designed minimum tsc binary sets is found to be rather negligible in comparison with minimum tsc real complex valued welch bound equality sets

a generalization of circulant hadamard and conference matrices abstract we study the existence and construction of circulant matrices c of order n 2 with diagonal entries d 0 off diagonal entries 1 and mutually orthogonal rows these matrices generalize circulant conference d 0 and circulant hadamard d 1 matrices we demonstrate that matrices c exist for every order n and for d chosen such that n 2 d 2 and we find all solutions c with this property furthermore we prove that if c is symmetric or n 1 is prime or d is not an odd integer then necessarily n 2 d 2 finally we conjecture that the relation n 2 d 2 holds for every matrix c which generalizes the circulant hadamard conjecture we support the proposed conjecture by computing all the existing solutions up to n 50

binary and quadriphase sequences with optimal autocorrelation properties a survey time discrete signals with good autocorrelation properties are used in various applications in communications engineering from an implementation point of view usually sequences with a small phase alphabet and a maximal energy efficiency i e a uniform envelope are most favorable for this reason known methods as well as several new construction techniques of binary and quadriphase sequences with optimal or best known autocorrelation properties are discussed in this correspondence in many cases the achievable correlation properties can be improved significantly if a single zero element per sequence is accepted these almost binary and almost quadriphase sequences are considered as well the optimality criteria used include the maximum absolute sidelobe and the merit factor of the periodic and the odd periodic autocorrelation function respectively for sequence lengths of up to 44 in the binary case and up to 32 in the quadriphase case the best known parameters obtained by computer search are compared with the constructed results

cdma codeword optimization interference avoidance and convergence via class warfare interference avoidance has been shown to reduce total square correlation tsc for given ensembles of user signature waveforms codewords in a synchronous code division multiple access cdma system in all experiments we have conducted sequential application of interference avoidance produces an optimal codeword set when starting from randomly chosen initial codewords here we provide the first formal proof of convergence to optimal codeword ensembles for greedy interference avoidance algorithms augmented by a technique called class warfare whereby users which reside in more heavily loaded areas of the signal space purposely interfere with attack the reception of users in less crowded areas coordination of deliberate interference by a complete class of aggrieved user is also sometimes necessary such attacks and subsequent codeword adjustment by attacked users are shown to strictly decrease tsc along the way we also show using linear algebra and a variant of stochastic ordering equivalence between minimization of tsc and maximization of sum capacity

optimal sequences for cdma under colored noise a schur saddle function property we consider direct sequence code division multiple access ds cdma modeling interference from users communicating with neighboring base stations by additive colored noise we consider two types of receiver structures first we consider the information theoretically optimal receiver and use the sum capacity of the channel as our performance measure second we consider the linear minimum mean square error lmmse receiver and use the signal to interference ratio sir of the estimate of the symbol transmitted as our performance measure our main result is a constructive characterization of the possible performance in both these scenarios a central contribution of this characterization is the derivation of a qualitative feature of the optimal performance measure in both the scenarios studied we show that the sum capacity is a saddle function it is convex in the additive noise covariances and concave in the user received powers in the linear receiver case we show that the mini average power required to meet a set of target performance requirements of the users is a saddle function it is convex in the additive noise covariances and concave in the set of performance requirements

prescribed absolute values character sums and spectrum integrality abstract let g be a group and let reg be the complex left regular representation of g we consider the following problem for which inverse closed subsets s g the spectrum of the matrix g s reg g is integral that is all of the eigenvalues of the matrix are integers for abelian g a complete characterization due to bridges and mena is known here we are interested in the case where g is the dihedral group d 2 n which turns out to be a far reaching generalization of the abelian case we obtain a complete characterization when n is an odd prime and present partial results when n is a prime power

nonexistence of abelian difference sets lander s conjecture for prime power orders in 1963 ryser conjectured that there are no circulant hadamard matrices of order 4 and no cyclic difference sets whose order is not coprime to the group order these conjectures are special cases of lander s conjecture which asserts that there is no abelian group with a cyclic sylow p subgroup containing a difference set of order divisible by p we verify lander s conjecture for all difference sets whose order is a power of a prime greater than 3

on equivalence classes of fuzzy connectives the case of fuzzy integrals an equivalence relation between connectives or operators in the framework of multiple criteria decision making is introduced two operators are said to be equivalent if they lead to the same ranking of alternatives some general results to find equivalence classes of operators are given through the concept of level surfaces in a second part these results are applied to the case of discrete fuzzy integrals which are considered here as n place operators first some general results on the situation of fuzzy integrals among fuzzy operators are given and then the equivalence classes of fuzzy integrals

weighted aggregation operators based on minimization minimization based aggregation operators a g d are discussed special attention is paid to weighting function g based cases related to some fixed dissimilarity function d when d 2 x y x y 2 we recognize mixture operators and we recall some sufficient conditions for g ensuring the monotonicity of a g d for d 1 x y x y and non decreasing non increasing g a g d is shown to be the upper lower median whenever a g d is an aggregation operator

planar functions relative difference sets and character theory planar functions from2nto3nare studied in this paper by investigating the character values of the corresponding relative difference sets we obtain some nonexistence results of planar functions in particular we show that there is no planar functions fromzpqto4pq wherepandqare any primes we also show that except for four undecided cases there is no planar function from5nto6nifnis not a prime andn 50 000

on the existence of cyclic hadamard difference sets the main conjecture of this article is the following if a cyclic v 4n 1 k 2n 1 spl lambda n 1 hadamard difference set exists the the value of v must be either a prime or a product of twin primes or one less than a power of 2 six cases v 399 495 627 651 783 and 975 which were once listed as the possible exceptions for v

achieving the welch bound with difference sets consider a codebook containing n unit norm complex vectors in a k dimensional space in a number of applications the codebook that minimizes the maximal cross correlation amplitude i sub max is often desirable relying on tools from combinatorial number theory we construct analytically optimal codebooks meeting in certain cases the welch lower bound when analytical constructions are not available we develop an efficient numerical search method based on a generalized lloyd algorithm which leads to considerable improvement on the achieved i sub max over existing alternatives we also derive a composite lower bound on the minimum achievable i sub max that is effective for any codebook size n

new bounds and optimal binary signature sets part ii aperiodic total squared correlation we derive new bounds on the aperiodic total squared correlation atsc of binary antipodal signature sets for any number of signatures k and any signature length l we then present optimal designs that achieve the new bounds for several k l cases as interesting arguably side results we show that individual maximal merit factor sequences for example barker sequences are single user atsc optimal while neither the familiar gold nor the kasami set designs are atsc optimal in general the atsc optimal signature set designs provided in this work are in this sense better suited for asynchronous and or multipath code division multiplexing applications

aggregation functions based on penalties this article studies a large class of averaging aggregation functions based on minimizing a distance from the vector of inputs or equivalently minimizing a penalty imposed for deviations of individual inputs from the aggregated value we provide a systematization of various types of penalty based aggregation functions and show how many special cases arise as the result we show how new aggregation functions can be constructed either analytically or numerically and provide many examples we establish connection with the maximum likelihood principle and present tools for averaging experimental noisy data with distinct noise distributions

two dimensional synchronization patterns for minimum ambiguity a number of closely related combinatorial problems corresponding to specific assumptions about the type of time frequency sequence which may be appropriate in a particular application are formulated in terms of square or rectangular arrays of dots with appropriate constraints on the two dimensional correlation function the current state of knowledge concerning each of these problems is summarized it is hoped that more general constructions may be found leading to larger families of solutions as well as better computational algorithms for finding individual solutions which may lie outside of the general families

cyclotomic integers and finite geometry the most powerful method for the study of finite geometries with regular or quasiregular automorphism groups g is to translate their definition into an equation over the integral group ring 2 g and to investigate this equation by applying complex representations of g for the definitions and the basic facts see section 2 if g is abelian this approach boils down to proving or disproving the existence of elements of 2 g with 0 1 coefficients whose character values are cyclotomic integers of certain prescribed absolute values up to now there have been two general methods to tackle this problem namely hall s multiplier concept and turyn s selfconjugacy approach however both methods need severe technical assumptions and thus are not applicable to many classes of problems despite many efforts over a period of more than 30 years no general method has been found to overcome these difficulties in this paper we present a new approach to the study of combinatorial structures via group ring equations which works without any restrictive assumptions in order to understand the method of the present paper it will be instructive to briefly discuss the self conjugacy concept first turyn 51 demonstrated that the character method for the study of group ring equations works very nicely under the so called self conjugacy condition an integer n is called self conjugate modulo m if all prime ideals above n in the mth cyclotomic field q m are invariant under complex conjugation under this condition it is possible to find all cyclotomic integers in q m of absolute value nt 2 for any positive integer t it is the complete knowledge of the cyclotomic integers of prescribed absolute value which makes the character method work so well under the self conjugacy condition since turyn s fundamental work 51 there have been dozens of papers extending and refining his approach however all these results are restricted to the case of self conjugacy and that is a very severe restriction indeed namely the probability that n is selfconjugate modulo m decreases exponentially fast in the number of distinct prime divisors of n and m see remark 2 2 this means that the self conjugacy method fails in almost all cases one may ask if it is possible to extend turyn s method in order to get rid of the self conjugacy assumption it turns out that in general this is impossible at least with present day methods the required complete knowledge of the cyclotomic integers of prescribed absolute value would yield an

on certain sets of polyphase sequences with sparse and highly structured zak and fourier transforms this paper describes a km2 m k q m km z zak space construction of zero correlation zone polyphase sequence sets of sequence length km3 and set size km with all zero cross correlation the construction includes the sets with an m 1 point and t2m 1 point zero autocorrelation zone where t2 is an arbitrary nontrivial factor of m all sequences in these sets have sparse highly structured semipolyphase finite zak transforms with constant nonzero magnitude at m points and zero magnitude at selectable km3 m points and sparse semipolyphase km3 point discrete fourier transforms with constant nonzero magnitude at m2 points and zero magnitude at selectable km3 m2 points

construction of orthogonal and nearly orthogonal designs for computer experiments this paper presents new infinite families of orthogonal designs for computer experiments in cases where orthogonal designs cannot exist we construct alternative nearly orthogonal designs our designs can accommodate many factors and a large set of levels no iterative computer search is required to build up the desired orthogonal designs we develop and use new infinite classes of periodic golay pairs

algebraic representations of the weighted mean abstract we introduce a general framework for the algebraic representation of the weighted mean in the case in which priorities and values refer to a common aggregation domain for instance in hierarchical multicriteria decision models of the ahp type the general framework proposed is based on the semifield structure of open interval domains and provides a natural algebraic description of weighted mean aggregation including the essential mechanism of normalization which transforms priorities into weights such description necessarily involves two operations addition abelian semigroup and multiplication abelian group which generalize the role of addition and multiplication in p 0 in this sense the semifield framework extends recent work by cavallo d apuzzo and squillante on the multiplicative group structure on the basis of the representation of pairwise comparison matrices and their associated priority vectors we consider open interval domains s r whose semifield structures are generated by bijections s r p continuous thus strictly monotonic bijections play a central role in such case continuous strict triangular conorms norms and uninorms emerge naturally in the representation of the semifield structure and in their weighted version they also provide the representation of the weighted mean in both the arithmetic and geometric forms

user capacity of asynchronous cdma systems with matched filter receivers and optimum signature sequences for a symbol asynchronous but chip synchronous single cell code division multiple access cdma system we define a system wide quantity called the total squared asynchronous correlation tsac which for arbitrary signature sets depends on the users delay profile we develop a lower bound for tsac that is independent of the users delays we show that if the signature set achieves this tsac lower bound then the user capacity of the asynchronous cdma system using matched filters becomes the same as that of a single cell synchronous cdma system in this case there is no loss in user capacity due to asynchronism we present iterative signature adaptation algorithms which when executed sequentially by the users appear to converge to these optimum signature sequences however the existence for all user delay profiles of signature sequences achieving this lower bound remains a significant open problem

environmental impact assessment using the evidential reasoning approach environmental impact assessment eia problems are often characterised by a large number of identified environmental factors that are qualitative in nature and can only be assessed on the basis of human judgments which inevitably involve various types of uncertainties such as ignorance and fuzziness so eia problems need to be modelled and analysed using methods that can handle uncertainties the evidential reasoning er approach provides such a modelling framework and analysis method in this paper the er approach will be applied to conduct eia analysis for the first time the environmental impact consequences are characterized by a set of assessment grades that are assumed to be collectively exhaustive and mutually exclusive all assessment information quantitative or qualitative complete or incomplete and precise or imprecise is modelled using a unified framework of a belief structure the original er approach with a recursive er algorithm will be introduced and a new analytical er algorithm will be investigated which provides a means for using the er approach in decision situations where an explicit er aggregation function is needed such as in optimisation problems the er approach will be used to aggregate multiple environmental factors resulting in an aggregated distributed assessment for each alternative policy a numerical example and its modified version are studied to illustrate the detailed implementation process of the er approach and demonstrate its potential applications in eia

finite step algorithms for constructing optimal cdma signature sequences a description of optimal sequences for direct spread code division multiple access ds cdma is a byproduct of recent characterizations of the sum capacity this paper restates the sequence design problem as an inverse singular value problem and shows that the problem can be solved with finite step algorithms from matrix theory it proposes a new one sided algorithm that is numerically stable and faster than previous methods

two dimensional perfect binary arrays with 64 elements perfect binary arrays can exist for numbers of elements that are even square numbers two dimensional 2 d perfect binary arrays are 4 16 36 and 144 elements are known perfect binary arrays with 64 elements can be constructed for three or more dimensions here two dimensional binary arrays with 64 elements are examined the results of computer search for symmetric binary arrays with 64 elements are presented in the form of two 2 d perfect binary arrays with sizes 8 8 and 4 16 applications of these perfect binary arrays are in 2 d synchronization time frequency coding and coding loudspeaker fields

a further discussion of a semiring based study of judgment matrices properties and models information sciences 181 2011 2166 2176 abstract in the paper a semiring based study of judgment matrices properties and models information sciences 181 2011 2166 2176 the semiring is applied to the discussion of judgment matrix properties this paper shows that the suggested semirings could be replaced by a more convenient algebraic structure

new binary sequences with optimal autocorrelation magnitude new binary sequences of period n 4 2m 1 for even m ges 4 are found where the sequences are described by a 4 x 2m 1 array structure the new sequences are almost balanced and have four valued autocorrelation i e n 0 plusmn4 which is optimal with respect to autocorrelation magnitude the complete autocorrelation distribution and the exact linear complexity of the sequences are mathematically derived finally it is shown that the sequences are implemented by a combination of linear feedback shift registers and a simple logic

periodic complementary binary sequences existence conditions and recursive construction procedures for sets of periodic complementary binary sequences are given relationships to sets of aperiodic complementary binary sequences and to perfect binary arrays whose two dimensional periodic autocorrelation function is a delta function are noted the connections of periodic complementary binary sequences and difference families are given sets of periodic complementary binary sequences which result from computer search are presented a diagram showing what is currently known about the existence of periodic complementary binary sequences with p

hidden behavior prediction of complex systems under testing influence based on semiquantitative information and belief rule base compared with the observable behavior it is difficult to predict the hidden behavior of a complex system in the existing methods for predicting the hidden behavior a lot of testing data usually quantitative information are needed to be sampled however some complex engineering systems have the following characteristics 1 the systems cannot be tested periodically and the observable information is incomplete 2 the change process of hidden behavior may be affected by the test and 3 only part of quantitative information and qualitative knowledge i e semiquantitative information may be obtained these characteristics all related to the test are named as testing influence for simplicity although a model and a corresponding optimal algorithm for training the model parameters have been proposed to predict the hidden behavior on the basis of semiquantitative information and belief rule base brb the testing influence has not been considered in order to solve the above problems a new brb based model which can use the semiquantitative information is proposed under testing influence in this paper in the newly proposed forecasting model there are some parameters of which the initial values are usually assigned by experts and may not be accurate which can lead to the inaccurate prediction results as such an improved optimal algorithm for training the parameters of the forecasting model is further developed on the basis of the expectation maximization idea and the covariance matrix adaption evolution strategy cma es by using the semiquantitative information the proposed brb based model and the improved cma es algorithm can operate together in an integrated manner so as to improve the forecasting precision a case study is examined to demonstrate the ability and applicability of the newly proposed brb based forecasting model and the improved cma es algorithm

aggregation functions construction methods conjunctive disjunctive and mixed classes in this second part of our state of the art overview on aggregation theory based again on our recent monograph on aggregation functions we focus on several construction methods for aggregation functions and on special classes of aggregation functions covering the well known conjunctive disjunctive and mixed aggregation functions some fields of applications are included

feature selection for clustering using instance based learning by exploring the nearest and farthest neighbors feature selection for clustering is an active research topic and is used to identify salient features that are helpful for data clustering while partitioning a dataset into clusters a data instance and its nearest neighbors will belong to the same cluster and this instance and its farthest neighbors will belong to different clusters we propose a new feature selection method to identify salient features that are useful for maintaining the instance s nearest neighbors and farthest neighbors referred to here as fsnf in particular fsnf uses the mutual information criterion to estimate feature salience by considering maintainability experiments on benchmark datasets demonstrate the effectiveness of fsnf within the context of cluster analysis

sum capacity and tsc bounds in collaborative multibase wireless systems we consider a wireless system with base stations which collaborate and derive bounds on sum capacity and total squared correlation for uniform channels between users and bases the correspondence also investigates structural properties which must be satisfied by user transmit covariance matrices at the optimal sum capacity total squared correlation tsc point and shows that for multibase systems maximizing sum capacity and minimizing tsc are in general not equivalent problems

sum capacity of equal power users in overloaded channels we consider the sum capacity of code division multiple access cdma signature sequence sets in overloaded channels that contain an orthogonal subset of dimension n we introduce a family of signature sequence sets that consists of a hierarchy of orthogonal subsets hos and show that various signature sequence sets designed for channel overloading belong to this family assuming an equal average energy eae constraint on the user signals an expression for the sum capacity of the hos family is derived we point out that the maximum sum capacity over the hos family is achieved by the multiple orthogonal m o cdma sequence sets the sum capacity of m o is only slightly less than the upper bound imposed by the gaussian multiple access channel moreover m o is superior to a system with n orthogonal sequences and k n pseudonoise pn sequences pn o which in turn outperforms a system with k pn sequences both for pn o and sequence sets over hos there is no additional loss in sum capacity if we require the sequences to consist of chips that are binary or quaternary valued

axiomatic foundation of the analytic hierarchy process this paper contains an axiomatic treatment of the analytic hierarchy process ahp the set of axioms corresponding to hierarchic structures are a special case of axioms for priority setting in systems with feedback which allow for a wide class of dependencies the axioms highlight 1 the reciprocal property that is basic in making paired comparisons 2 homogeneity that is characteristic of people s ability for making comparisons among things that are not too dissimilar with respect to a common property and hence the need for arranging them within an order preserving hierarchy 3 dependence of a lower level on the adjacent higher level 4 the idea that an outcome can only reflect expectations when the latter are well represented in the hierarchy the ahp neither assumes transitivity or the stronger condition of consistency nor does it include strong assumptions of the usual notions of rationality a number of facts are derived from these axioms providing an operational basis for the ahp

correlation and set size bounds of complementary sequences with low correlation zone the correlation lower bounds as well as the set size upper bounds of low correlation zone complementary sequences are presented in this paper they can be treated as an extension of tang fan matsufuji bounds in and which considered only the conventional non complementary low correlation zone sequence sets

on the limitation of linear mmse detection this correspondence highlights the performance limitation of linear minimum mean squared error mmse detection in underdetermined vector gaussian channels as in overloaded code division multiple access cdma systems where the number of symbols users exceeds the signal space dimension spread factor it is shown that for such a simple receiver it is not possible to construct signal sets or spreading codes to even satisfy the basic requirement that every user s symbol error probability decays exponentially as noise power vanishes this result holds for arbitrary received energies modulation schemes and any strictly underdetermined system with a finite signal space dimension and a finite number of users

on aperiodic and periodic complementary binary sequences we give direct and recursive constructions for aperiodic and periodic complementary sequences using these constructions many missing entries in the table of bomer and antweiler 1990 can be filled

basic concepts for a theory of evaluation the aggregative operator abstract starting with an explication of the aggregative concept and deducing a general structure which satisfies a number of minimal requirements properties of clustering the main features of a new mathematical theory called theory of evaluation are developed the theory sheds new light on such well known concepts as membership conjunction and disjunction and seems to be a very promising tool to handle representation problems as they grow from the fields of theory of fuzzy set and its many applications of human decision making and of multicriteria analysis

binary sequences with merit factor greater than 6 34 the maximum known asymptotic merit factor for binary sequences has been stuck at a value of 6 since the 1980s several authors have suggested that this value cannot be improved in this paper we construct an infinite family of binary sequences whose asymptotic merit factor we conjecture to be greater than 6 34 we present what we believe to be compelling evidence in support of this conjecture the numerical experimentation that led to this construction is a significant part of the story

aggregation functions means this two part state of the art overview on aggregation theory summarizes the essential information concerning aggregation issues an overview of aggregation properties is given including the basic classification on aggregation functions in this first part the stress is put on means i e averaging aggregation functions both with fixed arity n ary means and with multiple arities extended means

owa operators defined on complete lattices in this paper the concept of an ordered weighted average owa operator is extended to any complete lattice endowed with a t norm and a t conorm in the case of a complete distributive lattice it is shown to agree with a particular case of the discrete sugeno integral as an application we show several ways of aggregating closed intervals by using owa operators in a complementary way the notion of generalized atanassov s operators is weakened in order to be extended to intervals contained in any lattice this new approach allows us to build a kind of binary aggregation functions for complete lattices including owa operators

choquet like integrals abstract integrals based on a pseudo addition and a pseudo multiplication with properties similar to those of the choquet and the sugeno integral respectively are introduced the structure of convenient pseudo arithmetical operations leading to a choquet like integral is studied

birational mappings and matrix subalgebra from the chiral potts model we study birational transformations of the projective space originating from lattice statistical mechanics specifically from various chiral potts models associating these models with stable patterns and signed patterns we give general results which allow us to find all chiral q state spin edge potts models when the number of states q is a prime or the square of a prime as well as several q dependent family of models we also prove the absence of monocolor stable signed pattern with more than four states this demonstrates a conjecture about cyclic hadamard matrices in a particular case the birational transformations associated with these lattice spin edge models show complexity reduction in particular we recover a one parameter family of integrable transformations for which we give a matrix representation when the parameter has a suitable value

on the inference and approximation properties of belief rule based systems belief rule based brb system provides a generic inference framework for approximating complicated nonlinear causal relationships between antecedent inputs and output it has been successfully applied to a wide range of areas such as fault diagnosis system identification and decision analysis in this paper we provide analytical and theoretical analyses on the inference and approximation properties of brb systems we first investigate the unified multi model decomposition structure of brb systems under which the input space is partitioned into different local regions then we analyse the distributed approximation process of brb systems these analysis results unveil the underlying inference mechanisms that enable brb systems to have superior approximation performances furthermore by using the stone weierstrass theorem we constructively prove that brb systems can approximate any continuous function on a compact set with arbitrary accuracy this result provides a theoretical foundation for using and training brb systems in practical applications finally a numerical simulation study on the well known benchmark nonlinear system identification problem of box jenkins gas furnace is conducted to illustrate the validity of a brb system and show its inference and approximation capability

binary odd periodic complementary sequences a pair of binary sequences is called complementary if the sum of their aperiodic autocorrelation functions is zero except for zero shift such sequences are known for relatively few lengths this correspondence therefore introduces pairs of binary odd periodic complementary sequences which can be constructed using q ary m sequences for many more lengths

inconsistency and non additive capacities the analytic hierarchy process in the framework of choquet integration we examine the ahp in the framework of choquet integration and we propose an extension of the standard ahp aggregation scheme on the basis of the shapley values associated with the criteria in our model a measure of dominance inconsistency between criteria is defined in terms of the totally inconsistent matrix associated with the main pairwise comparison matrix of the ahp the measure of dominance inconsistency is then used to construct a non additive capacity whose associated shapley values reduce to the standard ahp priority weights in the consistency case in the general inconsistency case however the extended aggregation scheme based on the shapley weighted mean tends to attenuate resp emphasize the priority weights of the criteria with higher resp lower average dominance inconsistency with respect to the other criteria

aggregation with generalized mixture operators using weighting functions this paper regards weighted aggregation operators in multiple attribute decision making and its main goal is to investigate ways in which weights can depend on the satisfaction degrees of the various attributes criteria we propose and discuss two types of weighting functions that penalize poorly satisfied attributes and reward well satisfied attributes we discuss in detail the characteristics and properties of both functions moreover we present an illustrative example to clarify the use and behaviour of such weighting functions comparing the results with those of standard weighted averaging operators

sufficient conditions for a conjecture of ryser about hadamard circulant matrices let h be a hadamard circulant matrix of order n 4h2 where h 1 is an odd positive integer with at least two prime divisors such that the exponents of the prime numbers that divide h are big enough and such that the nonzero coefficients of the cyclotomic polynomial n t are bounded by a constant independent of n then for all the n n th primitive roots w of 1 p w n is not an algebraic integer in the cyclotomic field k q w where p t is the representer polynomial of h and is the euler function this implies that p w is not a real number

belief rule based classification system among the computational intelligence techniques employed to solve classification problems the fuzzy rule based classification system frbcs is a popular tool capable of building a linguistic model interpretable to users however it may face lack of accuracy in some complex applications by the fact that the inflexibility of the concept of the linguistic variable imposes hard restrictions on the fuzzy rule structure in this paper we extend the fuzzy rule in frbcs with a belief rule structure and develop a belief rule based classification system brbcs to address imprecise or incomplete information in complex classification problems the two components of the proposed brbcs i e the belief rule base brb and the belief reasoning method brm are designed specifically by taking into account the pattern noise that existes in many real world data sets four experiments based on benchmark data sets are carried out to evaluate the classification accuracy robustness interpretability and time complexity of the proposed method