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

marginal consistency upper bounding partition functions over commutative semirings many inference tasks in pattern recognition and artificial intelligence lead to partition functions in which addition and multiplication are abstract binary operations forming a commutative semiring by generalizing max sum diffusion one of convergent message passing algorithms for approximate map inference in graphical models we propose an iterative algorithm to upper bound such partition functions over commutative semirings the iteration of the algorithm is remarkably simple change any two factors of the partition function such that their product remains the same and their overlapping marginals become equal in many commutative semirings repeating this iteration for different pairs of factors converges to a fixed point when the overlapping marginals of every pair of factors coincide we call this state marginal consistency during that an upper bound on the partition function monotonically decreases this abstract algorithm unifies several existing algorithms including max sum diffusion and basic costraint propagation or local consistency algorithms in constraint programming we further construct a hierarchy of marginal consistencies of increasingly higher levels and show than any such level can be enforced by adding identity factors of higher arity order finally we discuss instances of the framework for several semirings including the distributive lattice and the max sum and sum product semirings

theories of causal ordering abstract this paper is a response to iwasaki and simon 14 which criticizes de kleer and brown 8 we argue that many of their criticisms particularly concerning causality modeling and stability originate from the difference of concerns between engineering and economics our notion of causality arises from considering the interconnections of components not equations when no feedback is present the ordering produced by our qualitative physics is similar to theirs however when feedback is present our qualitative physics determines a causal ordering around feedback loops as well causal ordering is a general technique not only applicable to qualitative reasoning therefore we also explore the relationship between causal ordering and propagation of constraints upon which the methods of qualitative physics are based

the generalized distributive law we discuss a general message passing algorithm which we call the generalized distributive law gdl the gdl is a synthesis of the work of many authors in information theory digital communications signal processing statistics and artificial intelligence it includes as special cases the baum welch algorithm the fast fourier transform fft on any finite abelian group the gallager tanner wiberg decoding algorithm viterbi s algorithm the bcjr algorithm pearl s belief propagation algorithm the shafer shenoy probability propagation algorithm and the turbo decoding algorithm although this algorithm is guaranteed to give exact answers only in certain cases the junction tree condition unfortunately not including the cases of gtw with cycles or turbo decoding there is much experimental evidence and a few theorems suggesting that it often works approximately even when it is not supposed to

constraint relaxation may be perfect abstract networks of constraints are a simple knowledge representation method useful for describing those problems whose solution is required to satisfy several simultaneous constraints the problem of solving a network of constraints with finite domains is np complete the standard solution technique for such networks of constraints is the backtrack search but many relaxation algorithms to be applied before backtracking have been developed they transform a network in an equivalent but more explicit one the idea is to make the backtrack search have a better average time complexity in fact if the network elaborated by the backtrack algorithm is more explicit the algorithm backtracks less in this paper we describe relaxation algorithms as sequences of applications of relaxation rules moreover we define perfect relaxation algorithms as relaxation algorithms which not only return a more explicit network but also exactly solve the given network of constraints by applying every relaxation rule only once finally we characterize a family of classes of networks on which certain perfect relaxation algorithms are very efficient the exact solution of each network in a class is found in linear time

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

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

a model for distributed systems based on graph rewriting in our model a graph describes a net of processes communicating through ports and at the same time its computation history consisting of a partial ordering of events stand alone evolution of processes is specified by context free productions from productions and a basic synchronization mechanism a set of context sensitive rewriting rules that models the evolution of processes connected to the same ports can be derived a computation is a sequence of graphs obtained by successive rewritings the result of a finite computation is its last graph whereas the result of an infinite computation is the limit infinite graph defined through a completion technique based on metric spaces a result characterizes a concurrent computation since it abstracts from any particular interleaving of concurrent events while in the meantime providing information about termination partial or complete deadlocks and fairness not every result is acceptable however but only the computations that produce a result no longer rewritable are successful infinite successful computations are shown to coincide with weakly fair computations and a scheduler yielding all and only such computations is defined

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

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

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

principal component transforms of triaxial recordings by singular value decomposition polarization analysis can be achieved efficiently by treating a time window of a single station triaxial recording as a matrix and doing a singular value decomposition svd of this seismic data matrix svd of the triaxial data matrix produces an eigenanalysis of the data covariance cross energy matrix and a rotation of the data onto the directions given by the eigenanalysis karhunen loeve transform all in one step svd provides a complete principal components analysis of the data in the analysis time window selection of this time window is crucial to the success of the analysis and is governed by three considerations the window should contain only one arrival the window should be such that the signal to noise ratio is maximized and the window should be long enough to be able to discriminate random noise from signal the svd analysis provides estimates of signal signal polarization directions and noise an f test is proposed which gives the confidence level for the hypothesis of rectilinear pol

instantaneous polarization attributes and directional filtering we introduce a systematic definition of instantaneous attributes for an arbitrary multicomponent seismic signal the definition is a natural generalization of known complex trace attributes of a one component signal instantaneous amplitude and all polarization parameters are defined as invariants of instantaneous phase rotation the principal feature of our approach is the unique definition of the instantaneous phase for a signal with any number of components plots of subtle polarization parameters of multicomponent seismic data are easily obtained using conventional seismic plotting routines we illustrate our approach on a synthetic example and apply it to real 3 component wide angle crustal data plots of polarization attributes provide evidence for shear wave splitting in an sg arrival having determined the instantaneous polarization vector we design a new type of time domain spatial directional filter the filter enhances linearly polarized events with specified instantaneous polarization the

solving weighted csp by maintaining arc consistency recently a general definition of arc consistency ac for soft constraint frameworks has been proposed by t schiex proc cp 2000 singapore 2000 pp 411 424 in this paper we specialize this definition to weighted csp and introduce two o ed3 enforcing algorithms then we refine the definition and introduce a stronger form of arc consistency ac along with two o n2d2 ed3 algorithms as in the csp case an important application of ac is to combine it with search we empirically demonstrate that a branch and bound algorithm that maintains either ac or ac is a state of the art general solver for weighted csp our experiments cover binary max csp and max sat problems

unifying tree decompositions for reasoning in graphical models the paper provides a unifying perspective of tree decomposition algorithms appearing in various automated reasoning areas such as join tree clustering for constraint satisfaction and the clique tree algorithm for probabilistic reasoning within this framework we introduce a new algorithm called bucket tree elimination bte that extends bucket elimination be to trees and show that it can provide a speed up of n over be for various reasoning tasks time space tradeoffs of tree decomposition processing are analyzed

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

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

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

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

graph rewriting for a partial ordering semantics of concurrent constraint programming abstract the concurrent constraint logic programming framework extends both logic programming and concurrent logic programming in that a program consists of the concurrent execution of agents which add i e tell and check i e ask constraints on a shared set of variables and whose behaviour is described by a set of clauses this formulation is very general and can be seen as a concurrent logic programming shell which is parametrized w r t the underlying constraint system graphs and graph grammars can be conveniently used to describe such a framework and the modelling is so elegant and expressive that they provide what we believe is the most natural abstract machine for concurrent constraint programming in fact basic notions like the possibility of asking or telling a constraint into the shared store are very easy to express in the algebraic approach to graph rewriting more precisely the shared store is represented as a hyper graph where nodes are variables and arcs are constraints or agents then both the entailment relation of the underlying constraint system and the local behaviour of agents is expressed by suitable sets of graph productions which transform the current global state of the system into a new one finally each computation is represented by a graph derivation in our setting the shared store is not seen as one constraint but as a set of constraints which possibly share variables this is in contrast with all the operational and denotational semantics already proposed for the concurrent constraint paradigm which treat the shared store as a monolith and thus are not useful for deriving any information about the causal dependencies among the agents or the maximal degree of parallelism on the contrary our approach can easily express such information in the form of a partial ordering associated to each graph derivation this can be regarded as the first attempt to give a true concurrency semantics to concurrent constraint programming and more generally to graph grammars

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

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

linear independence in bottleneck algebras abstract let r be a linearly ordered set a bottleneck algebra is the set r together with two operations a b max a b and a b min a b in this paper we suggest various definitions of linear independence of sets of n tuples over r study their characteristics and interrelations

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

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

a partial k arboretum of graphs with bounded treewidth the notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies this survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class also some mutual relations between such classes are discussed

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

semiring induced valuation algebras exact and approximate local computation algorithms local computation in join trees or acyclic hypertrees has been shown to be linked to a particular algebraic structure called valuation algebra there are many models of this algebraic structure ranging from probability theory to numerical analysis relational databases and various classical and non classical logics it turns out that many interesting models of valuation algebras may be derived from semiring valued mappings in this paper we study how valuation algebras are induced by semirings and how the structure of the valuation algebra is related to the algebraic structure of the semiring in particular c semirings with idempotent multiplication induce idempotent valuation algebras and therefore permit particularly efficient architectures for local computation also important are semirings whose multiplicative semigroup is embedded in a union of groups they induce valuation algebras with a partially defined division for these valuation algebras the well known architectures for bayesian networks apply we also extend the general computational framework to allow derivation of bounds and approximations for when exact computation is not feasible

semiring based constraint satisfaction and optimization we introduce a general framework for constraint satisfaction and optimization where classical csps fuzzy csps weighted csps partial constraint satisfaction and others can be easily cast the framework is based on a semiring structure where the set of the semiring specifies the values to be associated with each tuple of values of the variable domain and the two semiring operations and x model constraint projection and combination respectively local consistency algorithms as usually used for classical csps can be exploited in this general framework as well provided that certain conditions on the semiring operations are satisfied we then show how this framework can be used to model both old and new constraint solving and optimization schemes thus allowing one to both formally justify many informally taken choices in existing schemes and to prove that local consistency techniques can be used also in newly defined schemes

instantaneous polarization attributes based on an adaptive approximate covariance method we introduce a method for computing instantaneous polarization attributes from multicomponent signals this is an improvement on the standard covariance method scm because it does not depend on the window size used to compute the standard covariance matrix we overcome the window size problem by deriving an approximate analytical formula for the cross energy matrix in which we automatically and adaptively determine the time window the proposed method uses polarization analysis as applied to multicomponent seismic by waveform separation and filtering

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

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

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

arc consistency for soft constraints the notion of arc consistency plays a central role in constraint satisfaction r dechter constraint processing morgan kaufmann san mateo ca 2003 it is known since the introduction of valued and semi ring constraint networks in 1995 that the notion of local consistency can be extended to constraint optimisation problems defined by soft constraint frameworks based on an idempotent cost combination operator this excludes non idempotent operators such as which define problems which are very important in practical applications such as max csp where the aim is to minimise the number of violated constraints in this paper we show that using a weak additional axiom satisfied by most existing soft constraints proposals it is possible to define a notion of soft arc consistency that extends the classical notion of arc consistency and this even in the case of non idempotent cost combination operators a polynomial time algorithm for enforcing this soft arc consistency exists and its space and time complexities are identical to that of enforcing arc consistency in csps when the cost combination operator is strictly monotonic for example max csp a directional version of arc consistency first introduced by m c cooper reduction operations in fuzzy or valued constraint satisfaction fuzzy sets and systems 134 3 2003 311 342 is potentially even stronger than the non directional version since it allows non local propagation of penalties we demonstrate the utility of directional arc consistency by showing that it not only solves soft constraint problems on trees but that it also implies a form of local optimality which we call arc irreducibility

on conditions for mappings to preserve optimal solutions of semiring induced valuation algebras abstract the valuation algebra is a generic algebraic structure which links up with local computation and inference a projection problem in a valuation algebra concerns the focusing of a collection of information on a local domain in this paper according to a classification of variable sets we present some corresponding necessary conditions for mappings to preserve optimal solutions of projection problems in semiring induced valuation algebra systems we show that for a mapping between two semiring induced valuation algebras its properties of preserving optimal solutions and preserving the solution ordering are equivalent if it is order reflecting further we propose some necessary and sufficient conditions for a projection problem and its translation to have a same optimal solution set finally we show that a lower adjoint of a galois connection defined between c semirings preserves optimal solutions of projection problems if it is order preserving and surjective

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

mini buckets a general scheme for bounded inference this article presents a class of approximation algorithms that extend the idea of bounded complexity inference inspired by successful constraint propagation algorithms to probabilistic inference and combinatorial optimization the idea is to bound the dimensionality of dependencies created by inference algorithms this yields a parameterized scheme called mini buckets that offers adjustable trade off between accuracy and efficiency the mini bucket approach to optimization problems such as finding the most probable explanation mpe in bayesian networks generates both an approximate solution and bounds on the solution quality we present empirical results demonstrating successful performance of the proposed approximation scheme for the mpe task both on randomly generated problems and on realistic domains such as medical diagnosis and probabilistic decoding

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

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

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

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

probabilistic reasoning with graphical security models we develop a framework for probabilistic analysis of security scenarios with dependencies we combine the security model of attack defense trees adtrees with bayesian networks we prove that propositionally equivalent adtrees yield the same probability value we compare our computational method with the standard bottom up algorithm for adtrees we use semiring theory to improve the efficiency of our computations this work provides a computational framework for meaningful probabilistic evaluation of attack defense scenarios involving dependent actions we combine the graphical security modeling technique of attack defense trees with probabilistic information expressed in terms of bayesian networks in order to improve the efficiency of probability computations on attack defense trees we make use of inference algorithms and encoding techniques from constraint reasoning the proposed approach is illustrated on a running example and the computations are automated with the help of suitable software tools we show that the computational routines developed in this paper form a conservative generalization of the attack defense tree formalism defined previously we discuss the algebraic theory underlying our framework and point out several generalizations which are possible thanks to the use of semiring theory finally our results apply directly to the analysis of the industrially recognized model of attack trees