sensitivity analysis in multiobjective differential programming in this paper we deal with sensitivity analysis in multiobjective differential programs with equality constraints we analyze the quantitative behavior of the optimal solutions according to changes of right hand side values included in the original optimization problem one of the difficulties lies in the fact that the efficient solution in multiobjective optimization in general becomes a set if the preference of the decision maker is represented by a scalar utility which transforms optimal solutions in optima we may apply existing methods of sensitivity analysis however when dealing with a subset of optimal points the existence of a frechet differentiable selection of such a set valued map is usually assumed the aim of the paper is to investigate the derivative of certain set valued maps of efficient points we show that the sensitivity depends on a set valued map associated to the t lagrange multipliers and a projection of its sensitivity

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

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

stability in vector maximization a survey abstract stability and sensitivity analysis becomes more and more attractive also in the area of multicriteria decision making mcdm influences of parameter changes concerning the right hand side or the objective functions respectively or changes of the domination structure on the solution of various mathematical models of vectormaximization problems as developed in several publications are examined in this paper and a survey on the corresponding results is given the survey is subdivided with respect to the various model structures of the decision problem i e linear or nonlinear deterministic or stochastic static or dynamic and with respect to the above mentioned investigated changes

possibility versus probability the main objective of this note is to try to indicate that a possibility distribution at least in some applications can be interpreted as a family of probabilities possibly subjective an advantage of the latter interpretation is that subsequent derivations can be made by well proven probabilistic arguments rather than relying on an intuition concerning the properties of possibility distributions which is not well developed multistate reliability theory is given as an example of an area of application where the probabilistic approach seems far superior

the use of a fuzzy decision making method in a large scale computer system choice problem abstract we recently proposed a fuzzy decision making method for multiple objectives problems in an uncertain and ill defined environment this paper presents a real and large scale application of the method the problem is to decide what sort of computer system for research and education should be renewed in the department of computer engineering one member of a renewal committee appears as a decision maker after describing the outline of the fuzzy decision making method the decision analysis process objective hierarchy identification of decision maker s preference structure rating and ranking of alternatives and sensitivity analysis is presented

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

a note on the operativeness of neyman pearson tests with fuzzy information abstract in a previous paper we have studied the extension of the neyman pearson optimality criterion of testing statistical hypotheses when the available experimental information involves fuzzy imprecision this extension usually becomes unmanageable for small samples nevertheless we will verify that when the sample size is large enough the application of the central limit theorem determines an operative extension

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

a fuzzy decision making method and its application to a company choice problem abstract we propose a fuzzy decision making method for multiobjective decision problems its main features are the use of fuzzy connectives to represent the decision maker s preference structure and fuzzy probability to express imprecise and uncertain outcomes the preference structure is extracted through interaction between the decision maker and a computer the fuzzy connectives adopted here are zimmermann s operation and its two extensions the extended operations describe the preference structure better than the operation the proposed method consists of the following five steps 1 1 identification of the problem 2 2 a questionnaire process 3 3 parameter identification 4 4 evaluations of alternatives 5 5 aggregated rating and ranking of alternatives finally an application of this method to a company choice problem is presented

on some near fuzzy continuous functions between fuzzy topological spaces abstract the concepts of fuzzy almost strongly continuous fuzzy continuous fuzzy weekly continuous and fuzzy weakly continuous are introduced and studied in the light of the concept of q coincidence in a fuzzy setting together with the concept of q neighbourhoods the notions of fuzzy neighbourhoods and fuzzy neighbourhoods are defined to investigate the characterizations and properties of these functions finally a comparative study regarding the mutual interrelations among these maps along with fuzzy continuous maps is made

the envelope theorem for multiobjective convex programming via contingent derivatives the aim of this paper is to formulate an envelope theorem for vector convex programs the obtained result allows to quantify the changes of a certain set of optimal values according to changes of any of the parameters which appear in the constraints we show that the sensitivity depends on a set of associated lagrange multipliers and its sensitivity

stability and sensitivity analysis in convex vector optimization in this paper stability and sensitivity of the efficient set in convex vector optimization are considered the perturbation map is defined as a set valued map it associates with each parameter vector the set of all minimal points of the parametrized feasible set with respect to an ordering cone in the objective space sufficient conditions for the upper and lower semicontinuity of the perturbation map are obtained because of the convexity assumptions the conditions obtained are fairly simple if compared to those in the general case moreover a complete characterization of the contingent derivative of the perturbation map is obtained under some assumptions it provides quantitative information on the behavior of the perturbation map

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

a note on fuzzy weakly completely continuous functions in this paper we show that some results bhaumik and mukherjee 1993 are incorrect and we show that under which conditions these results are true

the efficacy of fuzzy representations of uncertainty advocates of the theory of fuzzy sets as a system for representing uncertainty have based their case on five basic arguments these are 1 the reality hypothesis which holds that imprecision is an inherent property of the world external to an observer 2 the subjectivity hypothesis which holds that probability is an exclusively objective measure of uncertainty and that therefore subjective uncertainty can only be represented with fuzzy sets 3 the behaviorist hypothesis which claims that uncertainty systems should emulate rather than prescribe human behavior in the face of uncertainty 4 the probability as fiction hypothesis which claims that probability does not comprise a field of study in its own right and 5 the superset hypothesis which holds that fuzzy set theory includes probability as a special case and thus provides a richer uncertainty modeling environment we discuss and criticize all five we then criticize the argument that fuzziness represents a type of uncertainty distinct from probability and also the inordinate complexity of fuzzy methods we present a method for assessing the efficacy of fuzzy representations of uncertainty and apply this method in three examples

vagueness and bayesian probability this paper is a response to michael laviolette and john w seaman jr s ibid vol 2 no 1 p 4 1994 position paper the efficacy of fuzzy representations of uncertainty which criticizes fuzzy representations of uncertainty and suggests that bayesian probability can do better the commenter argues that the author s make some misleading comments about bayesian probability and he briefly discusses the problem of giving a satisfactory interpretation of membership functions

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

fuzzy weakly completely continuous functions abstract a new class of functions called fuzzy weakly completely continuous functions is introduced as generalization of fuzzy completely continuous functions the concepts of fuzzy r map and fuzzy faintly continuous function are also introduced and their relationships with fuzzy weakly completely continuous functions are investigated the composition of fuzzy weakly completely continuous functions and its properties are studied the concept of fuzzy extremally disconnected space is also introduced

sensitivity analysis in multiple objective linear programming the tolerance approach abstract we consider a multiple objective linear program solved by the weighted sum approach a method is proposed to determine the maximum percentage by which all weights can deviate simultaneously and independently from their estimated values while retaining the same optimal basis it is also shown how a priori bounds on the ranges of the weights can be exploited to yield a larger maximum tolerance percentage

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

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

decomposition of the parametric space in multiobjective convex programs using the generalized tchebycheff norm abstract a method for decomposing the parametric space in multiobjective convex programs with or without parameters in the constraints using the generalized tchebycheff norm is presented this approach is rather simpler than the corresponding one using the nonnegative weighted sum of objectives also several results are introduced which relate two convex programs with each other one with parameters in the constraints and the other with parameters in the objective function such results make the study of the first type of problems rather simple

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

sensitivity analysis in convex programming the object of this paper is to perform an analysis of the sensitivity for convex vector programs with inequality constraints by examining the quantitative behavior of a certain set of optima according to changes of right hand side parameters included in the program the results in the paper prove that the sensitivity of the program depends on the solution of a dual program and its sensitivity

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

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

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

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

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

sensitivity analysis for convex multiobjective programming in abstract spaces the main object of this paper is to prove that for a linear or convex multiobjective program a dual program can be obtained which gives the primal sensitivity without any special hypothesis about the way of choosing the optimal solution in the efficient set

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