a possibility measure is not a fuzzy measure abstract in this note we show that a possibility measure is not a particular type of fuzzy measure except in trivial cases

measures of fuzzy sets and measures of fuzziness abstract the measures presented in this paper are defined by using weber s concept of decomposable measures m of crisp sets having in particular the archimedean decomposable operations in view section 2 measures m of fuzzy sets are introduced as integrals with respect to m for the archimedean cases weber s integral will be used as alternative to sugeno s and choquet s concepts section 3 what fuzziness means will be described by functions of fuzziness f another name entropy n functions with respect to a negation in addition to the types of functions of fuzziness which are induced by concave functions we discuss also the ones which are induced by fuzzy connectives section 4 now using m for measuring the importance of items and f for the fuzziness of the possible values of a fuzzy set m f serves us as a measure of the fuzziness f of the concepts of de luca and termini capocelli and de luca kaufmann knopfmacher loo gottwald dombi and under the restriction to the archimedean cases also the concepts of trillas and riera and yager turn out to be special cases section 5

semiconormed possibility integrals and multi feature pattern classification abstract the semiconormed possibility integrals are proposed as a multi feature pattern classification model a semiconormed possibility integral is a nonlinear integration of a function and its corresponding non normalized possibility measures over feature space the function of an object s feature vector represents the possibilities with uncertainty that the object belongs to a class the uncertainty is due to the similar characteristics of objects from different classes and the distortion of the original characteristic information caused by feature data acquisition systems the uncertainty is assessed by the non normalized possibility measures a possibility measure of a feature is considered as the credibility of the feature to provide reliable information for pattern classification integration of a function and the possibility measures effectively reduces the uncertainty and improves the pattern classification results a pattern classification algorithm based on the semiconormed possibility integrals was used to classify a set of ellipse data and the well known iris data the classification results were compared with those obtained by using bayes classifier

two integrals and some modified versions critical remarks the aim of this paper is to discuss different constructions of integrals sections 3 and 4 based on decomposable measures section 1 according to the classification of the continuous t conorms in essentially two types namely v and archimedean t conorms there exist mainly two types of integrals namely the constructions of sugeno section 3 and of weber section 4 further constructions corresponding to the archimedean case result to be special cases or not well defined section 4 in all cases a crucial property is some restricted distribution law for the pair with an appropriate operation section 2 some applications shall illustrate the use of the two integrals section 5

continuous from above possibility measures and f additive fuzzy measures on separable metric spaces characterization and regularity abstract this paper characterizes continuous from above possibility measures and f additive fuzzy measures on separable metric spaces a set function is a continuous from above possibility measure on a non empty set x or an f additive fuzzy measure on a separable metric space x if and only if there is a sequence x n s n x 0 1 such that lim n s n 0 and a sup s n x n a for every measurable set a in addition a continuous from above possibility measure on a t 1 space and an f additive fuzzy measure on a separable metric space are both regular i e for any measurable set a and any 0 there are open set g and closed set f such that f a g and a f f g a

the autocontinuity of set function and the fuzzy integral abstract the autocontinuity and some other concepts of a set function are introduced and sugeno s fuzzy measure with some annexed conditions is studied on a fuzzy measure space egoroffs theorem is proved it is also proved that f mean convergence is equivalent to convergence in measure for a sequence of measurable functions finally some convergence theorems of sequence of fuzzy integrals are proved especially using the concept of autocontinuity a necessary and sufficient condition for the convergence in measure theorem is given

notes on the norm map between the hecke algebras of the gelfand graev representations of gl 2 q2 and u 2 q abstract let g be a connected reductive algebraic group defined over the field f q and let f and f be two frobenius maps such that f m f m for some integer m let g f g f and g f m g f m be the finite groups of fixed points in this article we consider the case where g gl 2 f q f is the usual frobenius map so that g f gl 2 q and f is the twisted frobenius map such that g f u n q in this case f 2 f 2 and g f 2 g f 2 gl 2 q 2 this article provides connections between the complex representation theory of these groups using the norm maps see c curtis t shoji a norm map for endomorphism algebras of gelfand graev representations in progr math vol 141 1997 pp 185 194 from the gelfand graev hecke algebra of gl 2 q 2 to the gelfand graev hecke algebras of both gl 2 q and u 2 q

on the existence of a possibility distribution function we show that a continuous possibility space over the power set of a model space of continuum cardinality has a possibility distribution function the connection between possibility spaces without this property and measurable cardinals is established the main consequence of this connection is that any practical continuous possibility space has a possibility distribution function

fuzzy and random sets the two distinct concepts of fuzzy and random sets coexist to form the basics for modeling perception based information gathering processes in artificial intelligence these processes viewed as coarsening schemes provide also justifications for various types of uncertainty measures such as belief functions and possibility measures

markov chains with a transition possibility measure and fuzzy dynamic programming abstract this paper constructs a markoov fuzzy process which represents transitions of grades of fuzzy sets with a transition possibility measure and a general state space we analyse snell s optimal stopping problem for the process and we apply the results to solve fuzzy dynamic programming with optimal stopping times and with general state spaces and action spaces under fuzzy transitions

classification of fuzzy measures the aim of this paper is to study several classes of fuzzy measures and the relationships among them this classification is based on the one due to banon but it has some particularities first new kinds of fuzzy measures are considered but the most important feature is that the classification is not directly applied to fuzzy measures but to pairs of dual fuzzy measures

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

upper and lower fuzzy measures puri and ralescu 5 showed that a possibility measure is not in the general case a fuzzy measure this paper deals with determining a general framework where both possibility and fuzzy measures are included in order to do that the upper lower fuzzy measures which need not be lower upper continuous are considered the possibility necessity measures will be examples of such upper lower fuzzy measures finally the extensions of these concepts to fuzzy sets are also considered

reconstruction families of possibilistic structure systems abstract a method is presented for characterizing the family of overall systems reconstructable from a given possibilistic structure system the technique is elaborated in terms of fuzzy relation equations it is demonstrated that the reconstruction family of a given structure system is equivalent to the set of solutions of a special type of fuzzy relation equation the solution set is partially ordered and contains both minimal solutions and a unique maximum solution when these elements are identified all members of the reconstruction family are determined another characteristic of the reconstruction family is its reconstruction uncertainty a measure of which is also developed in this paper this measure is used to define an identifiability quotient that expresses the degree of confidence with which we may identify a single overall system given a particular structure system

a heuristic simulated annealing algorithm of learning possibility measures for multisource decision making abstract in multisource decision making non normalized possibility measures are used to gauge the credibilities of each subset of information sources in order to reduce the uncertainty introduced by the sources and minimize decision error the credibility of individual information source i e the possibility density is objectively learned from subjectively chosen training data a learning algorithm of the possibility measures is constructed based on the ideas of simulated annealing and feasible direction the algorithm is designed for large training data set two multifeature image segmentation experiments and a comparison of learning speed are presented

dynamics of xn 1 xn 2k 1xn 2k 1 αxn 2l abstract we investigate the global stability of all positive solutions of the difference equation x n 1 x n 2 k 1 x n 2 k 1 x n 2 l where is a positive real number k 1 2 l 0 1 and the initial conditions are positive real numbers when x 1 1 is globally asymptotically stable also when 1 we show that this equation possesses solutions that converge to the two cycle 0 1 0 1

possibility theory an integral theoretic approach this paper introduces possibility integrals as fuzzy integrals w r t possibility measures it is shown that this concept can be used to unify a lot of known results in possibility theory that up to now have been introduced on a more ad hoc basis the integral theoretic approach allows us amongst other things to introduce product and conditional possibility measures in very much the same way as product lebesgue measures and conditional probability measures are introduced furthermore to stress the fact that the concept of order relations is basic for possibility theory all the results are proved for a complete lattice as the evaluation set instead of the more familiar unit interval 0 1

reliability concepts under the theory of evidence abstract this paper presents an approach to reliability theory from the point of view of the theory of evidence the basic assumption is that the time to failure life of an equipment is a variable characterized by means of an evidence on the real line instead of a probability distribution the classical model firstly some concepts of dempster shafer s theory of evidence for a non necessarily finite set are given then the fundamental concepts under the formulation of dempster shafer s theory are introduced

generalization of an invertible mapping between probability and possibility a discrete bijective mapping between probability and possibility is generalized to the continuous case in n dimensions the mapping contains a parametrical function which can be chosen such that the probability possibility consistency relation and the uncertainty invariance principle are fulfilled simultaneously

a yosida hewitt decomposition for minitive set functions we prove for minitive set functions defined on a s algebra a similar decomposition theorem to the yosida hewitt s one for classical measures this way any minitive set function can be decomposed in a fuzzy minitive measure part and a purely minitive part a particular attention is given for the countable case where the canonical description of any s continuous necessity is fully elicited and provide a simple way to compute the choquet integral of any bounded sequence

seminormed possibility integrals for application oriented modelling abstract semiconormed possibility integrals are proposed as a family of models for decision making which have some special properties due to the non normalized possibility measures the semiconormed possibility integrals are developed from the semiconormed fuzzy integrals and the non normalized possibility measures the non normalized possibility measures induced from the fuzzy sets have the property that the measure of the universe canbe less than equal to one when the universe consists of a set of information sources the possibility measure of a subset of information sources is considered as the credivility of the subset sources the non normalization is due to the fact that an information source in application introduces certainty during data acquisition therefore an information source in reality usually is not fully credible to improve the precision of modelling the credibility values of each information source are learned form training data in term of learning computation a non normalized possibility measure is much simpler to construct than a fuzzy measure finally two applications of the semiconormed possibility integrals are presented