general chebyshev type inequalities for universal integral a new inequality for the universal integral on abstract spaces is obtained in a rather general form as two corollaries minkowski s and chebyshev s type inequalities for the universal integral are obtained the main results of this paper generalize some previous results obtained for special fuzzy integrals e g choquet and sugeno integrals furthermore related inequalities for seminormed integral are obtained

componentwise decomposition of some lattice valued fuzzy integrals lattice valued fuzzy measures are lattice valued set functions which assign the bottom element of the lattice to the empty set the top element of the lattice to the entire universe and satisfy the property of monotonicity if the lattice is complete then a lattice valued fuzzy integral of sugeno type with similar properties such as the sugeno integral in its original form can be introduced in a natural way the main result of the paper is a componentwise decomposition theorem of an l valued fuzzy integral to its l valued fuzzy integrals components where l is a complete lattice with negation and l a b a email protected l a email protected is organized as a complete lattice too this result is useful to obtain the properties of l valued fuzzy integrals from the properties of l valued fuzzy integrals and to calculate in a simple way the values of some integrals from the values of the components the important case l 0 1 when l becomes the lattice of the intuitionistic fuzzy values is distinctly discussed an idea of application to synthetic evaluation of objects is also suggested

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

on fuzzy measures defined by seminormed fuzzy integrals and semiconormed fuzzy integrals abstract in this paper we show that for the continuous t seminorms and continuous t semiconorms the properties of null addivity pseudo null addivity autocontinuity and pseudo autocontinuity of fuzzy measures g can be preserved by the fuzzy measures g h and g h defined by seminormed fuzzy integrals and semiconormed fuzzy integrals respectively at most under the conditions that x y 0 x y 0 and x y x y g can be preserved by the fuzzy measures g h under the condition that x y 0 x y 0

a unified approach to the monotone convergence theorem for nonlinear integrals abstract we present a unified approach to the monotone convergence theorem for nonlinear integrals such as the choquet the sipos the sugeno and the shilkret integral a nonlinear integral may be viewed as a nonlinear functional defined on a set of pairs of a nonadditive measure and a measurable function we thus formulate our general type of monotone convergence theorem for such a functional the key tool is a perturbation of functional that manages not only the monotonicity of the functional but also the small change of the functional value arising as a result of adding small amounts to a measure and a function in the domain of the functional our approach is also applicable to the lebesgue integral when a nonadditive measure is additive

generalized fuzzy integrals part i fundamental concepts abstract in this paper we introduce a definition of fuzzy integral which is a generalization of both s fuzzy integral defined by m sugeno and n fuzzy integral due to zhao ruhuaiand discuss the fundamen tal properties of this kind of fuzzy integral

on conditions under which some generalized sugeno integrals coincide a solution to dubois problem abstract in the paper we characterize the class of all pairs of fuzzy implications and dual fuzzy implications such that the q integral and q cointegral coincide this gives a solution to the problem posed by didier dubois during the conference fsta 2016 the 13th international conference on fuzzy set theory and applications as a corollary we obtain the necessary and sufficient conditions under which the seminormed fuzzy integral and the semiconormed fuzzy integral are equal for all measurable functions

on the monotone convergence theorem for conormed seminormed fuzzy integral abstract in this paper under the condition that the t conorm and t seminorm are continuous we prove the monotone convergence theorem of conormed seminormed fuzzy integral for non decreasing monotone measurable function sequence also we show that the result cannot be extended to the case of the non increasing function sequence

left right semi uninorms and coimplications on a complete lattice in this paper we firstly discuss the deresidual operations of left right semi uninorms and show which properties they satisfy then we investigate the left and right semi uninorms induced by a coimplication and give some conditions such that the operations induced by a coimplication constitute left or right semi uninorms finally we demonstrate that the meet semilattice of all disjunctive right left distributive left right semi uninorms is order reversing isomorphic to the join semilattice of all right distributive coimplications which satisfy the neutrality principle

the modularity condition for semi t operators and semi uninorms abstract the aim of this paper is mainly to solve the functional equations given by the modularity condition several years ago the modularity equations for t norms t conorms uninorms and t operators which are commutative and associative have been studied our investigations are motivated by modularity condition for generalizations of these operators by removing associativity or commutativity in this work the following main conclusions are proved 1 a continuous t norm with respect to a continuous semicopula is modular if and only if they are equal the case for a semicopula with respect to a strict t norm is also the same a semicopula with respect to a co semicopula is modular if and only if the semicopula is min and the co semicopula is max the modularity condition does not hold for a co semicopula with respect to a semicopula 2 necessary and sufficient conditions are given for a semi t operator with respect to a semi uninorm a pseudo uninorm with respect to a semi t operator to satisfy the modularity condition equation new solutions to the modularity condition equations of the case 1 are characterized

the convergence of dg fuzzy integrals abstract the definition of another kind of generalized fuzzy integrals is introduced by means of the so called generalized triangular conorm it is said to be dual generalized fuzzy integrals and is denoted by dg fuzzy integrals in this paper several equivalent forms of dg fuzzy integrals are given particularly the convergence theorem in fuzzy measure and the monotone convergence theorems are obtained

a behavioral foundation for fuzzy measures in savage 41 a behavioral foundation was given for subjective probabilities to be used in the maximization of expected utility this paper analogously gives a behavioral foundation for fuzzy measures to be used in the maximization of choquet expected utility this opens the way to empirical verification or falsification of fuzzy measures and frees them of their ad hoc character

a survey of weak connectives and the preservation of their properties by aggregations the aim of this paper is to choose diverse definitions of generalized logical connectives and to present them in a coherent order from the weakest to the richest such a rich list of notions allows us to consider the problem of admissible aggregations in the presented classes of unary and binary operations this gives a contribution to the discussion of tolerance analysis in soft computing decision making approximate reasoning and fuzzy control first we present a short survey of the development of mv logic s connectives next we discuss postulates used for generalized logical connectives finally we describe families of weak connectives and indicate the preservation of their properties by some aggregation functions

holder type inequality for sugeno integral two inequalities for the sugeno integral on abstract spaces are studied in rather general forms which generalize most of the results on the same topic obtained by other authors thus closing the series of papers on this topic as an application a holder type inequality is obtained finally some conclusions are drawn and some problems for further investigation are suggested

on a class of transformations of copulas and quasi copulas the theory of copulas is by now a very well established one recently larger classes of functions c 0 1 n 0 1 that are increasing in each variable and satisfy some conditions at the boundary like quasi copulas have been the object of fruitful research several authors have considered the action of a class of transformations on some aggregation operators as t norms copulas quasi copulas and so on these simple transformations do not preserve in general all properties of copulas or quasi copulas in particular the fact that only some properties are preserved by these transformations suggested the introduction of semi copulas the purpose of the present contribution is to give a fairly complete picture concerning such action on copulas and quasi copulas in particular we prove results concerning inclusions and strict inclusions among these classes of operators and those of their transforms

sharp bounds of jensen type for the generalized sugeno integral abstract in this paper we provide two sided attainable bounds of jensen type for the generalized sugeno integral of any measurable function the results extend the previous results of roman flores et al for increasing functions and abbaszadeh et al for convex and concave functions we also give corrections of some results of abbaszadeh et al as a by product we obtain sharp inequalities for symmetric integral of grabisch to the best of our knowledge the results in the real valued functions context are presented for the first time here

multivariable fuzzy controller under go del s implication abstract in this paper the upper bounds for a multivariable fuzzy logic controller under godel s implication are investigated and a generalized multivariable structure of fuzzy controller are proposed contribution operators such as max operation ensure the greatest upper bound as well as the least upper bound conditions which determine an appropriate upper bound are also determined this theory has applications in the design of fuzzy logic controllers

possibility and necessity integrals abstract in this paper we introduce seminormed and semiconormed fuzzy integrals associated with confidence measures these confidence measures have a field of sets as their domain and a complete lattice as their codomain in introducing these integrals the analogy with the classical introduction of lebesgue integrals is explored and exploited it is amongst other things shown that our integrals are the most general integrals that satisfy a number of natural basic properties in this way our dual classes of fuzzy integrals constitute a significant generalization of sugeno s fuzzy integrals a large number of important general properties of these integrals is studied furthermore and most importantly the combination of seminormed fuzzy integrals and possibility measures on the one hand and semiconormed fuzzy integrals and necessity measures on the other hand is extensively studied it is shown that these combinations are very natural and have properties which are analogous to the combination of lebesgue integrals and classical measures using these results the very basis is laid for a unifying measure and integral theoretic account of possibility and necessity theory in very much the same way as the theory of lebesgue integration provides a proper framework for a unifying and formal account of probability theory

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

the fuzzy integral on product spaces for nsa measures abstract this paper deals with the study of fuzzy integrals defined as a generalization of kruse s fuzzy integral 4 for fuzzy nsa measures given by weber 17 as opposed to sugeno s measures several properties and convergence theorems such as the monotone convergence theorem the dominated convergence theorem and fatou s lemma are shown for this fuzzy integral a fuzzy nsa measure will be constructed on a product space based on product of these kinds of measures with the same additive generator and we extend the above integral on to a product space further a version of fubini s theorem will be proved

fuzzy sets and their operations ii among the basic operations which can be performed on fuzzy sets are the operations of union intersection complement algebraic product and algebraic sum in addition to these operations new operations called bounded sum and bounded difference were defined by l a zadeh to investigate the fuzzy reasoning which provides a way of dealing with the reasoning problems which are too complex for precise solution this paper investigates the algebraic properties of fuzzy sets under these nex operations of bounded sum and bounded difference and the properties of fuzzy sets in the case where these new operations are combined with the well known operations of union intersection algebraic product and algebraic sum

cvar superquantile norm stochastic case abstract the concept of conditional value at risk cvar is used in various applications in uncertain environment this paper introduces cvar superquantile norm for a random variable which is by definition cvar of absolute value of this random variable it is proved that cvar norm is indeed a norm in the space of random variables cvar norm is defined in two variations scaled and non scaled l 1 and l infinity norms are limiting cases of the cvar norm in continuous case scaled cvar norm is a conditional expectation of the random variable a similar representation of cvar norm is valid for discrete random variables several properties for scaled and non scaled cvar norm as a function of confidence level were proved dual norm for cvar norm is proved to be the maximum of l 1 and scaled l infinity norms cvar norm as a measure of error is related to a regular risk quadrangle trimmed l1 norm which is a non convex extension for cvar norm is introduced analogously to function l p for p

fuzzy measures and integrals we present fuzzy measures and fuzzy integrals as special poset homeomorphisms besides general fuzzy integrals regular fuzzy integrals are introduced and some of their properties are discussed state of art of fuzzy measure and fuzzy integral theory are briefly summarized and some further streaming is sketched

semi copulas capacities and families of level sets we point out how capacities non additive measures can be used to provide explanations about the concept of bivariate ageing function the latter had been introduced to describe the family of the level sets of a survival function and motivated the interest toward the concept of semi copula

subdistributivity and superdistributivity of binary operations recently the property of distributivity of binary operations on 0 1 is of great interest both for practical as well as fundamental reasons in this paper we summarize some facts connected with distributivity and non distributivity of binary operations on 0 1 motivated by non distributive logical connectives in fuzzy set theory we show some new results concerning the above property a new direction of investigations mainly concerns the distributivity inequalities for triangular norms and conorms and their diverse generalizations in particular we look for examples of binary operations fulfilling the distributivity inequalities

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 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

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

on unitary lie superalgebras from the spin orbit supersymmetrisation procedure from the basis elements of a clifford algebra cl n the authors generate a grading leading to a unitary lie superalgebra when n is even such a construction is motivated by the understanding of the specific properties of the fermionic variables in the so called spin orbit coupling procedure of supersymmetrisation in n 2 supersymmetric quantum mechanics the n odd case is also considered and some specific examples are discussed

problems of classification in a fuzzy environment this paper presents a classification model in a fuzzy environment by using possibility distributions and fuzzy measures optimal in bayes sense membership functions are induced these functions are similar to decision rules used in classical discriminant analysis the relations between fuzzy measures and possibility measures are also discussed to formulate a classification model where sugeno s fuzzy measures and integrals are used

internal direct product of integral ν distributive binary aggregation functions and the classification of all integral ν distributive binary aggregation functions of length 3 we present some relations between an external direct product and an internal direct product of a family of integral distributive binary aggregation functions relations between a direct decomposition of the unit and a family of pairwise comaximal elements in a lattice with an integral distributive binary aggregation function are investigated using these results the classification of all integral distributive binary aggregation functions on a lattice of length 3 and a description of all lattices of length 3 with an integral distributive binary aggregation function are given

two families of fuzzy integrals abstract in this paper we present two definitions of fuzzy integrals arising from the t seminorm and the t semiconorm concepts we show that sugeno s fuzzy integral is a particular case of them and we study their principal properties finally we suggest some applications of these results

hermite hadamard type inequality for sugeno integrals abstract in this paper hermite hadamard type inequality for sugeno integrals based on m convex function is studied some examples are given to illustrate the results

generalized fuzzy integrals of set valued functions in this paper based on wu s generalized fuzzy integrals of point valued function c wu et al fuzzy sets and systems 70 1995 75 a theory of generalized fuzzy integrals of fuzzy valued functions will be investigated it includes definitions properties and various kinds of convergence theorems these are extensions of results in c wu et al fuzzy sets and systems 70 1995 75 d zhang and z wang fuzzy sets and systems 54 1993 63

λ generalized sugeno integral and its application sugeno integral is a useful tool for many problems in several domains especially in game theory measure theory decision making probability image processing and finance in this paper we introduce the concept of generalized sugeno integral then we establish general versions of chebyshev type inequality for this kind of sugeno integral by using a monotone measure our results generalize and improve the corresponding ones in the literature finally some conclusions and problems for further investigations are given

a note on yoshida s optimal stopping model for option pricing abstract we argue that the optimal stopping model which has been used by yoshida to discuss option pricing can many times lead to an overoptimistic evaluation of payoffs put option prices this effect is due to the method used to compare fuzzy payoffs using a sugeno integral it is shown that each fuzzy payoff can be associated to an indifferent non fuzzy payoff which is never smaller than the highest value having membership 1 several examples are given in which this property seems to be incovenient we also show that this inconvenience cannot be avoided by replacing sugeno integrals by any other integral like functional like a t seminormed integral or a choquet integral finally we suggest to use the campos gonzalez ranking criterion instead

a concept of duality for multivariate exchangeable survival models in some past works by the author and collaborators the notion of ageing function of an exchangeable survival model was introduced and several properties of it were analyzed generally the ageing function turns out to be a semi copula here we focus attention on the special class of survival models whose ageing function is actually a copula for pairs of models in this class we define a notion of duality such a notion can provide a better explanation of the analogies existing between the ageing function and the survival copula the formulation of the notion of duality presented here came out some years ago in the frame of research activity in collaboration with bruno bassan

holder minkowski type inequality for generalized sugeno integral abstract we give a necessary and sufficient condition for validity of the holder minkowski type inequality for the generalized sugeno integral any monotone measure and the class of associated functions we also show a connection between integral inequalities and the problem of finding binary operations satisfying the distributivity inequalities we characterize all semicopulas satisfying holder and minkowski inequalities for the seminormed fuzzy integral one result has been obtained for the recently introduced q integral we describe the relationships among the existing sufficient conditions and show that our result generalizes most known holder minkowski type inequalities for comonotone functions in the available literature we also provide two other methods to get the above mentioned inequality for the sugeno integral and the class of m subadditive functions as well as for the sugeno integral of 0 1 valued functions using a duality approach we point out some flaws and correct the corresponding false statements appearing in the literature at the end we pose several problems and questions for further research

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