on some advanced type inequalities for sugeno integral and t s evaluators in this paper strengthened versions of the minkowski chebyshev jensen and holder inequalities for sugeno integral and t s evaluators are given as an application some equivalent forms and some particular results have been established

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

quasi and pseudo inverses of monotone functions and the construction of t norms abstract several properties of quasi and pseudo inverses of a non decreasing real function are discussed based on a result of schweizer and sklar for a given triangular norm t and non decreasing function f a construction method leading to a commutative fully ordered semigroup on the unit interval is given a similar construction based on the pseudo inverse implies that the resulting operation will be bounded from above by the minimum but then the associativity may be violated several sufficient conditions for constructing new t norms from a given one and a non decreasing function f based on its quasi inverses and on its pseudo inverse respectively are discussed together with illustrative examples

permanence criteria for semi free profinite groups we introduce the condition of a profinite group being semi free which is more general than being free and more restrictive than being quasi free in particular every projective semi free profinite group is free we prove that the usual permanence properties of free groups carry over to semi free groups using this we conclude that if k is a separably closed field then many field extensions of k x y have free absolute galois groups

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

lipschitz continuity of triangular subnorms this paper deals with the lipschitz property of triangular subnorms unlike the case of triangular norms for these operations the problem is still open and presents an interesting variety of situations we provide some characterization results by weakening the notion of convexity introducing two generalized versions of convexity for real functions called a lower convexity and sub convexity the a lower convex and sub convex real mappings present characteristics quite different from the usual convex real mappings we will discuss the link between such kind of functions and the generators and their pseudo inverse of continuous archimedean triangular subnorms

reversed version of a generalized sharp holder s inequality and its applications in this paper we give a reversed version of a generalized sharp holder s inequality which is due to wu the results are then used to improve beckenbach s inequality and minkowski s inequality moreover as an application in information theory we present a refinement of singh s inequality which is one generalized shannon s inequality

general barnes godunova levin type inequalities for sugeno integral integral inequalities play important roles in classical probability and measure theory non additive measure is a generalization of additive probability measure sugeno s integral is a useful tool in several theoretical and applied statistics which has been built on non additive measure for instance in decision theory the sugeno integral is a median which is indeed a qualitative counterpart to the averaging operation underlying expected utility in this paper barnes godunova levin type inequalities for the sugeno integral on abstract spaces are studied in a rather general form and for this we introduce some new technics for the treatment of concave functions in the sugeno integration context also several examples are given to illustrate the validity of this inequality moreover a strengthened version of barnes godunova levin type inequality for sugeno integrals on a real interval based on a binary operation is presented

linguistic quantifiers modeled by sugeno integrals since quantifiers have the ability of summarizing the properties of a class of objects without enumerating them linguistic quantification is a very important topic in the field of high level knowledge representation and reasoning this paper introduces a new framework for modeling quantifiers in natural languages in which each linguistic quantifier is represented by a family of fuzzy measures and the truth value of a quantified proposition is evaluated by using sugeno s integral this framework allows us to have some elegant logical properties of linguistic quantifiers we compare carefully our new model of quantification and other approaches to linguistic quantifiers a set of criteria for linguistic quantification was proposed in the previous literature the relationship between these criteria and the results obtained in the present paper is clarified some simple applications of the sugeno s integral semantics of quantifiers are presented

generalizations of the chebyshev type inequality for choquet like expectation this paper proves generalizations of the chebyshev type inequality for choquet like expectation some previous results are obtained as corollaries

the sugeno integral with respect to α preinvex functions abstract in this paper we establish the left hand side of the hermite hadamard inequality for preinvex functions and illustrate that the hermite hadamard inequality for preinvex functions is not valid for the sugeno integral moreover we give several upper bounds for the sugeno integral related to preinvex functions some examples are also provided to show the validity of our results

on the comonotonic property for sugeno integral the so called comonotonic property for sugeno integral is introduced and investigated where 0 2 0 is a binary operation under the assumption that lim b a email protected a and lim a a email protected b we prove that sugeno integral possesses comonotonic property if and only if equals to one of the four operators minimum maximum pf the first projection and pl the last projection we also discuss comonotonic property when this assumption does not hold

sugeno integral of monotone functions based on lebesgue measure roman flores et al h roman flores a flores franulic y chalco cano the fuzzy integral for monotone functions applied mathematics and computation 185 2007 492 498 gave some optimal upper bounds for the sugeno integral of continuous and strictly monotone functions and provided yong type inequalities for the sugeno integral these results are generalized to monotone functions in this paper two algorithms are given for calculating the sugeno integral of monotone functions based on lebesgue measure several illustrative examples are presented

chebyshev type inequalities for general fuzzy integrals abstract in this article we first introduce a class of binary operation called g seminorm which generalizes the concept of t seminorm then we use the g seminorm to define a class of sugeno like integral finally we establish some new chebyshev type inequalities for this kind of integral

a note on the ordinal sum theorem and its consequence for the construction of triangular norms in this paper the well known ordinal sum theorem of semigroups is generalized and applied to construct new families of triangular subnorms and triangular norms t norms among them one can find several new families of left continuous t norms too

weighted ordinal means the concept of weighted ordinal arithmetic means and other related weighted ordinal means is studied based on the relevant results on the scale 0 1 new types of weighted ordinal means are proposed in some cases these ordinal means coincide with those proposed by godo and torra but not in the case when ordinal means introduced by them are not idempotent based on divisible ordinal t conorms and modifying the approach of godo and torra we show how the previously introduced weighted ordinal means can be obtained without exploiting the formal similarity of the structure of continuous t conorms on 0 1 and divisible ordinal t conorms

convergences and topology via sequences of multifunctions in this paper we define different types of convergences for sequences of multifunctions and establish relationships among them using the convergence in fuzzy measure we obtain a topological structure on a space of multifunctions

absolute continuity of the periodic magnetic schrodinger operator we prove that the spectrum of the schrodinger operator with periodic electric and magnetic potentials is absolutely continuous

on the construction of boundary weak triangular norms through additive generators abstract recently m urbanski and j wasowski fuzzy arithmetic based on boundary weak t norms international journal of uncertainty fuzziness and knowledge based systems 13 2005 27 37 extended the triangular norm operators to a new class of operators called the boundary weak triangular norms this extension is based on the replacement of the condition t x 1 x by the weaker one t x 1 x for x 0 1 in this paper we discuss the construction of the boundary weak triangular norms based on their additive generators continuous decreasing functions f 0 1 0 which generate proper boundary weak triangular norms are completely characterized several examples are included

fast full search in motion estimation by hierarchical use of minkowski s inequality humi abstract in this paper we extend the idea of successive elimination algorithm sea to obtain a fast full search fs algorithm accelerating the block matching procedure of motion estimation based on the monotonic relation between the accumulated absolution distortions aad obtained for distinct layers of a pyramid structure the proposed method successfully rejects many impossible candidates considered in the fs the derivation of the monotonicity relation repeatedly uses in a four dimensional vector space the l 1 version of minkowski s inequality an inequality which is quite well known in the field of mathematics simulation results show that the processing speed is faster than that of several well known fast full search methods including the sea that uses just once the minkowski s inequality in a vector space of 256 dimension when the block size is 16 16 the processing speed of the proposed method is also competitive with that of the three step search tss which is often used for block matching in interframe video coding although the visual quality performance of tss is usually a little poorer than that of the fs

an inequality related to minkowski type for sugeno integrals an inequality related to minkowski type for the sugeno integral on abstract spaces is studied in a rather general form some previous results on chebyshev type inequality obtained by the authors are generalized several examples are given to illustrate the validity of this inequality the conditions such that this inequality becomes an equality are also discussed finally conclusions and some problems for further investigations are included

hilbertian fields and galois representations we prove a new hilbertianity criterion for fields in towers whose steps are galois with galois group either abelian or a product of finite simple groups we then apply this criterion to fields arising from galois representations in particular we settle a conjecture of jarden on abelian varieties

the smallest semicopula based universal integrals i properties and characterizations abstract in this article we provide a detailed study of basic properties of the smallest universal integral i s with s being the underlying semicopula and review some of the recent developments in this direction the class of integrals under study is also known under the name seminormed integrals and includes the well known sugeno and shilkret integrals as special cases we present some representations and equivalent formulations for i s further we discuss basic properties such as translatability linearity homogeneity and maxitivity in particular we provide the characterizations of the two prominent integrals of sugeno and shilkret we also raise and discuss some open questions

continuous triangular subnorms triangular subnorms are associative commutative non decreasing operations on the unit interval upper bounded by the minimum continuous triangular subnorms are shown to be ordinal sum of archimedean continuous t subnorms with at most one proper t subnorm summand special attention is paid to generate continuous t subnorms an application of continuous t subnorms to the construction of left continuous t norms is shown several illustrative examples are included

on stolarsky inequality for sugeno and choquet integrals recently flores franulic roman flores and chalco cano proved the stolarsky type inequality for sugeno integral with respect to the lebesgue measure l the present paper is devoted to generalize this result by relaxing some of its requirements moreover stolarsky inequality for choquet integral is added too

fibred triangular norms abstract in this paper we deal with the formula g t f x f y where f g are functions mapping from the unit interval to itself and t is a triangular norm we are interested in the conditions under which this formula yields a triangular norm the case when f is continuous is investigated in detail as a result a new method which generates new triangular norms from an arbitrary triangular norm is developed these new triangular norms are the so called fibred triangular norms which are closely related to the homomorphism of semigroups it is well known that continuous archimedean triangular norms can be generated with additive generator functions we investigate a possible generalization of the additive generator function and characterize the class of t norms which can be generated with them this class turns out to be the class of fibred continuous archimedean t norms finally some examples are given for the case when f is not continuous

on additive generators of overlap functions in this paper we introduce the notion of additive generator pair for overlap functions we also study how some of the properties that can be demanded to an overlap function can be expressed in terms of its generator pair in particular given a continuous and positive t norm t we analyze the overlap functions which are obtained by the distortion of t by a pseudo automorphism showing that the additive generator pair of such overlap function may be given in terms of the considered pseudo automorphism and the additive generator of t finally we also consider the influence of the migrativity homogeneity and idempotency properties for the overlap functions obtained by such distortion in terms of their respective additive generator pairs

fuzzy measures and integrals defined on algebras of fuzzy subsets over complete residuated lattices this paper presents basic notions about fuzzy measures over algebras of fuzzy subsets of a fuzzy set it also presents basic ideas on fuzzy integrals defined using these fuzzy measures definitions of new types of fuzzy measures and integrals are motivated by our research on generalized quantifiers several useful properties of fuzzy measures and fuzzy integrals are stated and proved definitions presented in this paper and its results will be employed in subsequent papers on generalized quantifiers defined using this type of fuzzy integral

a note to a construction of t norms based on pseudo inverses of monotone functions abstract many constructions of t norms are known in the literature this paper discusses a construction of t norms by pseudo inverse of a non decreasing function the necessity and the sufficiency of some conditions of this construction are analyzed some easily verifiable sufficient conditions of this construction are given

generalization of the jensen inequality for pseudo integral generalizations of the jensen integral inequality for the pseudo integral are proven there are considered two cases of the real semiring with pseudo operations one when pseudo operations are defined by monotone and continuous function g then the pseudo integral reduces on g integral and the second semiring a b max where the pseudo multiplication is generated

some observations about the convex combination of continuous triangular norms abstract the convex combination of continuous triangular norms is discussed let c 1 be the class of all nilpotent t norms c 2 be the class of all strict t norms and c 3 be the class of all continuous non archimedean t norms it is shown that for any t norms t 1 t 2 which are taken from two different classes of c i i 1 2 3 the convex combination t 1 t 1 t 2 is not associative for any 0 1 the case of two continuous non archimedean t norms is also investigated by our results the problem of whether or not two continuous t norms can be combined with each other is reduced to that of whether two strict or two nilpotent t norms can be combined with each other or not

extended triangular norms the paper is devoted to classical t norms extended to operations on fuzzy quantities in accordance with the generalized zadeh extension principle such extended t norms are used for calculating intersection of type 2 fuzzy sets analytical expressions for membership functions of some extended t norms are derived assuming special classes of fuzzy quantities i e fuzzy truth intervals or fuzzy truth numbers the possibility of applying these results in the construction of type 2 adaptive network fuzzy inference systems is illustrated on several examples

on chebyshev type inequalities for generalized sugeno integrals abstract we give the necessary and sufficient conditions guaranteeing the validity of chebyshev type inequalities for generalized sugeno integrals in the case of functions belonging to a much wider class than the comonotone functions for several choices of operators we characterize the classes of functions for which the chebyshev type inequality for the classical sugeno integral is satisfied

uniform approximation of bloch functions and the boundedness of the integration operator on h abstract we obtain a necessary and sufficient condition for the operator of integration to be bounded on h in a simply connected domain the main ingredient of the proof is a new result on uniform approximation of bloch functions

general minkowski type inequalities for sugeno integrals minkowski type inequalities for the sugeno integral on abstract spaces are studied in a rather general form thus closing the series of papers on the topic dealing with special cases restricted to the pseudo additive operation

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

fuzzy integral based perceptron for two class pattern classification problems the single layer perceptron with single output node is a well known neural network for two class classification problems furthermore the sigmoid or logistic function is usually used as the activation function in the output neuron a critical step is to compute the sum of the products of the connection weights with the corresponding inputs which indicates the assumption of additivity among individual variables unfortunately because the input variables are not always independent of each other an assumption of additivity may not be reasonable enough in this paper the inner product can be replaced with an aggregation value obtained by a useful fuzzy integral by viewing each of the connection weights as a value of a l fuzzy measure for the corresponding variable a genetic algorithm is then employed to obtain connection weights by maximizing the number of correctly classified training patterns and minimizing the errors between the actual and desired outputs of individual training patterns the experimental results further demonstrate that the proposed method outperforms the traditional single layer perceptron and performs well in comparison with other fuzzy or non fuzzy classification methods

fuzzy integral based information fusion for classification of highly confusable non speech sounds acoustic event classification may help to describe acoustic scenes and contribute to improve the robustness of speech technologies in this work fusion of different information sources with the fuzzy integral fi and the associated fuzzy measure fm are applied to the problem of classifying a small set of highly confusable human non speech sounds as fi is a meaningful formalism for combining classifier outputs that can capture interactions among the various sources of information it shows in our experiments a significantly better performance than that of any single classifier entering the fi fusion module actually that fi decision level fusion approach shows comparable results to the high performing svm feature level fusion and thus it seems to be a good choice when feature level fusion is not an option we have also observed that the importance and the degree of interaction among the various feature types given by the fm can be used for feature selection and gives a valuable insight into the problem

on some algebraic and topological properties of generated border continuous triangular norms in the class of all border continuous triangular norms generated by strictly decreasing additive generators the following algebraic and topological properties are studied in detail the continuity left continuity right continuity the border continuity the conditional cancellation law the cancellation law the archimedean property the diagonal property the continuity on the diagonal and also the associative law the relations among these properties are examined a special attention is devoted to the set of all idempotent elements of generated functions and to the set of all points of discontinuity of an additive generator the necessary and sufficient conditions for a generated function to be a border continuous triangular norm are expressed in terms of properties of generated functions some relevant examples and counterexamples are indicated

diamond theorem for a finitely generated free profinite group we extend haran s diamond theorem to closed subgroups of a finitely generated free profinite group this gives an affirmative answer to problem 25 4 9 of fried and jarden in field arithmetic 2nd edn springer berlin heidelberg new york 2005

general chebyshev type inequalities for sugeno integrals chebyshev type inequalities for the sugeno integral on abstract spaces are studied in a rather general form thus closing the series of papers on the topic dealing with special cases restricted to the real line and product operation

a note on fuzzy integral inequality of stolarsky type abstract in this paper we prove a stolarsky type inequality for fuzzy integrals more precisely we show that 0 1 f x 1 a b d 0 1 f x 1 a d 0 1 f x 1 b d where a b 0 f 0 1 0 1 is a continuous and strictly monotone function and is the lebesgue measure on r

a jensen type inequality for fuzzy integrals in this paper we show a jensen type inequality for the sugeno integral we also discuss some conditions assuring the satisfaction of opposite inequality reverse jensen inequality

on the regularities of fuzzy set multifunctions with applications in variation extensions and fuzzy set valued integrability problems in this paper we continue our studies 6 7 concerning regularity in this sense we obtain extension results by preserving regularity and we establish basic properties and continuity properties for the variation of fuzzy set multifunctions this enables us to get relationships among different types of regularity and also to point out regularity properties of the fuzzy set valued integral 20

particle swarm optimization for determining fuzzy measures from data fuzzy measures and fuzzy integrals have been successfully used in many real applications how to determine fuzzy measures is the most difficult problem in these applications though there have existed some methodologies for solving this problem such as genetic algorithms gradient descent algorithms and neural networks it is hard to say which one is more appropriate and more feasible each method has its advantages and limitations therefore it is necessary to develop new methods or techniques to learn distinct fuzzy measures in this paper we make the first attempt to design a special particle swarm algorithm to determine a type of general fuzzy measures from data and demonstrate that the algorithm is effective and efficient furthermore we extend this algorithm to identify and revise other types of fuzzy measures to test our algorithms we compare them with the basic particle swarm algorithms gradient descent algorithms and genetic algorithms in literatures in addition for verifying whether our algorithms are robust in noisy situations a number of numerical experiments are conducted theoretical analysis and experimental results show that for determining fuzzy measures the particle swarm optimization is feasible and has a better performance than the existing genetic algorithms and gradient descent algorithms

some integral inequalities for fuzzy interval valued functions abstract this study presents new fuzzy versions of minkowski and beckenbach s integral inequalities without making use of the sugeno integral these new inequalities generalize the interval versions of the minkowski and beckenbach inequalities recently published and are obtained by introducing the p f a integrability concept for fuzzy interval valued functions by means of the kaleva integral and a fuzzy order relation this fuzzy order relation is defined level wise through the kulisch miranker order relation given on the interval space numerical examples that illustrate the applicability of the theory developed in this study are presented

integrals based on monotone set functions an overview of various integrals is given which can be defined on arbitrary monotone set functions vanishing in the empty set called here monotone measures our survey includes not only the choquet integral 1954 10 the shilkret integral 1971 66 and the sugeno integral 1974 71 and some of their properties but also some more general and more recent concepts as universal integrals klement et al 2010 27 and decomposition integrals even 2014 13 together with some of their properties such as integral inequalities and convergence theorems

h continuity of fuzzy measures and set defuzzification the purpose of this work is to analyze the continuity of fuzzy measures with respect to the hausdorff metric on k r n the class of all nonempty compact subsets of r n as an application we study the continuity of set defuzzification processes on r n which are defined by aumann integral methods

pseudo lp space and convergence in the framework of the pseudo analysis the classical l p space is generalized and there are proved important properties of introduced space three types of convergence of sequences of measurable functions are considered in this space the inequalities for integrals based on pseudo integral have been recently proposed as the holder minkowski and markov inequalities which are applied in observing relationship among introduced convergences

berwald type inequality for sugeno integral abstract nonadditive measure is a generalization of additive probability measure sugeno integral is a useful tool in several theoretical and applied statistics which has been built on non additive measure integral inequalities play important roles in classical probability and measure theory the classical berwald integral inequality is one of the famous inequalities this inequality turns out to have interesting applications in information theory in this paper berwald type inequality for the sugeno integral based on a concave function is studied several examples are given to illustrate the validity of this inequality finally a conclusion is drawn and a problem for further investigations is given

a chebyshev type inequality for fuzzy integrals abstract in this paper we prove a chebyshev type inequality for fuzzy integrals more precisely we show that 0 1 fg d 0 1 f d 0 1 g d where is the lebesgue measure on r and f g 0 1 0 are two continuous and strictly monotone functions both increasing or both decreasing also some examples and applications are presented

fatou s lemma for sugeno integral abstract fatou s lemma plays an important role in classical probability and measure theory non additive measure is a generalization of additive probability measure sugeno s integral is a useful tool in several theoretical and applied statistics which have been built on non additive measure in this paper a fatou type lemma for sugeno integral is shown the studied inequality is based on the classical fatou lemma for lebesgue integral to illustrate the proposed inequalities some examples are given

fuzzy measures and integrals in evaluation of strategies artificial intelligence ai techniques have been applied to games for a long time in this paper we will explore the use of fuzzy measures and integrals to evaluate strategies in games we will show their use in decision making when modeling auctions the paper describes the role of fuzzy measures and integrals in decision making and reviews some computational aspects which are important for building real applications

pade approximants density of rational functions in a ω and smoothness of the integration operator first we establish some generic universalities for pade approximants in the closure x in the space a of all rational functions with poles off the closure of the domain c is taken with respect to the finite plane c next we give sufficient conditions on so that x a some of these conditions imply that even if the boundary of a jordan domain has infinite length the integration operator on preserves h and a as well we also give an example of a jordan domain and a function f a such that its antiderivative is not bounded on finally we restate these results for volterra operators on the open unit disc d and we complete them by some generic results

generators of copulas and aggregation the most applied class of copulas for fitting purposes is undoubtedly the class of archimedean copulas due to their representation by means of single functions of one variable i e by means of additive generators or the corresponding pseudo inverses in this paper we characterize aggregation functions preserving additive generators pseudo inverses of additive generators of archimedean copulas as a by product we obtain an efficient method to construct new additive generators from some given ones

a hybrid approach for image recognition combining type 2 fuzzy logic modular neural networks and the sugeno integral in this paper a hybrid approach for image recognition combining type 2 fuzzy logic modular neural networks and the sugeno integral is described interval type 2 fuzzy inference systems are used to perform edge detection and to calculate fuzzy densities for the decision process a type 2 fuzzy system is used for edge detection which is a pre processing applied to the training data for better use in the neural networks another type 2 fuzzy system calculates the fuzzy densities necessary for the sugeno integral which is used to integrate results of the neural network modules in this case fuzzy logic is shown to be a good methodology to improve the results of a neural system facilitating the representation of the human perception a comparative study is also made to verify that the proposed approach is better than existing approaches and improves the performance over type 1 fuzzy logic

the fuzzy integral for monotone functions abstract in this paper we give some optimal upper bounds for the sugeno s integral of monotone functions more precisely we show that if g 0 0 is a continuous and strictly monotone function then the fuzzy integral value p 0 a g d with respect to the lebesgue measure verifies the following sharp inequalities a g a p p for the increasing case and b g p p for the decreasing case moreover we show that under adequate conditions these optimal inequalities provides a powerful tool for solving fuzzy integrals also some examples and application are presented

dependence of exchangeable residual lifetimes subject to failure abstract we provide exact formulas about the survival copula of an exchangeable random vector of residual lifetimes when some of the components have failed specific computations are carried out in the case of archimedean copulas and the evolution of dependence after successive failures of some components is shown numerically via measures of association

generalization of the lyapunov type inequality for pseudo integrals we prove two kinds of lyapunov type inequalities for pseudo integrals one discusses pseudo integrals where pseudo operations are given by a monotone and continuous function g the other one focuses on the pseudo integrals based on a semiring 0 1 sup where the pseudo multiplication is generated some examples are given to illustrate the validity of these inequalities

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

new property of a generalized holder s inequality and its applications in this paper we present a new property of a generalized holder s inequality and then we obtain a new refinement of the generalized holder s inequality as applications we give a generalization and refinement of the opial beesack inequality by using the obtained result moreover as an application in information theory we give a refinement of singh s inequality which is a generalized shannon s inequality

on the convex combination of td and continuous triangular norms the problem of when t l 1 l t d lt l 0 1 is a triangular norm where t d is the drastic product and t is a continuous triangular norm is studied it is shown that t l cannot be a triangular norm when t is nilpotent it is also shown that t l is a triangular norm if t is strict and its additive generator f satisfies f lx f x f l for all x 0 1 the cases that t t m and t is the ordinal sum of continuous archimedean summands are also discussed some left continuous t norms which can be combined with each other are given

localized versions of function spaces and generic results abstract we consider generalizations of classical function spaces by requiring that a holomorphic in function satisfies some property when we approach from not the whole boundary but only a part of it these spaces endowed with their natural topology are frechet spaces we prove some generic non extendability results in such spaces and generic nowhere differentiability on the corresponding part of

a theory of fuzzy measures representations the choquet integral and null sets abstract some theorems of t murofushi and m sugeno fuzzy sets and systems 29 1989 201 227 concerning representation of fuzzy measures and the choquet integral are generalized it is shown that if there is a certain relation between two measurable functions then the choquet integral is additive for these two functions in addition this article discusses null sets with respect to fuzzy measures and also fuzzy measures defined on a class which is not a algebra