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

decomposable measures and nonlinear equations abstract using integrals based on decomposable measures with respect to a pseudo addition related to a semiring a b a b a unified method is given for solving some nonlinear differential ordinary and partial difference and optimization equations for that purpose important tools as pseudo superposition principle and pseudolaplace transform are used

on the equality of integrals considering a finite space x several necessary conditions and one rather general sufficient condition describing when the choquet integral coincides with the pan integral with respect to the standard arithmetic operations are shown these conditions are characterized by using the minimal atoms of monotone measure under the introduced constraints the calculation of these coinciding two integrals is also given

a limit theorem for triangle functions a wide class of triangle functions that can be interpreted as generalized pseudo convolutions of distribution functions has been considered in order to find out whether a nontrivial limit for the sequence of the pseudo convolutions of distribution functions exists or not some pseudo laplace type transformations have been introduced the main result is illustrated with a family of pseudo convolutions based on a family of schweizer sklar t norms and another example is given with a calculation of the analytical form of the limit function

the range of null additive fuzzy and non fuzzy measures abstract in this paper a wide class of non additive set functions is investigated for finite null additive fuzzy and non fuzzy measures saks decomposition type theorem theorem on darboux property and lyapunov s type theorems are proved

pseudo analysis and its applications in railway routing using as a base the pseudo analysis the problem of railway routing is treated first a deterministic approach is applied on three and four stations these problems are treated also with a stochastic approach when one variable is randomized

discrete bipolar pseudo integrals abstract in the authors paper strboja et al 2016 42 the notion of the bipolar pseudo integral has been introduced this paper extends investigations related to this new type of bipolar integrals defined with respect to decomposable bi capacities we consider the main properties of the discrete bipolar pseudo integral a characterization theorem for the discrete bipolar pseudo integral is proven monotone convergence theorems and the fatou type lemma for the discrete bipolar pseudo integral are considered in order to illustrate obtained results many interesting examples are provided

pseudo additive measures and integrals abstract we suggest pseudo additive measures based on a pseudo addition and discuss integrals with respect to pseudo additive measures a pseudo additive measure is a special type of fuzzy measures to define an integral a multiplication corresponding to a pseudo addition is introduced the resulting integral is an extension of the lebesgue integral in this context radon nikodym like theorems are shown

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

a unified approach to define fuzzy integrals recently the two most general and well known fuzzy integrals sugeno s integral and choquet s integral were characterized it was also shown how both integrals fitted the same formal model and they only differed in the operators used in this paper we try to analyze whether it is possible to improve those characterization theorems and we also study the possibility of defining other fuzzy integrals following the same model but using other operators in a recent paper campos and bolafios 6 characterized two general and well known fuzzy integrals sugeno s integral 11 and choquet s integral 7 the last one also called monotone expectation 2 4 5 6 the two characterization theorems are based on the same formal model of four properties which only differ in the operators used sum and product for choquet s integral maximum and minimum for sugeno s integral two important questions remained open one involved the characterization theorems of these integrals in an attempt to further refine them the second question was to investigate the possibility of defining other fuzzy integrals using different operators but following the same model in this paper we give answers to those problems section 2 is devoted to describing fuzzy integrals defined on sugeno s fuzzy measures particularly sugeno s and choquet s integrals and their characterizations in section 3 we show how the characterization of choquet s integral can be refined whereas the same cannot be made for sugeno s integral finally other fuzzy integrals fitting our formal model are obtained in section 4

convergence in measure theorems of nonlinear integrals of functions integrable to the pth power abstract one can find a subadditive measure and a sequence f n n n of nonnegative measurable functions converging in measure to such a function f with the property that for any p 1 f n p no longer converges in measure to f p therefore in nonadditive measure theory an additional and intrinsic discussion is needed to prove integral convergence theorems for functions integrable to the pth power the purpose of the paper is to propose a method for automatically deriving pth power versions of convergence in measure theorems of nonlinear integrals from already established ones the proposed method is based on the robustness of some properties of integral functional under the operation f f p raising a nonnegative function f to the pth power

smilansky s model of irreversible quantum graphs i the absolutely continuous spectrum in the model suggested by smilansky 2004 waves random media 14 143 53 one studies an operator describing the interaction between a quantum graph and a system of k one dimensional oscillators attached at several different points in the graph the present paper is the first one in which the case k 1 is investigated for the sake of simplicity we consider k 2 but our argument is of a general character in this first of two papers on the problem we describe the absolutely continuous spectrum our approach is based upon scattering theory

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

chebyshev type inequalities for pseudo integrals abstract chebyshev type inequalities for two classes of pseudo integrals are shown one of them concerning the pseudo integrals based on a function reduces on the g integral where pseudo operations are defined by a monotone and continuous function g another one concerns the pseudo integrals based on a semiring a b max where is generated moreover a strengthened version of chebyshev s inequality for pseudo integrals is proved

on set valued fuzzy measures so far there have been many discussions on sugeno s fuzzy measures and fuzzy integrals but most of them are concentrated on single valued functions motivated by aumann s set valued integral j math anal appl 12 1965 1 we have introduced the fuzzy integral of set valued functions fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341 ph d dissertation harbin institute of technology 1998 it is a well behaved extension of fuzzy integrals of single valued functions it is well known that arstein s set valued measure trans am math soc 165 1972 103 is an important branch in set valued analysis set valued analysis birkhauser berlin 1990 or theory of correspondences theory of correspondences wiley new york 1984 compared to it the present paper will try to establish the basic idea of set valued fuzzy measures which are monotone set valued set functions it is also a natural generalization of single valued fuzzy measures as well as an extension of set valued measures in the case of one dimension these works include the concept of set valued fuzzy measures set valued fuzzy measures defined by set valued fuzzy integrals and set valued pseudo additive measures it can be viewed as a continuation of previous work fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341

aggregating membership values by a choquet fuzzy integral based operator a new type of aggregator the choquet fuzzy integral based operator is introduced and applied in aggregation of membership values in this paper we generalized the definition of the fuzzy integral as a tool for membership aggregation the generalization involves replacing the max or min operator in information integration with a choquet fuzzy integral based aggregator resulting in increased flexibility the characteristics of the choquet fuzzy integral are studied and a two phase aggregating process is proposed also we demonstrate a good classification result using the proposed aggregator to integrate the memberships of several clusters in a complex unconstrained handwritten digit recognition domain

generalized transformed t conorm integral and multifold integral fuzzy integrals are commonly used as aggregation operators in this paper we present new composite models based on fuzzy integrals with several t conorms these models permit to further increase the computational power of the previous models basic properties of new composite models are studied in particular it is shown that for composite models the only meaningful case is when not all the t conorms are the same

different interpretations of triangular norms and related operations triangular norms and triangular conorms and uni norms can be treated as semigroup two place function also as commutative semiring multiplications it can also be derived from the difference operation in a difference poset we discuss here these different interpretations and their consequences

weak convergence of nonadditive measures based on nonlinear integral functionals abstract in this paper we formulate a general portmanteau theorem for a perturbative nonlinear integral functional and discuss the uniformity of weak convergence of nonadditive measures based on such a functional as their direct consequences it turns out that levy convergence of nonadditive measures coincides with every one of three types of weak convergence that is weak choquet weak sugeno and weak shilkret convergence and they are uniform on every bounded subset of lipschitz functions those results are applied when discussing the metrizability of the levy topology on the space of nonadditive measures and defining the fortet mourier type metrics on a uniformly equi autocontinuous set of nonadditive measures

jensen type inequality for the bipolar pseudo integrals abstract the main purpose of this paper is to establish conditions under which the jensen type inequality for the discrete bipolar pseudo integral is valid besides we extend investigations of the properties of the bipolar pseudo integral the observations concern the discrete bipolar pseudo integrals based on the following three canonical cases of two binary symmetric operations in the first case they are generated by an odd strictly increasing and continuous function in the remaining two cases a symmetric addition is the symmetric maximum while in the second case the corresponding pseudo multiplication is a non idempotent operation and in the third case it is the symmetric minimum

transformation theorems of abstract integrals on fuzzy sets abstract the concept of abstract integrals on fuzzy sets is introduced and some elementary properties for such type of integrals are given this paper also proves some transformation theorems for abstract integrals on fuzzy sets and presents some convergence theorems of a sequence of abstract integrals

a conjugate gradient projection method for solving equations with convex constraints abstract in this paper we propose a derivative free iterative method for a class of equations with convex constraints appearing in a variety of the practical problems such as compressing sensing fluid mechanics plasma physics nonlinear optics and solid state in the iteration our search direction can be viewed as an extension of a modified three term cg method by an appropriate line search and the projection step our method is convergent to the solution our method inherits the advantages of cg method and projection method and thus is suitable for solving large scale non smooth problem under the assumption that f is lipschitz continuous and satisfies a weaker condition of monotonicity our method is globally convergent numerical results show the efficiency of the proposed method