In this paper, we use the Choquet integrals to define some induced fuzzy number intuitionistic fuzzy aggregating operators, including induced fuzzy number intuitionistic fuzzy correlated averaging(I-FIFCA) operator, induced fuzzy number intuitionistic fuzzy correlated geometric(I-FIFCG) operator. We also establish various properties of these operators, such as commutativity, idempotency and mon...

We prove the convexity and compactness of the closure of the lower partition range of an Rn-valued, nonatomic, supermodular capacity, employing a useful relationship between convex games and their Choquet integrals. The main result is applied to fair division problems, and the existence of Pareto optimal α-fair partitions is demonstrated for the case of nonadditive measures.

It is known that several discrete integrals, including the Choquet and Sugeno integrals as well as some of their generalizations, are comonotonically modular functions. Based on a recent description of the class of comonotonically modular functions, we axiomatically identify more general families of discrete integrals that are comonotonically modular, including signed Choquet integrals and symm...

Three different types of universal integral based on level dependent capacities are introduced and discussed. Two extremal types are based on Caratheodory’s idea of inner and outer measures, while the third type is introduced for copula-based universal integrals only. Keywords—Choquet integral, Copula, Fuzzy measure, Level dependent capacities, Sugeno integral, Universal integral.

The paper introduces a new class of functions from [0,1]n to [0,n] called d-Choquet integrals. These are generalization the “standard” Choquet integral obtained by replacing difference in definition usual dissimilarity function. In particular, all integrals encompasses but use dissimilarities provides higher flexibility and generality. We show that some aggregation/pre-aggregation/averaging/fun...

By using the concepts of fuzzy number fuzzy measures and fuzzy valued functions a theory of fuzzy integrals is investigated. In this paper we have established the fuzzy version of Generalised monotone Convergence theorem and generalised Fatous lemma. 1. Introduction In the preceding paper [2], it is introduced that a concept of fuzzy number fuzzy measures, defined the fuzzy integral of a functi...

The paper deals with the aggregation of classification rules by means of fuzzy integrals, in particular with the fuzzy measures employed in that aggregation. It points out that the kinds of fuzzy measures commonly encountered in this context do not take into account the diversity of classification rules. As a remedy, a new kind of fuzzy measures is proposed, called similarity-aware measures, an...

Choquet integrals are one of the appropriate methods for fusing numerical information. They aggregate numerical values with respect to a fuzzy measure, a way to represent importance that is an alternative to the weights in a weighted mean. The use of fuzzy measures, although extremely flexible when compared with weighting vectors, presents some difficulties when used in real applications: to de...

Our paper deals with the necessary properties in Fuzzy Measures. Therefore, it belongs to Fuzzy Mathematical Analysis. The Possibility Theory was created by Zadeh in a paper of 1978. As general purpose, to obtain a way to model flexible restrictions constructed from vague pieces of information. If we study the counterparts of expectations (from Probability Theory) in Possibility Theory, we obta...

In this paper we propose a new approach to fuzzy stochastic integrals of Itô and Aumann type. Then a fuzzy equation with fuzzy stochastic integrals is investigated. The existence and uniqueness of solution is proven. Some typical properties of the solution are also obtained. Similar results to set-valued stochastic integral equations are stated.