This paper clarifies the connection between multiple criteria decision-making and decision under uncertainty in a qualitative setting relying on a finite value scale. While their mathematical formulations are very similar, the underlying assumptions differ and the latter problem turns out to be a special case of the former. Sugeno integrals are very general aggregation operations that can repre...

In this paper Hermite—Hadamard type inequalities for m-convex and (α,m)-convex functions for fuzzy integrals are given. Some examples are also given to illustrate the results.

The evaluation of quantified sentences is used for solving several problems. Most of the methods proposed are not satisfactory because they do not verify some intuitive properties. In this paper we propose an extension of both possibilistic and probabilistic methods, based on the Sugeno and the Choquet fuzzy integrals respectively, for the evaluation of type II sentences, the most general kind ...

In order to solve the optimization problem of selecting the decision with maximal chance to meet the Sugeno event in Sugeno environment, dependent-chance programming on Sugeno measure space is proposed, which can be considered as a generalized extension of the stochastic dependent-chance programming. Firstly, the theoretical framework of dependent-chance programming on Sugeno measure space is e...

The expected value and variance of a fuzzy variable have been well studied in the literature, and they provide important characterizations of the possibility distribution for the fuzzy variable. In this paper, we seek a similar characterization of the joint possibility distribution for a pair of fuzzy variables. In view of the success of introducing the expected value and variance as fuzzy inte...

We give the necessary and su cient 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 satis ed.

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 in...

The cube of opposition is a logical structure that underlies many information representation settings. When applied to multiple criteria decision, it displays various possible aggregation attitudes. Situations are usually assessed by combinations of properties they satisfy, but also by combinations of properties they do not satisfy. The cube of opposition applies to qualitative evaluation when ...

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 Legesgue integrals is explored and exploited. It is amongst other things shown that our integ...

This paper presents four schemes for soft fusion of the outputs of multiple classi®ers. In the ®rst three approaches, the weights assigned to the classi®ers or groups of them are data dependent. The ®rst approach involves the calculation of fuzzy integrals. The second scheme performs weighted averaging with data-dependent weights. The third approach performs linear combination of the outputs of...