In this paper, we first use a fuzzy preference relation with a membership function representing preference degree forcomparing two interval-valued fuzzy numbers and then utilize a relative preference relation improved from the fuzzypreference relation to rank a set of interval-valued fuzzy numbers. Since the fuzzy preference relation is a total orderingrelation that satisfies reciprocal and tra...

We generalise belief functions to many-valued events which are represented by elements of Lindenbaum algebra of infinite-valued Łukasiewicz propositional logic. Our approach is based on mass assignments used in the Dempster–Shafer theory of evidence. A generalised belief function is totally monotone and it has Choquet integral representation with respect to a unique belief measure on Boolean ev...

This paper introduces a novel approach to integrals with respect to capacities. Any random variable is decomposed as a combination of indicators. A prespecified set of collections of events indicates which decompositions are allowed and which are not. Each allowable decomposition has a value determined by the capacity. The decomposition-integral of a random variable is defined as the highest of...

This paper introduces a novel approach to integrals with respect to capacities. Any random variable is decomposed as a combination of indicators. A pre-speci ed set of collections of events indicates which decompositions are allowed and which are not. Each allowable decomposition has a value determined by the capacity. The decomposition-integral of a random variable is de ned as the highest of ...

Using a nonadditive set function to describe the interaction among attributes, a new nonlinear nonnegative multiregression is established based on Choquet integrals with respect to the set function. Regarding the values of the set function as unknown regression parameters, an evolutionary computation can be used to determine them when necessary data are available. Such a model is a generalizati...