In works dealing with capacities (fuzzy measures) and the Choquet integral on finite spaces, it is usually considered that all subsets of the universe are measureable. Hence, all functions are integrable in the sense of Choquet. We consider the situation where some subsets are not measurable (not feasible), so that there are nonintegrable functions. Since this is a severe limitation in applicat...

Abstract Using an intrinsic approach, we study some properties of random fields which appear as tail regularly varying stationary fields. The index set is allowed to be a general locally compact Hausdorff Abelian group $${\mathbb G}$$ G . values are taken in measurable cone, equipped with pseudo norm. We firs...

In this paper, the well-known Egoroff’s theorem in classical measure theory is established on monotone non-additive measure spaces. Taylor’s theorem, which concerns almost everywhere convergence of measurable function sequence in classical measure theory, is also generalized. The converse problem of the theorems are discussed, and a necessary and sufficient condition for the Egoroff’s theorem i...

Hellinger distance is a distance between two additive measures defined in terms of the RadonNikodym derivative of these two measures. This measure proposed in 1909 has been used in a large variety of contexts. In this paper we define an analogous measure for fuzzy measures. We discuss them for distorted probabilities and give two examples.

We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in amedical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised...

Based on the axiom de nition of distance measure, some new formulas of fuzzy entropy induced by distance measure and some new properties of distance measure are given. A characterization of a -distance measure is a metric de ned on all fuzzy sets is obtained. c © 2001 Elsevier Science B.V. All rights reserved.