Several necessary and suucient conditions for the pseudometric generating property of non-additive set functions are given. The relation among the pseudometric generating property and autocontinuity of fuzzy measures is depicted by using the absolute continuity and exhaustivity. Moreover, any uniformly autocontinuous nite fuzzy measure is equivalent to a subadditive nite fuzzy measure. A furthe...

in this paper, we present a revised similarity measure based onchen-and-chen's similarity measure for fuzzy risk analysis. the revisedsimilarity measure uses the corrected formulae to calculate the centre ofgravity points, therefore it is more  effective than the chen-and-chen'smethod. the revised similarity measure can overcome the drawbacks of theexisting methods. we have also proposed a new ...

In non-additive measure and integration (or fuzzy measure and integral) one tries to generalise the issues of product measure and conditional expectation from the additive theory. In the discrete case successful attempts have been made via the max-min additive representation of the monotone measure and the corresponding integrals. The present paper intends to find, for arbitrary monotone measur...

Traditional probabilistic description of uncertainty is based on additive probability measures. To describe nonprobabilistic uncertainty, it is therefore reasonable to consider non-additive measures. An important class of non-additive measures are possibility measures, for which μ(A ∪ B) = max(μ(A), μ(B)). In this paper, we show that possibility measures are, in some sense, universal approximat...

We extend the concept of fuzzy integral based on ⊕-decomposable measure from nonnegative fuzzy measurable function to extended real-valued fuzzy measurable function. Further investigations of fuzzy integrals based on pseudo-additive decomposable measure are carried out. Meanwhile, the space (S(μ),σ(·,·)) of all fuzzy measurable function will be proved to be a pseudo-metric space. Finally, as an...

This paper focusses on the investigation of a pattern recognition method based on the fuzzy integral. Until now this method has used a general fuzzy measure, which is characterized by exponential complexity. Naturally this led to some difficulties in practical applications of this pattern recognition method. In this paper, a heuristic algorithm for the identification of the 2-additive fuzzy mea...

In view of the problem that it is difficult to quantitatively assess interactivity between attributes in identification process 2-order additive fuzzy measure, this work uses intuitionistic sets (IFSs) describe and deal with attributes. Firstly, defined by supermodular game theory. On basis, experts employ number (IFN) attributes, Secondly, opinions all are aggregated using weighted average ope...

Fuzzy valued measure ([7], [10], [3], [5]) is a natural generalization of a set valued measure ([6]). Infinite addition is defined ([12]) as a Zadeh’s extension principle of continuity. In [9], using an additive fuzzy valued measure, an integral of single valued function is defined and some basic properties are given. In this paper we proceed to investigate specific properties of integrals in f...

In 1974, Sugeno introduced the notion of fuzzy measure and integral to evaluate nonadditive or non-linear quality in systems engineering. In the same year, Dobrakov independently introduced the notion of submeasure from mathematical point of view to show that most of the theory of countably additive measures remain valid for such measures. Fuzzy measures and submeasures are both special kinds o...

A fuzzy approach is proposed here for restoring color images that are corrupted with additive noise. The proposed fuzzy approach consists of two sub-filters, where the first fuzzy sub-filter computes the fuzzy distances between the color components of the central pixel and its neighborhood using Gaussian combination membership function, and the second sub-filter corrects the pixels where color ...