Fuzzy measures as extensions of stochastic measures

Fuzzy Measures on Finite Scales as Families of Possibility Measures

We show that any capacity or fuzzy measure ranging on a qualitative scale can be viewed both as the lower bound of a set of possibility measures, and the upper bound of a set of necessity measures. An algorithm is provided to compute the minimal set of possibility measures dominating a given capacity. This algorithm relies on the representation of the capacity by means of its qualitative Moebiu...

Multi-attribute target-based utilities and extensions of fuzzy measures

We introduce a formal description of the Target-Based approach to utility theory for the case of n > 1 attributes and point out the connections with aggregationbased extensions of capacities. Our discussion provides economic interpretations of different concepts of the theory of fuzzy measures. In particular, we analyze the meaning of extensions of capacities based on n-dimensional copulas. The...

Measures of fuzzy semicompactness in $L$-fuzzy topological spaces

In this paper, the notion of fuzzy semicompactness degrees isintroduced in $L$-fuzzy topological spaces by means of theimplication operation of $L$. Characterizations of fuzzysemicompactness degrees in $L$-fuzzy topological spaces  areobtained, and some properties of fuzzy semicompactness degrees areresearched.

S-measures, T-measures and distinguished classes of fuzzy measures

ON TRUNCATED MEASURES OF INCOME INEQUALITY FROM A FUZZY PERSPECTIVE

In most statistical analysis, inequality or extent of variation in income isrepresented in terms of certain summary measures. But some authors arguedthat the concept of inequality is vague and thus cannot be measured as anexact concept. Therefore, fuzzy set theory provides naturally a useful toolfor such circumstances. In this paper we have introduced a real-valued fuzzymethod of illustrating t...