Introduction In a series of papers culminating in [Ta84], M.Talagrand, the second author and others investigated at length the properties and structure of pointwise compact sets of measurable functions. A number of problems, interesting in themselves and important for the theory of Pettis integration, were solved subject to various special axioms. It was left unclear just how far the special ax...

The main attribution of this paper is to propose two methods to construct entropy of interval valued fuzzy sets (IVFSs). First, we use an IVFS to construct two FSs and define entropy by similarity measure of the two FSs; then we use an IVFS to construct two IVFSs and also define entropy by similarity measure of the two IVFSs. At the same time, we give two examples to show that our methods are e...

A fuzzy ideal on a set X is a non empty collection of subsets of X with heredity property which is also closed under arbitrary union and finite intersections. In this paper, we introduce a weak form of fuzzy ideals namely fuzzy pre-ideals and a way to obtain new fuzzy topologies is presented in this paper. Furthermore some interesting results for fuzzy ideals are generalized to fuzzy pre-ideal.

In a recent paper we studied how a fuzzy measure can be defined from a fuzzy graph. In this paper we explore its applicability to information retrieval, and, more specifically, to compute similarities between sets of words.

In last years, a variety of papers on fuzzy sets and other fuzzy topics was concerned with set-algebraic operations for and properties of fuzzy sets. However, only few remarks are devoted to fuzzy cardinals. In classical set theory the cardinality of a set is a measure of its size or "power". In the fuzzy case one has to differentiate: there are measures of fuzziness and measures of power. Here...

Abstract Assuming that ∗ is any operation defined on a product set X × Y and taking values on a set Z,it can be extended to intuitionistic fuzzy sets by means of the extended form of the Zadeh’s extension principle for the intuitionistic fuzzy sets. Given an IFS C of Z, it is here shown how to solve the equation A ∗ B = C (or A ∗ B ⊆ C) when an intuitionistic fuzzy subset A of X (or an intuitio...

The paper considers the centroids of fuzzy numbers in the general condition. It suggests a pair of formulae for determining the centroid of a fuzzy number. The proposed formulae are correct in the sense described by Wangs’ paper. They are available for all fuzzy numbers and can be applied to ranking fuzzy numbers.

MM is one of the central ideas in the nowadays mathematics education. In an earlier paper applying ideas from fuzzy logic we have developed a model formalizing the MM process and we have used the total possibilistic uncertainty as a measure of students’ MM capacities. In the present paper we develop two alternative fuzzy measures for MM. The first of them concerns an adaptation for use in a fuz...

Abstract— In the present paper, a new fuzzy inaccuracy measure is proposed to measure the inaccuracy of a fuzzy set with respect to another fuzzy set. This measure is a modified version of fuzzy inaccuracy proposed in our earlier work. The measure is demonstrated to satisfy some interesting properties, which prepare ground for applications in multi-criteria decision making problems. A method to...