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...

This paper provides a discussion on difference representations of the asymmetric Choquet integral with respect to a signed fuzzy measure with bounded chain variation. There are given difference representations of the Choquet integral with respect to a signed fuzzy measure based on its representation as difference of two fuzzy measures.

We continue to develop a construction of an L-fuzzy valued measure by extending a measure defined on a σalgebra of crisp sets to an L-fuzzy valued measure defined on a TM-tribe in the case when operations with L-sets and L-fuzzy numbers are defined by using the minimum triangular norm TM . We introduce an L-fuzzy valued integral over an L-set with respect to an L-fuzzy valued measure, consider ...