Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. Recently, uncertainty measures of soft sets and fuzzy soft sets have gained attentions from researchers. This paper is devoted to the study of uncertainty measures of fuzzy soft sets. The axioms for similarity measure and entropy are proposed. A new category of similarity meas...

In this study, a fuzzy similarity approach for Arabic web pages classification is presented. The approach uses a fuzzy term-category relation by manipulating membership degree for the training data and the degree value for a test web page. Six measures are used and compared in this study. These measures include: Einstein, Algebraic, Hamacher, MinMax, Special case fuzzy and Bounded Difference ap...

In this study, a fuzzy similarity approach for Arabic web pages classification is presented. The approach uses a fuzzy term-category relation by manipulating membership degree for the training data and the degree value for a test web page. Six measures are used and compared in this study. These measures include: Einstein, Algebraic, Hamacher, MinMax, Special case fuzzy and Bounded Difference ap...

The weight is one of the most useful tools to measure the attribute importance when individuals make a decision or evaluate the alternatives. Among the methods which measure the weight, fuzzy measures is are subjective scales for the degrees of fuzziness and widely used to determine the degrees of subjective importance of evaluation items in numerous studies for the time being. The purpose of t...

In the present communication, three new divergence measures between fuzzy sets are proposed. The validity of these divergence measures is examined axiomatically. Relation of the proposed divergence measures with the cardinality of a universe of discourse is established. Some properties of these divergence measures are established. Relation of divergence between fuzzy sets with aggregation opera...

The main aim of this contribution is to define the notions of Kullback-Leibler divergence and conditional mutual information in fuzzy probability spaces and to derive the basic properties of the suggested measures. In particular, chain rules for mutual information of fuzzy partitions and for Kullback-Leibler divergence with respect to fuzzy P-measures are established. In addition, a convexity o...

Similarity measure is a very important topic in fuzzy set theory. Torra (2010) proposed the notion of hesitant fuzzy set(HFS), which is a generalization of the notion of Zadeh’ fuzzy set. In this paper, some new similarity measures for HFSs are developed. Based on the proposed similarity measures, a method of multiple attribute decision making under hesitant fuzzy environment is also introduced...

In fuzzy set theory, comparison of fuzzy sets plays an important role. Among the several ways to compare fuzzy sets, we address the logical theoretic approach using fuzzy implications. We propose a general framework allowing to generate many measures of comparison: inclusion, similarity and distance, and study their properties. Since the literature on the use fuzzy implications for defining suc...