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...

We present a new and natural interpretation of fuzzy sets and fuzzy relations where the basic notions and operations have quite natural meanings. We interpret fuzzy sets and fuzzy relations in a cumulative Heyting valued model for intuitionistic set theory, and de0ne the basic notions and operations naturally in the model. As far as fuzzy sets and fuzzy relations are considered as extensions of...

We discuss relations and differences between fuzzy and case based reasoning methods in order to indicate possibilities for future research activities. We interpret the basic concepts of each approach in terms of the other one and discuss the computational methods in particular from an knowledge engineering point of view. I. Preliminary Remarks The intention of this note is to point out relation...

We present a fuzzy similarity approach to solve a text categorization problem. The effectiveness of various fuzzy conjunction and disjunction operators used in fuzzy similarity formula and several document representations were evaluated using test sets from three text document collections. Based on empirical results obtained from using these collections, a special case of the fuzzy similarity f...

The concept of similarity plays a fundamental role in case-based reasoning. However, the meaning of “similarity” can vary in situations and is largely domain dependent. This paper proposes a novel similarity model consisting of linguistic fuzzy rules as the knowledge container. We believe that fuzzy rules representation offers a more flexible means to express the knowledge and criteria for simi...

This study presents a new similarity measure based on the geometric-mean averaging operator to handle the similarity measure problems of generalized fuzzy numbers. Some properties of the proposed similarity measure are demonstrated, and 26 sets of generalized fuzzy numbers are used to compare the proposed method with existing similarity measures. Comparison results indicate that the proposed si...

We study graded properties (α–properties) of fuzzy relations, which are parameterized versions of fuzzy relation properties defined by L.A. Zadeh. Namely, we take into account fuzzy relations which are: α–reflexive, α– irreflexive, α–symmetric, α–antisymmetric, α–asymmetric, α–connected, α–transitive, where α ∈ [0, 1]. We also pay our attention to the composed versions of these basic properties...

This paper presents a formal characterization of the major concepts and constructs o f fuzzy logic in terms of notions o f distance, closeness, and similarity between pairs o f possible worlds. The formalism is a direct extension (by recognition of multiple degrees o f accessibility, conceivability, or reachability) of the major modal logic concepts of possible and necessary truth. Given a func...

Abstract: Interval-valued fuzzy set (IVFS) is an extension of fuzzy set in which it presents a fuzzy set with an interval-valued membership. A similarity measure is a useful tool for determining the similarity degree between two objects. It is also an important measure for fuzzy concepts. In this paper, we propose a new similarity measure between IVFSs. Some properties of this similarity measur...

This paper exemplifies the implementation of an efficient Information Retrieval (IR) System to compute the similarity between a dataset and a query using Fuzzy Logic. TREC dataset has been used for the same purpose. The dataset is parsed to generate keywords index which is used for the similarity comparison with the user query. Each query is assigned a score value based on its fuzzy similarity ...