Abstract
Multiple set is a newborn member of the family of generalized sets, which can model uncertainty together with multiplicity. It has the power to handle numerous uncertain features of objects in a multiple way. Multiple set theory has the edge over the well established fuzzy set theory by its capability to handle uncertainty and multiplicity simultaneously. Similarity measure of fuzzy sets is well addressed in literature and has found prominent applications in various domains. As multiple set is an efficient generalization of fuzzy set, the concept and theory of similarity measure can be extended to multiple set theory and can be developed probable applications in various real-life problems. This paper introduces the concept of similarity measure of multiple sets and proposes two different similarity measures of multiple sets and investigates their properties. Finally, this work substantiates application of the concept of similarity measure of multiple sets to pattern recognition. A numerical illustration demonstrates the effectiveness of the proposed technique to this application.
Highlights
Various mathematical models are available in the literature to represent the concepts like uncertainty, vagueness and inexactness
The main advantage of multi fuzzy set over fuzzy set is that it can simultaneously manage numerous uncertain characteristics of objects, but fails to handle the multiplicity of objects
This paper proposes two different types of similarity measures- one is based on similarity measure of fuzzy sets; other one is based on the similarity measure of fuzzy sets and fuzzy aggregation operators
Summary
Various mathematical models are available in the literature to represent the concepts like uncertainty, vagueness and inexactness. Similarity measure of interval valued intuitionistic fuzzy sets was proposed and it has found applications in pattern recognition and multi-criteria decision making[41]. Xu et al.[58] proposed a new similarity measure of fuzzy sets based on the extension of the Dice and cosine similarity measures and applied the variation coefficient similarity to the emergency group decision-making problems They gave a practical example to evaluate the emergency management capability of major snow disaster in Hunan province of China. We strongly believe that similarity measure of multiple set can handle uncertain information in a better way It must, have a better scope of real life applications.
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