Similarity measures of intuitionistic fuzzy sets based on cosine function for the decision making of mechanical design schemes

Article type: Research Article

Authors: Ye, Jun^*

Affiliations: Department of Electrical and Information Engineering, Shaoxing University, Shaoxing, Zhejiang Province, P.R. China

Correspondence: [*] Corresponding author. Jun Ye, Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing, Zhejiang Province 312000, P.R. China. Tel.: +86 575 88327323; E-mail: yehjun@aliyun.com.

Abstract: Based on cosine function and the information carried by the membership degrees, nonmembership degree and hesitancy degree in intuitionistic fuzzy sets (IFSs), this paper proposes two new cosine similarity measures and weighted cosine similarity measures between IFSs. Then, we give the comparative analysis of various trigonometric similarity measures by several numerical examples to illustrate the effectiveness of the developed cosine similarity measures of IFSs. Furthermore, we develop a decision-making method using the weighted cosine similarity measures for choosing mechanical design schemes (alternatives). Finally, a decision-making example on choosing mechanical design schemes is given to demonstrate the applications and efficiency of the proposed decision-making method.

Keywords: Mechanical design scheme, intuitionistic fuzzy set, cosine function, cosine similarity measure, decision making

DOI: 10.3233/IFS-151741

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 1, pp. 151-158, 2016