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An extension of TOPSIS for fuzzy MCDM based on vague set theory

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Abstract

This paper extends the TOPSIS to fuzzy MCDM based on vague set theory, where the characteristics of the alternatives are represented by vague sets. A novel score function is proposed in order to determine the vague positive-ideal solution (VPIS) and vague negative-ideal solution (VNIS). We present a weighted difference index to calculate the distance between vague values, by means of which the distance of alternatives to VPIS and VNIS can be calculated. Finally, the relative closeness values of various alternatives to the positive-ideal solution are ranked to determine the best alternative. An example is shown to illustrate the procedure of the proposed method at the end of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Xidian University, China

    Jue Wang, San-Yang Liu & Jie Zhang

Authors
  1. Jue Wang
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  2. San-Yang Liu
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  3. Jie Zhang
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Additional information

Jue Wang received the B. Sc degree in mathematics from Qingdao University, 2000. From August 2000, she has been pursuing his Doctor degree in Xidian University, Xi’an, China. Her research interests include optimization theory and applications, intelligent information processing, rough sets theory and application in data mining, signal processing, etc. She has published over ten journal and conference papers.

San-Yang Liu was born in Xi’an, China, in 1959. From 1985 to 1989, he was with the department of mathematics of Xi’an Jiaotong University, where he received the Ph. D. degree in Mathematics. He is currently a professor and Doctor advisor at the Xidian University. His interests include optimization theory and applications.

Jie Zhang was born in Huaibei, Anhui province, P.R. China., in 1975. He received his B. Sc. in Applied Mathematics, in 1999 from Anhui Normal University and M. Sc. in Operation Research, in 2002 from Xidian University. From 2002, he has been pursuing his Doctor Degree in the National Key laboratory for Radar Signal Processing, Xidian Univ. His research interests lie in the area of signal and information processing with application to wireless communications.

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Wang, J., Liu, SY. & Zhang, J. An extension of TOPSIS for fuzzy MCDM based on vague set theory. J. Syst. Sci. Syst. Eng. 14, 73–84 (2005). https://doi.org/10.1007/s11518-006-0182-y

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  • DOI: https://doi.org/10.1007/s11518-006-0182-y

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