An automatic iterative decision-making method for intuitionistic fuzzy linguistic preference relations

ABSTRACT

As a new preference structure, the intuitionistic fuzzy linguistic preference relation (IFLPR) was recently introduced to efficiently deal with situations in which the membership and non-membership are represented as linguistic terms. In this paper, we study the issues of additive consistency and the derivation of the intuitionistic fuzzy weight vector of an IFLPR. First, the new concepts of order consistency, additive consistency and weak transitivity for IFLPRs are introduced, and followed by a discussion of the characterisation about additive consistent IFLPRs. Then, a parameterised transformation approach is investigated to convert the normalised intuitionistic fuzzy weight vector into additive consistent IFLPRs. After that, a linear optimisation model is established to derive the normalised intuitionistic fuzzy weights for IFLPRs, and a consistency index is defined to measure the deviation degree between an IFLPR and its additive consistent IFLPR. Furthermore, we develop an automatic iterative decision-making method to improve the IFLPRs with unacceptable additive consistency until the adjusted IFLPRs are acceptable additive consistent, and it helps the decision-maker to obtain the reasonable and reliable decision-making results. Finally, an illustrative example is provided to demonstrate the validity and applicability of the proposed method.

KEYWORDS:

• Intuitionistic fuzzy linguistic preference relation
• additive consistency
• consistency index
• acceptable additive consistency
• automatic iterative decision-making method

Acknowledgments

The authors are thankful to the anonymous reviewers and the editor for their valuable comments and constructive suggestions that have led to an improved version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Key Project of Natural Science Research in Colleges and Universities in Anhui Province Key Project of Natural Science Research in Colleges and Universities in Anhui Province [grant number KJ2016A250]; National Natural Science Foundation of China [grant number 71371011], [grant number 7150102], [grant number 91546108].

Notes on contributors

Lidan Pei

Lidan Pei was born in Henan, China. She received her M.S. degree from the Anhui University of School of Mathematical Sciences, China, in 2014. She is currently working toward the Ph.D. degree at the School of Mathematical Sciences, Anhui University, China. Her research interests include graph theory and decision making theory.

Feifei Jin

Feifei Jin was born in Anhui, China. He received his M.S. degree in School of Mathematical Sciences from Anhui University, Hefei, China, in 2014. He is currently a Ph.D. student with the School of Management, Hefei University of Technology, Hefei, China. His research interests include aggregation operators, fuzzy decision making, combination forecasting, and their applications.

Zhiwei Ni

Zhiwei Ni was born in Anhui, China. He received his B.S. and M.S. degrees in computer software and theory from the Hefei University of Technology, China, in 1984 and 1991, respectively, Ph.D. degree in computer software and theory from the University of Science and Technology of China, China, in 2002. In November 2003, he was a visiting professor at the Australia Swinburne University of Technology Institute of Information Technology. He is currently a professor with the School of Management, Hefei University of Technology, China. Meanwhile, he is the director of the Institute of intelligent management. His research interests are data mining and artificial intelligence.

Huayou Chen

Huayou Chen was born in Anhui, China. He received the B.S. and M.S. degrees in School of Mathematical Sciences from Anhui University, Hefei, China, in 1991 and 1994, respectively, and the Ph.D. degree in School of Mathematical Sciences from University of Science Technology of China, Hefei, China, in 2002. He is currently a Professor with the School of Mathematical Sciences, Anhui University, Hefei, China. He is the author or coauthor of more than 130 publications. His research interests include aggregation operators, fuzzy decision making, combination forecasting, and their applications.

Zhifu Tao

Zhifu Tao was born in Anhui, China. He received a Ph.D. degree in Statistics from Anhui University in 2015. He is a lecturer of School of Economics, Anhui University, China. He has contributed over 20 journal articles to professional journals including IEEE Transactions on Systems, Man and Cybernetics: Systems, Fuzzy Sets and Systems, Applied Soft Computing, Knowledge-Based Systems and Computers & Industrial Engineering, et al. His current research interests include decision making theory, forecasting, information fusion and fuzzy mathematics.