Multi-criteria decision-making method with double risk parameters in interval-valued intuitionistic fuzzy environments
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ORIGINAL ARTICLE
Multi-criteria decision-making method with double risk parameters in interval-valued intuitionistic fuzzy environments Li‑li Niu1 · Jian Li2 · Feilong Li3 · Zhong‑xing Wang4 Received: 9 December 2019 / Accepted: 3 June 2020 © The Author(s) 2020
Abstract In the multi-criteria decision-making (MCDM) process, decision-makers with different risk attitudes may have different decision results. To address this issue and present decision-makers’ mentality, this paper introduces two mentality parameters. These parameters reflect the decision-makers’ risk attitudes in determining the membership and non-membership degrees of the evaluation information. In addition, the parameters demonstrate the risk attitude in terms of the hesitancy degree under interval-valued intuitionistic fuzzy information. Then, a new score function of interval-valued intuitionistic fuzzy numbers (IVIFNs) is proposed that uses the introduced mentality parameters. Meanwhile, certain properties of the proposed score function are discussed. Furthermore, the weighted comprehensive score value of IVIFNs is introduced, and an MCDM method is developed in an interval-valued intuitionistic fuzzy environment. Finally, a numerical example and comparative analyses are provided to illustrate the feasibility and effectiveness of the proposed method. Keywords Multi-criteria decision-making · Risk attitudes · Interval-valued intuitionistic fuzzy numbers · Score function · Mentality parameter
Introduction In 1986, Atanassov [1] proposed intuitionistic fuzzy sets (IFSs), which are an extension of fuzzy sets [2]. In IFSs, the membership, non-membership, and hesitancy degrees of an element that belongs to a set are considered. These new sets are more flexible and practical than traditional fuzzy sets in dealing with the uncertainty of the objectives [3–9]. For example, Melliani and Castillo [7] introduced recent advances in intuitionistic fuzzy logic systems, Roeva and Michalikova [8] proposed a generalized net model based on intuitionistic fuzzy logic control, and Atanassov and * Jian Li [email protected] 1
Guangxi University Xingjian College of Science and Liberal Arts, Nanning 530005, People’s Republic of China
2
School of Logistics Management and Engineering, Nanning Normal University, Nanning 530001, People’s Republic of China
3
Guangxi Medical University Affiliated Tumor Hospital, Nanning 530021, People’s Republic of China
4
School of Mathematics and Information Science, Guangxi University, Nanning 530004, People’s Republic of China
Sotirov [9] discussed neural networks with interval valued intuitionistic fuzzy conditions. However, in some complex decision-making situations, decision-makers may not have sufficient knowledge to provide crisp values of membership and non-membership degrees. Nonetheless, their ranges can be indicated. Therefore, in 1989, Atanassov and Gargov [10] introduced the concept of interval-valued intuitionistic fuzzy sets (IVIFSs), whose membership and non-membership are closed intervals instead of cris
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