A group decision making method with intuitionistic triangular fuzzy preference relations and its application
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A group decision making method with intuitionistic triangular fuzzy preference relations and its application Shaolin Zhang 1
&
Fanyong Meng 1
# Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper aims to offer an intuitionistic triangular fuzzy group decision making method by preference relations. For this purpose, the concept of intuitionistic triangular fuzzy preference relations (ITFPRs) is first offered. Then, an additive consistency concept for ITFPRs is introduced. Meanwhile, a programming model is built to check the consistency of ITFPRs. Considering the case where incomplete ITFPRs are obtained, two programming models are constructed, which aim at maximizing the consistency and minimizing the uncertainty of missing information. To achieve the goals of the minimum total adjustment and the smallest number of adjusted elements, two programming models are established to repair inconsistent ITFPRs. In addition, the weights of decision makers are considered, and the consensus levels of individual ITFPRs are studied to ensure the representativeness of decision results. When individual ITFPRs do not meet the consensus requirement, a programming model to reach the consensus threshold is constructed, which permits different intuitionistic triangular fuzzy variables (ITFVs) to have different adjustments and minimizes the total adjustment. Finally, a group decision making algorithm with ITFPRs is proposed, and its feasibility and efficiency are demonstrated through an example of evaluating the intelligent traditional Chinese medicine decocting centers. Keywords Group decision making . ITFPR . Additive consistency . Programming model . Consensus
1 Introduction Preference relations (PRs) originate from Saaty’s analytic hierarchy process (AHP) method [1], which is a decisionmaking technology based on pairwise comparison between objects to explore the ranking results. At present, various types of PRs have been developed, such as fuzzy interval PRs (FIPRs) [2, 3] and linguistic PRs (LPRs) [4, 5]. The commonness of the above-mentioned PRs is that only the decision makers (DMs)’ preferred information on pairwise comparison of objects is considered. To express the DMs’ preferred and non-preferred judgments synchronously, Xu [6] introduced intuitionistic fuzzy PRs (IFPRs) on the basis of Atanassov intuitionistic fuzzy variables (AIFVs) [7]. The main limitation of IFPRs is that it only allows DMs to express the preferred and non-preferred judgements by crisp values in [0, 1]. To reflect the uncertainty of DMs’ subjective intuitionistic fuzzy judgements, Xu and Chen [8] proposed
* Fanyong Meng [email protected] 1
School of Business, Central South University, Changsha 410083, China
interval-valued intuitionistic fuzzy variables (IVIFVs) and introduced them into PRs, which are known as interval-valued IFPRs (IVIFPRs). It should be noted that IVIFVs assume that all values in the interval preferred and non-preferred degrees have the same membership and non-membership levels. However, thi
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