Multiplicative Consistency Adjustment Model and Data Envelopment Analysis-Driven Decision-Making Process with Probabilis
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Multiplicative Consistency Adjustment Model and Data Envelopment Analysis-Driven Decision-Making Process with Probabilistic Hesitant Fuzzy Preference Relations Feifei Jin1 • Harish Garg2
•
Lidan Pei3 • Jinpei Liu1 • Huayou Chen4
Received: 3 June 2020 / Revised: 3 June 2020 / Accepted: 10 August 2020 Taiwan Fuzzy Systems Association 2020
Abstract Unlike other fuzzy modellings, probabilistic fuzzy sets can reflect clearly the importance of different numerical values. In group decision-making (GDM) problems, it is quite common for decision-makers (DMs) to elicit their knowledge with probabilistic hesitant fuzzy preference relations (PHFPRs), in which consistency adjustment and alternatives’ weight vector determination play a key role in the decision-making process. This study aims at constructing a decision-making model with PHFPRs. First, several new concepts are introduced, including the multiplicative consistency and consistency index of PHFPRs. Then, we present a construction approach for the multiplicative consistent PHFPRs, and a convergent local consistency improvement process for PHFPRs is designed to detect and improve their consistency when the PHFPRs do not meet the consistency level. The local adjustment strategy is utilized to retain the preference evaluation of DMs as much as possible. Afterwards, based on the obtained efficiency score values, we propose a new data envelopment analysis model to derive
& Harish Garg [email protected] & Jinpei Liu [email protected] 1
School of Business, Anhui University, Hefei 230601, Anhui, China
2
School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala 147004, Punjab, India
3
School of Mathematics and Statistics, Hefei Normal University, Hefei 230601, Anhui, China
4
School of Mathematical Sciences, Anhui University, Hefei 230601, Anhui, China
the weight values of alternatives. Furthermore, we explore a decision-making method with PHFPRs to obtain the optimal selection from the alternatives. Finally, an applied case about logistics company assessment is presented, and the effectiveness and rationality of the explored method are verified by the comparison with the various approaches. Keywords Probabilistic hesitant fuzzy preference relations Consistency adjustment algorithm Data envelopment analysis Decision-making method
1 Introduction As a pivotal part of administration activities, group decision-making (GDM) has an extensive application in diverse fields [1]. Practical problems in everyday life are always complicated and uncertain. Meanwhile, people have a limited cognition in knowledge and imagination. Thus, it is challenging for decision-makers (DMs) to give their opinions with precise values. To break through such limitation, preference relations (PRs) have been developed to describe vague elements. This tool provided a novel way to express evaluation information [2, 3]. Fuzzy PRs (FPRs) [4–7] and multiplicative PRs (MPRs) [8–10] are the most common forms of PRs to describe DMs’ opinions. Exte
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