Multi-criteria group decision making with incomplete hesitant fuzzy preference relations |
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Affiliation: | 1. College of Mathematics and Information Science, Hebei University, Baoding, Hebei 071002, China;2. School of Economics and Management, Hebei University of Engineering, Handan, Hebei 056038, China;3. School of Computer Science and Technology, Hebei University, Baoding, Hebei 071002, China;1. Department of Information Management, College of Management, Chang Gung University, 259, Wen-Hwa 1st Road, Kwei-Shan, Taoyuan 333, Taiwan;2. Department of Industrial and Business Management, Graduate Institute of Business and Management, College of Management, Chang Gung University, 259, Wen-Hwa 1st Road, Kwei-Shan, Taoyuan 333, Taiwan;1. Electrical and Electronic Engineering, İnönü University, 44060 Malatya, Turkey;2. Electrical and Electronic Engineering, Batman University, 72060 Batman, Turkey |
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Abstract: | In order to simulate the hesitancy and uncertainty associated with impression or vagueness, a decision maker may give her/his judgments by means of hesitant fuzzy preference relations in the process of decision making. The study of their consistency becomes a very important aspect to avoid a misleading solution. This paper defines the concept of additive consistent hesitant fuzzy preference relations. The characterizations of additive consistent hesitant fuzzy preference relations are studied in detail. Owing to the limitations of the experts’ professional knowledge and experience, the provided preferences in a hesitant fuzzy preference relation are usually incomplete. Consequently, this paper introduces the concepts of incomplete hesitant fuzzy preference relation, acceptable incomplete hesitant fuzzy preference relation, and additive consistent incomplete hesitant fuzzy preference relation. Then, two estimation procedures are developed to estimate the missing information in an expert's incomplete hesitant fuzzy preference relation. The first procedure is used to construct an additive consistent hesitant fuzzy preference relation from the lowest possible number, (n − 1), of pairwise comparisons. The second one is designed for the estimation of missing elements of the acceptable incomplete hesitant fuzzy preference relations with more known judgments. Moreover, an algorithm is given to solve the multi-criteria group decision making problem with incomplete hesitant fuzzy preference relations. Finally, a numerical example is provided to illustrate the solution processes of the developed algorithm and to verify its effectiveness and practicality. |
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Keywords: | Hesitant fuzzy set Hesitant fuzzy preference relation Incomplete hesitant fuzzy preference relation Multi-criteria group decision making Additive consistency |
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