This paper aims to develop a Fermatean fuzzy ELECTRE method for solving multi-criteria group decision-making problems with unknown weights of decision makers and incomplete weights of criteria. First, a new distance measure between Fermatean fuzzy sets is proposed based on the Jensen–Shannon divergence. The cross entropy for Fermatean fuzzy sets is defined. Three kinds of dominance relationships for Fermatean fuzzy sets are proposed. Then, two optimization models are constructed to obtain positive ideal decision-making information and negative ideal decision-making information, respectively. Accordingly, the credibility degree of each decision maker is calculated. Decision makers’ dynamic weights are determined by their credibility degrees. Besides, to obtain the weights of criteria, an optimization model is constructed based on grey relational analysis for Fermatean fuzzy numbers. Finally, the strong, medium and weak Fermatean fuzzy concordance and discordance sets are identified to construct the Fermatean fuzzy concordance and discordance matrices, respectively. A practical case study is carried out to illustrate the feasibility and applicability of the proposed ELECTRE method. Comparative analyses are performed to demonstrate the superiority and effectiveness of the proposed ELECTRE method.
Volume 31, Issue 3 (2020), pp. 621–658
As the tourism and mobile internet develop, car sharing is becoming more and more popular. How to select an appropriate car sharing platform is an important issue to tourists. The car sharing platform selection can be regarded as a kind of multi-attribute group decision making (MAGDM) problems. The probabilistic linguistic term set (PLTS) is a powerful tool to express tourists’ evaluations in the car sharing platform selection. This paper develops a probabilistic linguistic group decision making method for selecting a suitable car sharing platform. First, two aggregation operators of PLTSs are proposed. Subsequently, a fuzzy entropy and a hesitancy entropy of a PLTS are developed to measure the fuzziness and hesitancy of a PLTS, respectively. Combining the fuzzy entropy and hesitancy entropy, a total entropy of a PLTS is generated. Furthermore, a cross entropy between PLTSs is proposed as well. Using the total entropy and cross entropy, DMs’ weights and attribute weights are determined, respectively. By defining preference functions with PLTSs, an improved PL-PROMETHEE approach is developed to rank alternatives. Thereby, a novel method is proposed for solving MAGDM with PLTSs. A car sharing platform selection is examined at length to show the application and superiority of the proposed method.
Pub. online:1 Jan 2016Type:Research ArticleOpen Access
Volume 27, Issue 4 (2016), pp. 863–892
This paper investigates a kind of hybrid multiple attribute decision making (MADM) problems with incomplete attribute weight information and develops a hesitant fuzzy programming method based on the linear programming technique for multidimensional analysis of preference (LINMAP). In this method, decision maker (DM) gives preferences over alternatives by the pair-wise comparison with hesitant fuzzy truth degrees and the evaluation values are expressed as crisp numbers, intervals, intuitionistic fuzzy sets (IFSs), linguistic variables and hesitant fuzzy sets (HFSs). First, by calculating the relative projections of alternatives on the positive ideal solution (PIS) and negative ideal solution (NIS), the overall relative closeness degrees of alternatives associated with attribute weights are derived. Then, the hesitant fuzzy consistency and inconsistency measures are defined. Through minimizing the inconsistency measure and maximizing the consistency measure simultaneously, a new bi-objective hesitant fuzzy programming model is constructed and a novel solution method is developed. Thereby, the weights of attributes are determined objectively. Subsequently, the ranking order of alternatives is generated based on the overall relative closeness degrees of alternatives. Finally, a supplier selection example is provided to show the validity and applicability of the proposed method.