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As an extension of intuitionistic fuzzy sets, picture fuzzy sets can deal with vague, uncertain, incomplete and inconsistent information. The similarity measure is an important technique to distinguish two objects. In this study, a similarity measure between picture fuzzy sets based on relationship matrix is proposed. The new similarity measure satisfies the axiomatic definition of similarity measure. It can be testified from a numerical experiment that the new similarity measure is more effective. Finally, we apply the proposed similarity measure to multiple-attribute decision making.

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.

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.

This paper reviews the existing definitions and formulas of entropy for interval-valued intuitionistic fuzzy sets (IVIFSs) and demonstrates that they cannot fully capture the uncertainty of IVIFSs. Then considering both fuzziness and intuitionism of IVIFSs, we introduce a novel axiomatic definition of entropy for IVIFSs and develop several entropy formulas. Example analyses show that the developed entropy formulas can fully reflect both fuzziness and intuitionism of IVIFSs. Furthermore, based on the entropy formulas of IVIFSs, a method is proposed to solve multi-attribute decision making problems with IVIFSs. Additionally, an investment alternative selection example is provided to validate the practicality and effectiveness of the method.

With respect to multi-attribute decision making under uncertain linguistic environment, a new interval-valued 2-tuple linguistic representation model is introduced. To deal with the situation where the elements in a set are interdependent, several generalized interval-valued 2-tuple linguistic correlated aggregation operators are defined. It is worth pointing out that some interval-valued 2-tuple linguistic operators based on additive measures are special cases of our operators. Meanwhile, several special cases and desirable properties are discussed. Furthermore, models based on the correlation coefficient are constructed, by which the optimal weight vector can be obtained. Moreover, an approach to multi-attribute group decision making with uncertain linguistic information is developed. Finally, an example is selected to show the effectivity and feasibility of the developed procedure.