The Dempster-Shafer (D-S) evidence theory has been widely used in many fields from probabilistic inference, information fusion to decision analysis due to its superiority to formulate uncertain and incomplete information under a weaker condition than the Bayesian probability theory. To support the elicitation of basic probability assignment (BPA), numerous uncertainty measures have been proposed in the recent decades, which take into account nonspecificity and structural conflict (SC) in either the entropy-alike or nonentropy form. This article is focused primarily on developing a generalized belief entropy to measure and quantify the uncertainty of BPA in a consistent and comprehensive way. The definition of the proposed belief entropy involves three components. Specifically, the first component is Shannon's definition of entropy of probability functions which can be interpreted as the measure of discord of the mass function among various focal elements. The second component is the measure of total nonspecificity which is the generalization of Dubois-Prade's definition of nonspecificity measure. Furthermore, the critical component introduced in this article is the utilization of the SC coefficient within an evidence, which fully considers the intersection between each pair of focal elements of the BPA. The characteristics and properties of the new generalized belief entropy are analyzed systematically with theoretical proofs. Finally, the proposed belief entropy is embedded to a three-tuple approach to deal with a practical multiple attribute decision-making (MADM) problem to demonstrate its validity and strengths of measuring nonspecificity and SC in uncertain decision making.

In the consensus reaching process (CRP) of social network group decision making, the noncooperative behavior exhibited by experts will hinder the achievement of group consensus. This article develops a noncooperative behavior management framework based on trust propagation and dynamic cooperation index under bidirectional feedback context. On the one hand, a trust propagation operator with trust decay is established to enhance the trust relationship between noncooperative experts. On the other hand, the fuzzy preference relations are utilized as preference expression structure, and the mutual reinforcing effect between consensus and trust is explored to achieve the dynamic enhancement of cooperation index, thereby facilitating the transformation of nonscooperative behavior. Specifically, a cooperation index is formulated to identify the noncooperation behavior. Subsequently, a noncooperative behavior transformation method by dynamic cooperation index is investigated. Finally, a bidirectional feedback mechanism is provided for group consensus reaching. This paper provides an innovative strategy for detecting and managing noncooperative behavior, an illustrative example and some analyses are presented to verify the validity of proposed method.

In a multiple attribute decision making (MADM) problem, quantitative and qualitative attributes can be assessed by numerical values and subjective judgements. Numerical value can be accurate or uncertain, while qualitative attribute can be evaluated

This article proposes a comprehensive star rating approach for cruise ships by the combination of subject and objective evaluation. To do that, it firstly established a index system of star rating for cruise ships. Then, the modified TOPSIS is adopted to tackle objective data for obtaining star ratings for basic cruise indicators and service capabilities of cruise ships. Thus, the concept of distributed linguistic star rating function (DLSRF) is defined to analyze the subjective evaluation from experts and users. Hence, a novel weight calculation method with interactive group decision making is presented to assign the importance of the main indicators. Particularly, in order to enable decision makers to effectively deal with the uncertainty in this star rating process, it adopts the personalized individual semantics (PIS) model. Finally, data of nine cruise ships is collected to obtain their final star rating results and some suggestions for improving cruise service capabilities and star indicators were put forward.