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People make decisions based on their cognitive information about the objective world. Zadeh's Z-number allows people to better express their cognition of the real world by considering the fuzzy restriction and reliability restriction of information. However, the Z-number is a complex construct, and some important issues must be discussed in its study. Here, a computationally simple method of ranking Z-numbers for multi-criteria decision-making (MCDM) problems is proposed, and a comprehensive possibility degree of Z-numbers is defined, as inspired by the possibility degree concept of interval numbers. The outranking relations of Z-numbers are also discussed on the basis of the proposed method. Then, a weight acquisition algorithm relative to the possibility degree of Z-numbers is presented. Finally, an extended Preference Ranking Organization Method for Enrichment Evaluation II (PROMETHEE II) based on the possibility degree of Z-numbers is developed for the MCDM problem under Z-evaluation, and a numerical example about the selection of travel plans is used to illustrate the validity of the proposed method. The applicability and superiority of the proposed method is demonstrated through sensitivity and comparative analyses along with other existing methods. [ABSTRACT FROM AUTHOR]

This study develops an approach that incorporates power aggregation operators with the evaluation based on distance from average solution (EDAS) method under linguistic neutrosophic situations to solve fuzzy multi-criteria group decision-making problems. Firstly, the existing operational laws and comparison methods of linguistic neutrosophic numbers (LNNs) are analysed. Secondly, the distance measurement between two LNNs is defined. Thirdly, the power-weighted averaging operator and the power-weighted geometric operator with LNNs are developed to support the decision makers' evaluation information. The models to derive the criteria weights are also constructed based on the proposed distance measurements. Finally, the EDAS method is extended to resolve group decision-making problems in the linguistic neutrosophic environment. An illustrative example of the property management company selection is given to verify the effectiveness and practicality of the proposed approach. [ABSTRACT FROM AUTHOR]

An appropriate greenhouse gas (GHG) emissions' institution largely affects long-term development of cement corporates. The primary objective of this paper is to investigate a scientific method for selecting an optimal institution for a cement corporate. The paper mainly makes the following contributions to effectively resolving this selection problem. Given the capacity of picture 2-tuple linguistic sets (P2TLSs) in depicting voting information, they are used as evaluation representation in this case. Another contribution is that this paper newly proposes a prospect theory-based score function to rank picture 2-tuple linguistic numbers (P2TLNs). The proposed score function effectively overcomes the limitations in the existing score function by considering the voting potential of those decision-makers (DMs) who hold "abstain" opinion. Meanwhile, this proposed score function also adequately considers the rational-bounded behavior of DMs, thereby making the evaluation more approximate to the reality. Furthermore, this paper investigates a hybrid outranking method to select institution in the context of P2TLSs. It takes different types of preference functions and the Elimination and Choice Translating Reality (ELECTRE) method into account simultaneously. Compared with other similar type methods, this hybrid method can flexibly choose criteria type and provide specific values to represent quantitative dominance relation rather than qualitative judgment. Finally, an illustrative example and comparative analyses are provided to certify the availability and reliability of the proposed method. [ABSTRACT FROM AUTHOR]