Multi-criteria sorting decision making based on dominance and opposition relations with probabilistic linguistic informa
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Multi-criteria sorting decision making based on dominance and opposition relations with probabilistic linguistic information Hong-gang Peng1 · Jian-qiang Wang1
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The probabilistic linguistic term set (PLTS) is a powerful tool for describing linguistic evaluations derived from expert teams and has adequate capability to identify preferences among different evaluations. Due to the practicability of PLTSs, probabilistic linguistic decision making problems have been widely investigated in recent years. However, no study on probabilistic linguistic outranking relations has been conducted. This study aims to explore effective processing for the complex two-dimension structure of PLTSs and formulate probabilistic linguistic dominance and opposition relations for multi-criteria sorting decision making. Linguistic scale functions, which can generate different semantics for linguistic variables under different decision making environments, are introduced to deal with the linguistic terms in PLTSs. In this way, the probabilistic linguistic dominance degree, concordance and discordance indices are defined by systematically comparing the probabilities of PLTSs. Then, two kinds of outranking relations with dominance and opposition for PLTSs are formulated based on the defined outranking indices. Subsequently, an innovative sorting decision making framework is constructed by exploring the outranking relations between alternatives and characteristic actions under multiple criteria and implementing the outranking aggregation and exploitation. Finally, this framework is demonstrated using an illustrative example with result analyses and comparison discussions. Keywords Multi-criteria sorting decision making · Dominance relation · Opposition relation · Probabilistic linguistic term set
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Jian-qiang Wang jqwang@csu.edu.cn School of Business, Central South University, Changsha 410083, People’s Republic of China
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H. Peng, J. Wang
1 Introduction Multi-criteria sorting (MCS) refers to the assignment of a set of alternatives to predefined ordered categories in accordance with the evaluation information under multiple criteria. MCS problems widely exist in various fields, such as risk assessment, program management, and disease diagnosis. In the past half century, various sorting methods based on different tools, such as value functions, distance models, decision rules, and outranking relations, have been developed to address real-world MCS problems. Among the abovementioned sorting tools, outranking relations are popular and are widely used to formulate MCS decision making. Almeida-Dias et al. (2010) introduced characteristic reference actions to define sorting categories and proposed an MCS method named Elimination and Choice Translating Reality (ELECTRE) Tri-C. Fernandez and Navarro (2011) presented a new MCS method based on fuzzy outranking relations. Wang and Chen (2015) defined the interval intuitionistic fuzzy mean likelihood of outranking relati
