Multi-criteria outranking method based on probability distribution with probabilistic linguistic information

Abstract The probabilistic linguistic term set (PLTS) is a powerful tool for describing qualitative evaluations derived from teams of experts, and it has adequate description capability in identifying preferences among different evaluations. The structure of PLTSs is complex, however, and many existing studies do not deal with probabilistic linguistic information appropriately. Hence, this study explores the simple and effective processing of PLTSs and develops an applicable multi-criteria decision-making (MCDM) method to address real-world problems. First, PLTSs are characterised as probability distributions, and the corresponding cumulative distribution functions are presented. In this manner, the concordance and discordance indices of PLTSs are defined by the systematic comparison between different cumulative distribution functions. Subsequently, four kinds of novel binary relations for PLTSs are proposed. Then, an innovative multi-criteria outranking method is developed by modelling pseudo-criteria and implementing outranking aggregation and exploitation. Finally, an illustrative example concerning new energy selection is provided to elucidate the application of the developed method. The strengths of this method are verified further by some analyses and discussions.

[1]  Zhibin Wu,et al.  Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations , 2016 .

[2]  Francisco Herrera,et al.  A model of consensus in group decision making under linguistic assessments , 1996, Fuzzy Sets Syst..

[3]  Zeshui Xu,et al.  Hesitant fuzzy linguistic projection model to multi-criteria decision making for hospital decision support systems , 2018, Comput. Ind. Eng..

[4]  Hong-yu Zhang,et al.  Cloud decision support model for selecting hotels on TripAdvisor.com with probabilistic linguistic information , 2018 .

[5]  Salvatore Greco,et al.  Multiple Criteria Hierarchy Process for ELECTRE Tri methods , 2016, Eur. J. Oper. Res..

[6]  Zeshui Xu,et al.  Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets , 2016, Inf. Sci..

[7]  Chen-Tung Chen,et al.  Extensions of the TOPSIS for group decision-making under fuzzy environment , 2000, Fuzzy Sets Syst..

[8]  Zeshui Xu,et al.  Two new approaches based on ELECTRE II to solve the multiple criteria decision making problems with hesitant fuzzy linguistic term sets , 2018, Appl. Soft Comput..

[9]  Ren Zhang,et al.  Comparisons of probabilistic linguistic term sets for multi-criteria decision making , 2017, Knowl. Based Syst..

[10]  Francisco Herrera,et al.  A Fuzzy Linguistic Methodology to Deal With Unbalanced Linguistic Term Sets , 2008, IEEE Transactions on Fuzzy Systems.

[11]  Peide Liu,et al.  Some generalized dependent aggregation operators with intuitionistic linguistic numbers and their application to group decision making , 2013, J. Comput. Syst. Sci..

[12]  Zeshui Xu,et al.  A method based on linguistic aggregation operators for group decision making with linguistic preference relations , 2004, Inf. Sci..

[13]  Zeshui Xu,et al.  Probabilistic linguistic term sets in multi-attribute group decision making , 2016, Inf. Sci..

[14]  Jian-qiang Wang,et al.  Prospect Theory-Based Consistency Recovery Strategies with Multiplicative Probabilistic Linguistic Preference Relations in Managing Group Decision Making , 2020, Arabian Journal for Science and Engineering.

[15]  Bernard Roy,et al.  Determining the weights of criteria in the ELECTRE type methods with a revised Simos' procedure , 2002, Eur. J. Oper. Res..

[16]  Jianqiang Wang,et al.  Distance‐based multicriteria group decision‐making approach with probabilistic linguistic term sets , 2018, Expert Syst. J. Knowl. Eng..

[17]  Zeshui Xu,et al.  Venture capital group decision-making with interaction under probabilistic linguistic environment , 2018, Knowl. Based Syst..

[18]  Decui Liang,et al.  Grey Relational Analysis Method for Probabilistic Linguistic Multi-criteria Group Decision-Making Based on Geometric Bonferroni Mean , 2017, International Journal of Fuzzy Systems.

[19]  Chen Ye,et al.  Project evaluation method using non-formatted text information based on multi-granular linguistic labels , 2015, Inf. Fusion.

[20]  Eleftherios Siskos,et al.  Elicitation of criteria importance weights through the Simos method: A robustness concern , 2015, Eur. J. Oper. Res..

[21]  Jian-Bo Yang,et al.  On the evidential reasoning algorithm for multiple attribute decision analysis under uncertainty , 2002, IEEE Trans. Syst. Man Cybern. Part A.

[22]  Qi Sun,et al.  An attitudinal consensus degree to control the feedback mechanism in group decision making with different adjustment cost , 2019, Knowl. Based Syst..

[23]  Francisco Herrera,et al.  A fusion approach for managing multi-granularity linguistic term sets in decision making , 2000, Fuzzy Sets Syst..

[24]  Jian-Bo Yang,et al.  Evidential reasoning rule for MADM with both weights and reliabilities in group decision making , 2017, Knowl. Based Syst..

[25]  Li Zheng,et al.  New unbalanced linguistic scale sets: The linguistic information representations and applications , 2017, Comput. Ind. Eng..

[26]  Huchang Liao,et al.  A consensus-based probabilistic linguistic gained and lost dominance score method , 2019, Eur. J. Oper. Res..

[27]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[28]  Jian-Bo Yang,et al.  Evidential reasoning approach for MADM based on incomplete interval value , 2017, J. Intell. Fuzzy Syst..

[29]  Zhang-peng Tian,et al.  Signed distance-based consensus in multi-criteria group decision-making with multi-granular hesitant unbalanced linguistic information , 2018, Comput. Ind. Eng..

[30]  Jianqiang Wang,et al.  Investment risk evaluation for new energy resources: An integrated decision support model based on regret theory and ELECTRE III , 2019, Energy Conversion and Management.

[31]  Jian-qiang Wang,et al.  Multi-criteria game model based on the pairwise comparisons of strategies with Z-numbers , 2019, Appl. Soft Comput..

[32]  Francisco Herrera,et al.  Hesitant Fuzzy Linguistic Term Sets for Decision Making , 2012, IEEE Transactions on Fuzzy Systems.

[33]  Zeshui Xu,et al.  Probabilistic linguistic vector-term set and its application in group decision making with multi-granular linguistic information , 2016, Appl. Soft Comput..

[34]  Huchang Liao,et al.  An approach to quality function deployment based on probabilistic linguistic term sets and ORESTE method for multi-expert multi-criteria decision making , 2018, Inf. Fusion.

[35]  Min Wu,et al.  A new method for probabilistic linguistic multi-attribute group decision making: Application to the selection of financial technologies , 2019, Appl. Soft Comput..

[36]  Ronald R. Yager,et al.  An Attitudinal Trust Recommendation Mechanism to Balance Consensus and Harmony in Group Decision Making , 2019, IEEE Transactions on Fuzzy Systems.

[37]  Francisco Herrera,et al.  A linear programming method for multiple criteria decision making with probabilistic linguistic information , 2017, Inf. Sci..

[38]  Stelios H. Zanakis,et al.  Multi-attribute decision making: A simulation comparison of select methods , 1998, Eur. J. Oper. Res..

[39]  Hong-yu Zhang,et al.  Selecting an outsourcing provider based on the combined MABAC-ELECTRE method using single-valued neutrosophic linguistic sets , 2018, Comput. Ind. Eng..

[40]  Jianqiang Wang,et al.  Cloud-based ERP system selection based on extended probabilistic linguistic MULTIMOORA method and Choquet integral operator , 2019, Computational and Applied Mathematics.

[41]  Zeshui Xu,et al.  A consensus process for group decision making with probabilistic linguistic preference relations , 2017, Inf. Sci..

[42]  Zheng Pei,et al.  An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers , 2015, Int. J. Comput. Intell. Syst..

[43]  Peide Liu,et al.  Multi-attribute decision making method based on generalized maclaurin symmetric mean aggregation operators for probabilistic linguistic information , 2019, Comput. Ind. Eng..

[44]  Zeshui Xu,et al.  Multi-attribute group decision-making under probabilistic uncertain linguistic environment , 2018, J. Oper. Res. Soc..

[45]  Tarik Aouam,et al.  Fuzzy MADM: An outranking method , 2003, Eur. J. Oper. Res..

[46]  Changyong Liang,et al.  A trust propagation and collaborative filtering based method for incomplete information in social network group decision making with type-2 linguistic trust , 2019, Comput. Ind. Eng..

[47]  Shyi-Ming Chen,et al.  Fuzzy decision making based on likelihood-based comparison relations of hesitant fuzzy linguistic term sets and hesitant fuzzy linguistic operators , 2015, Inf. Sci..

[48]  S. Greco,et al.  A robust ranking method extending ELECTRE III to hierarchy of interacting criteria, imprecise weights and stochastic analysis , 2017 .

[49]  Jian-Bo Yang,et al.  Evidential reasoning approach with multiple kinds of attributes and entropy-based weight assignment , 2019, Knowl. Based Syst..

[50]  Dong-Ling Xu,et al.  Evidential reasoning rule for evidence combination , 2013, Artif. Intell..

[51]  Huchang Liao,et al.  Unbalanced double hierarchy linguistic term set: The TOPSIS method for multi-expert qualitative decision making involving green mine selection , 2019, Inf. Fusion.

[52]  Peide Liu,et al.  Probabilistic linguistic TODIM approach for multiple attribute decision-making , 2017, GRC 2017.

[53]  Zhang-peng Tian,et al.  Probabilistic linguistic multi-criteria decision-making based on evidential reasoning and combined ranking methods considering decision-makers’ psychological preferences , 2020, J. Oper. Res. Soc..