Unbalanced double hierarchy linguistic term set: The TOPSIS method for multi-expert qualitative decision making involving green mine selection

Abstract The double hierarchy linguistic term set is a linguistic technique to elaborately and accurately represent complex linguistic information for qualitative decision-making problems. Considering that unbalanced semantics may appear in the first and second hierarchy linguistic term sets, the unbalanced double hierarchy linguistic term set (UDHLTS) is proposed in this paper. To characterize the unbalanced distribution of semantics of the second hierarchy linguistic terms, we propose three linguistic scale functions with cognitive bias parameters. Then, a non-linear fitting method is presented to determine these parameters. Combining the first and second hierarchy linguistic term set, we construct eight semantic models with distinct risk appetite parameters and linguistic cognitive bias parameters to capture the semantics of linguistic terms in the UDHLTS. In this way, we can use specific semantic model to represent experts’ opinions associated with the UDHLTS. In addition, by using the semantic model of the UDHLTS, linguistic information from different experts can be compared and aggregated quantitatively. To illustrate the applicability of the UDHLTS, we develop a UDHL-TOPSIS method for multi-expert qualitative decision making problems. An engineering example concerning green mine selection is given to illustrate the proposed method.

[1]  Zeshui Xu,et al.  Generalized asymmetric linguistic term set and its application to qualitative decision making involving risk appetites , 2016, Eur. J. Oper. Res..

[2]  V. Torra.  Negation functions based semantics for ordered linguistic labels , 1996 .

[3]  Francisco Herrera,et al.  Multiple criteria decision making based on distance and similarity measures under double hierarchy hesitant fuzzy linguistic environment , 2018, Comput. Ind. Eng..

[4]  Wei Fa-jie.  Research on Method of Analyzing the Posterior Weight of Experts Based on New Evaluation Scale of Linguistic Information , 2011 .

[5]  Hai Wang,et al.  Extended hesitant fuzzy linguistic term sets and their aggregation in group decision making , 2015, Int. J. Comput. Intell. Syst..

[6]  Francisco Herrera,et al.  Double hierarchy hesitant fuzzy linguistic term set and MULTIMOORA method: A case of study to evaluate the implementation status of haze controlling measures , 2017, Inf. Fusion.

[7]  Hong-yu Zhang,et al.  Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems , 2014, Inf. Sci..

[8]  María Teresa Lamata,et al.  The LTOPSIS: An alternative to TOPSIS decision-making approach for linguistic variables , 2012, Expert Syst. Appl..

[9]  Francisco Herrera,et al.  Consensus reaching process for large-scale group decision making with double hierarchy hesitant fuzzy linguistic preference relations , 2018, Knowl. Based Syst..

[10]  Miroslav Kárný.  Algorithms for determining the model structure of a controlled system , 1983, Kybernetika.

[11]  Zeshui Xu,et al.  Approaches to manage hesitant fuzzy linguistic information based on the cosine distance and similarity measures for HFLTSs and their application in qualitative decision making , 2015, Expert Syst. Appl..

[12]  Zeshui Xu,et al.  Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment , 2004, Inf. Sci..

[13]  Francisco Herrera,et al.  Linguistic decision analysis: steps for solving decision problems under linguistic information , 2000, Fuzzy Sets Syst..

[14]  Hong-yu Zhang,et al.  A likelihood-based TODIM approach based on multi-hesitant fuzzy linguistic information for evaluation in logistics outsourcing , 2016, Comput. Ind. Eng..

[15]  V. Torra,et al.  A framework for linguistic logic programming , 2010 .

[16]  Zhi Pei,et al.  A note on the TOPSIS method in MADM problems with linguistic evaluations , 2015, Appl. Soft Comput..

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

[18]  Peter E.D. Love,et al.  Quantitative and qualitative decision‐making methods in simulation modelling , 2002 .

[19]  Zeshui Xu,et al.  Hesitant fuzzy linguistic term sets for linguistic decision making: Current developments, issues and challenges , 2018, Inf. Fusion.

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

[21]  Morteza Yazdani,et al.  A state-of the-art survey of TOPSIS applications , 2012, Expert Syst. Appl..

[22]  Yi Yang,et al.  Proportional hesitant fuzzy linguistic term set for multiple criteria group decision making , 2016, Inf. Sci..

[23]  Isis Truck,et al.  Comparison and links between two 2-tuple linguistic models for decision making , 2015, Knowl. Based Syst..

[24]  Isis Truck,et al.  Towards an extension of the 2-tuple linguistic model to deal with unbalanced linguistic term sets , 2013, Kybernetika.

[25]  Tabasam Rashid,et al.  TOPSIS for Hesitant Fuzzy Linguistic Term Sets , 2013, Int. J. Intell. Syst..

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

[27]  Sheng-Lin Chang,et al.  Assessment of supplier performance based on product-development strategy by applying multi-granularity linguistic term sets ☆ , 2009 .

[28]  Francisco Herrera,et al.  A 2-tuple fuzzy linguistic representation model for computing with words , 2000, IEEE Trans. Fuzzy Syst..

[29]  Jin-Hsien Wang,et al.  A new version of 2-tuple fuzzy linguistic representation model for computing with words , 2006, IEEE Trans. Fuzzy Syst..

[30]  Francisco Herrera,et al.  Score-HeDLiSF: A score function of hesitant fuzzy linguistic term set based on hesitant degrees and linguistic scale functions: An application to unbalanced hesitant fuzzy linguistic MULTIMOORA , 2019, Inf. Fusion.

[31]  Jae Kyu Lee,et al.  MULTIPLE‐CRITERIA DECISION MAKING INCLUDING QUALITATIVE FACTORS: THE POST‐MODEL ANALYSIS APPROACH , 1988 .

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

[33]  Zeshui Xu,et al.  Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets , 2015, Knowl. Based Syst..

[34]  Zeshui Xu.  Deviation measures of linguistic preference relations in group decision making , 2005 .

[35]  Francisco Herrera,et al.  Hesitant Fuzzy Linguistic Term Set and Its Application in Decision Making: A State-of-the-Art Survey , 2017, International Journal of Fuzzy Systems.

[36]  Zeshui Xu,et al.  Hesitant fuzzy linguistic entropy and cross-entropy measures and alternative queuing method for multiple criteria decision making , 2017, Inf. Sci..

[37]  Cathal M. Brugha,et al.  The structure of qualitative decision-making , 1998 .

[38]  Didier Dubois,et al.  The role of fuzzy sets in decision sciences: Old techniques and new directions , 2011, Fuzzy Sets Syst..

[39]  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.

[40]  Isis Truck,et al.  A new proposal to deal with hesitant linguistic expressions on preference assessments , 2018, Inf. Fusion.

[41]  Gui-Wu Wei,et al.  Extension of TOPSIS method for 2-tuple linguistic multiple attribute group decision making with incomplete weight information , 2010, Knowledge and Information Systems.

[42]  Enrique Herrera-Viedma,et al.  A model of an information retrieval system with unbalanced fuzzy linguistic information , 2007, Int. J. Intell. Syst..

[43]  Ming Tang,et al.  Managing information measures for hesitant fuzzy linguistic term sets and their applications in designing clustering algorithms , 2019, Inf. Fusion.

[44]  Wang Ling-ling.  Improved two-tuple linguistic representation model based on new linguistic evaluation scale , 2010 .

[45]  Francisco Herrera,et al.  Underground Mining Method Selection With the Hesitant Fuzzy Linguistic Gained and Lost Dominance Score Method , 2018, IEEE Access.

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

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

[48]  Jianfeng Cai,et al.  The power average operator for unbalanced linguistic term sets , 2015, Inf. Fusion.