Multi-criteria decision-making approaches based on distance measures for linguistic hesitant fuzzy sets

Abstract Linguistic hesitant fuzzy sets (LHFSs), which can be used to both represent decision-makers’ qualitative preferences and reflect their hesitancy and inconsistency, have attracted much attention due to their flexibility and efficiency. In this paper, some distance-based approaches for resolving multi-criteria decision-making (MCDM) problems with linguistic hesitant fuzzy information are introduced. To begin, a new order relationship between LHFSs, based on the defined LHFSs, is presented. Then, distance measures for LHFSs are proposed, which include the generalised, Hamming, and Euclidean distance measures. Additionally, some approaches for handling MCDM problems with linguistic hesitant fuzzy information are proposed, which are based on the TOPSIS, VIKOR, and TODIM methods, as well as the proposed distance measures. Finally, an illustrative example is provided to show the feasibility and usability of the methods, which are then compared with the existing method.

[1]  Ding-Hong Peng,et al.  Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision-making , 2013 .

[2]  Zeshui Xu,et al.  The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment , 2014, Knowl. Based Syst..

[3]  B. Farhadinia,et al.  Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets , 2013, Inf. Sci..

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

[5]  Qing Sun,et al.  Group decision making based on induced uncertain linguistic OWA operators , 2013, Decis. Support Syst..

[6]  Zhang-peng Tian,et al.  Multicriteria decision-making approach based on gray linguistic weighted Bonferroni mean operator , 2018, Int. Trans. Oper. Res..

[7]  Rodolfo Lourenzutti,et al.  A study of TODIM in a intuitionistic fuzzy and random environment , 2013, Expert Syst. Appl..

[8]  Egidijus Rytas Vaidogas,et al.  Multi-attribute Decision-making in Economics of Fire Protection , 2011 .

[9]  Zhang-peng Tian,et al.  A Likelihood-Based Qualitative Flexible Approach with Hesitant Fuzzy Linguistic Information , 2016, Cognitive Computation.

[10]  Gwo-Hshiung Tzeng,et al.  Multicriteria Planning of Post‐Earthquake Sustainable Reconstruction , 2002 .

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

[12]  Vicenç Torra,et al.  On hesitant fuzzy sets and decision , 2009, 2009 IEEE International Conference on Fuzzy Systems.

[13]  Z. S. Xu,et al.  An Overview of Distance and Similarity Measures of Intuitionistic Fuzzy Sets , 2008, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[14]  Jianqiang Wang,et al.  An Uncertain Linguistic Multi-criteria Group Decision-Making Method Based on a Cloud Model , 2014, Group Decision and Negotiation.

[15]  Zhang-peng Tian,et al.  Simplified Neutrosophic Linguistic Multi-criteria Group Decision-Making Approach to Green Product Development , 2017 .

[16]  Karel Skokan.  Technological and Economic Development of Economy , 2011 .

[17]  Yejun Xu,et al.  Distance measure for linguistic decision making , 2011 .

[18]  Qianhui Liu,et al.  An extended TOPSIS method for multiple attribute decision making problems with unknown weight based on 2-dimension uncertain linguistic variables , 2014, J. Intell. Fuzzy Syst..

[19]  Jian-qiang Wang,et al.  Intuitionistic hesitant linguistic sets and their application in multi-criteria decision-making problems , 2015, Operational Research.

[20]  Hong-yu Zhang,et al.  Multi-criteria decision-making based on hesitant fuzzy linguistic term sets: An outranking approach , 2015, Knowl. Based Syst..

[21]  Zeshui Xu,et al.  Distance and similarity measures for hesitant fuzzy sets , 2011, Inf. Sci..

[22]  Ching-Lai Hwang,et al.  Multiple Attribute Decision Making: Methods and Applications - A State-of-the-Art Survey , 1981, Lecture Notes in Economics and Mathematical Systems.

[23]  Z. S. Xu,et al.  Eowa And Eowg Operators For Aggregating Linguistic Labels Based On Linguistic Preference Relations , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[24]  Jian-qiang Wang,et al.  Novel Multi-criteria Decision-making Approaches Based on Hesitant Fuzzy Sets and Prospect Theory , 2016, Int. J. Inf. Technol. Decis. Mak..

[25]  John Farr,et al.  Evaluation of multi-attribute decision making systems applied during the concept design of new microplasma devices , 2013, Expert Syst. Appl..

[26]  Kavita Devi,et al.  Extension of VIKOR method in intuitionistic fuzzy environment for robot selection , 2011, Expert Syst. Appl..

[27]  Qiang Zhang,et al.  Multi-attribute decision analysis under a linguistic hesitant fuzzy environment , 2014, Inf. Sci..

[28]  Tamer Boyaci,et al.  Effects of upstream and downstream mergers on supply chain profitability , 2016, Eur. J. Oper. Res..

[29]  Peide Liu,et al.  Risk Evaluation Method of High-technology Based on Uncertain Linguistic Variable and TOPSIS Method , 2009, J. Comput..

[30]  Hong-yu Zhang,et al.  Linguistic hesitant fuzzy multi-criteria decision-making method based on evidential reasoning , 2016, Int. J. Syst. Sci..

[31]  Peide Liu,et al.  Multi‐attribute decision‐making method research based on interval vague set and TOPSIS method , 2009 .

[32]  Xiao Zhang,et al.  Extended TODIM method for hybrid multiple attribute decision making problems , 2013, Knowl. Based Syst..

[33]  Xiaohong Chen,et al.  A Multi-Criteria Decision-Making Method Based on Heronian Mean Operators Under a Linguistic Hesitant Fuzzy Environment , 2015, Asia Pac. J. Oper. Res..

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

[35]  Zeshui Xu,et al.  Hesitant fuzzy information aggregation in decision making , 2011, Int. J. Approx. Reason..

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

[37]  Guiwu Wei,et al.  Models for selecting an ERP system with hesitant fuzzy linguistic information , 2014, J. Intell. Fuzzy Syst..

[38]  Zeshui Xu,et al.  Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group , 2009, Fuzzy Optim. Decis. Mak..

[39]  Radko Mesiar,et al.  Hesitant L ‐Fuzzy Sets , 2017, Int. J. Intell. Syst..

[40]  Hu-Chen Liu,et al.  Material selection using an interval 2-tuple linguistic VIKOR method considering subjective and objective weights , 2013 .

[41]  Zeshui Xu,et al.  Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information , 2013, Knowl. Based Syst..

[42]  E. Ertugrul Karsak,et al.  Distance-based fuzzy MCDM approach for evaluating flexible manufacturing system alternatives , 2002 .

[43]  Laura Riesgo,et al.  An MCDM analysis of agricultural risk aversion , 2003, Eur. J. Oper. Res..

[44]  Hong-yu Zhang,et al.  Multi-criteria decision-making methods based on the Hausdorff distance of hesitant fuzzy linguistic numbers , 2015, Soft Computing.

[45]  Hong-yu Zhang,et al.  Multi-criteria Group Decision-Making Approach Based on 2-Tuple Linguistic Aggregation Operators with Multi-hesitant Fuzzy Linguistic Information , 2015, International Journal of Fuzzy Systems.

[46]  Z. Fan,et al.  A Method for Linguistic Multiple Attribute Decision Making Based on TODIM , 2011, 2011 International Conference on Management and Service Science.

[47]  Renato A. Krohling,et al.  IF-TODIM: An intuitionistic fuzzy TODIM to multi-criteria decision making , 2013, Knowl. Based Syst..

[48]  XuZeshui,et al.  Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information , 2013 .

[49]  B. Farhadinia,et al.  Distance and similarity measures for higher order hesitant fuzzy sets , 2014, Knowl. Based Syst..

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

[51]  Yanbing Ju,et al.  Extension of VIKOR method for multi-criteria group decision making problem with linguistic information , 2013 .

[52]  Yin-xiang Ma,et al.  2-tuple linguistic aggregation operators based on subjective sensation and objective numerical scales for multi-criteria group decision-making problems , 2016 .

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

[54]  G. Wei,et al.  Extension of VIKOR method for decision making problem based on hesitant fuzzy set , 2013 .

[55]  Hong-yu Zhang,et al.  An outranking approach for multi-criteria decision-making problems with interval-valued neutrosophic sets , 2015, Neural Computing and Applications.

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