A Multi-Criteria Decision-Making Method Based on Heronian Mean Operators Under a Linguistic Hesitant Fuzzy Environment

Linguistic hesitant fuzzy sets (LHFSs) are a very useful and appropriate means of expressing preferences of decision-makers; moreover their basic operations and comparison methods have been defined and applied to the solving of MCDM problems. However, there are a number of limitations in the related studies. In this paper, using information from existing studies, several new operations and a new order relationship are defined; moreover four linguistic hesitant fuzzy Heronian mean operators are proposed: the linguistic hesitant fuzzy arithmetic Heronian mean (LHFAHM) operator; the linguistic hesitant fuzzy weighted arithmetic Heronian mean (LHFWAHM) operator; the linguistic hesitant fuzzy geometric Heronian mean (LHFGHM) operator; and the linguistic hesitant fuzzy weighted geometric Heronian mean (LHFWGHM) operator. Furthermore, some useful and desirable properties of these operators are analyzed in some special cases, with respect to the different parameter values in these operators, are discussed. Additionally, an approach based on the LHFWAHM and LHFWGHM operators for solving MCDM problems is proposed. Finally, an illustrative example is provided to verify the validity and feasibility of the proposed approaches, and a comparison analysis is also presented to demonstrate the influences of different parameters on the results of decision-making.

[1]  Yejun Xu,et al.  Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment , 2011, Appl. Soft Comput..

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

[3]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[4]  Li-Jun Yang,et al.  An extension of ELECTRE to multi-criteria decision-making problems with multi-hesitant fuzzy sets , 2015, Inf. Sci..

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

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

[7]  Na Chen,et al.  Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis , 2013 .

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

[9]  Hong-yu Zhang,et al.  Multi-criteria outranking approach with hesitant fuzzy sets , 2013, OR Spectrum.

[10]  Ronald R. Yager,et al.  Multiple objective decision-making using fuzzy sets , 1977 .

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

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

[13]  Zhiming Zhang,et al.  Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making , 2013, Inf. Sci..

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

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

[16]  Yan Zhang,et al.  Multi-criteria decision making method based on possibility degree of interval type-2 fuzzy number , 2013, Knowl. Based Syst..

[17]  Jing Wang,et al.  Simplified neutrosophic linguistic normalized weighted Bonferroni mean operator and its application to multi-criteria decision-making problems , 2015 .

[18]  Hong-yu Zhang,et al.  Atanassov's Interval-Valued Intuitionistic Linguistic Multicriteria Group Decision-Making Method Based on the Trapezium Cloud Model , 2015, IEEE Transactions on Fuzzy Systems.

[19]  Mariano Eriz.  Aggregation Functions: A Guide for Practitioners , 2010 .

[20]  Zeshui Xu,et al.  Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making , 2014, Inf. Sci..

[21]  Na Zhao,et al.  Operators and Comparisons of Hesitant Fuzzy Linguistic Term Sets , 2014, IEEE Transactions on Fuzzy Systems.

[22]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

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

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

[25]  Guiwu Wei,et al.  Hesitant fuzzy prioritized operators and their application to multiple attribute decision making , 2012, Knowl. Based Syst..

[26]  Lu Peng,et al.  Method of multi-criteria group decision-making based on cloud aggregation operators with linguistic information , 2014, Inf. Sci..

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

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

[29]  Jian-qiang Wang,et al.  Multi-criteria group decision making method based on intuitionistic linguistic aggregation operators , 2014, J. Intell. Fuzzy Syst..

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

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

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

[33]  I. Turksen.  Interval valued fuzzy sets based on normal forms , 1986 .

[34]  Zeshui Xu,et al.  Hesitant fuzzy geometric Bonferroni means , 2012, Inf. Sci..

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

[36]  Gin-Shuh Liang,et al.  A soft computing method of performance evaluation with MCDM based on interval-valued fuzzy numbers , 2012, Appl. Soft Comput..

[37]  Zeshui Xu,et al.  On distance and correlation measures of hesitant fuzzy information , 2011, Int. J. Intell. Syst..

[38]  Mao-Jiun J. Wang,et al.  Personnel selection using fuzzy MCDM algorithm , 1994 .

[39]  José L. Verdegay,et al.  Linguistic decision‐making models , 1992, Int. J. Intell. Syst..

[40]  Xin Zhang,et al.  Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making , 2014, Appl. Math. Comput..

[41]  Yi Peng,et al.  Evaluation of clustering algorithms for financial risk analysis using MCDM methods , 2014, Inf. Sci..

[42]  B. Farhadinia,et al.  A Novel Method of Ranking Hesitant Fuzzy Values for Multiple Attribute Decision‐Making Problems , 2013, Int. J. Intell. Syst..

[43]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[44]  Ying-Ming Wang,et al.  Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment , 2006, Expert Syst. Appl..

[45]  Francisco Herrera,et al.  An overview on the 2-tuple linguistic model for computing with words in decision making: Extensions, applications and challenges , 2012, Inf. Sci..

[46]  Xu Ze,et al.  A Method Based on Fuzzy Linguistic Assessments and Linguistic Ordered Weighted Averaging(OWA) Operator for Multi-Attribute Group Decision-Making Problems , 2002 .

[47]  Peide Liu,et al.  Some Hamacher Aggregation Operators Based on the Interval-Valued Intuitionistic Fuzzy Numbers and Their Application to Group Decision Making , 2014, IEEE Transactions on Fuzzy Systems.

[48]  Francisco Herrera,et al.  Hesitant Fuzzy Linguistic Term Sets , 2011 .

[49]  Hong-yu Zhang,et al.  Multi-criteria group decision making method based on interval 2-tuple linguistic information and Choquet integral aggregation operators , 2014, Soft Computing.

[50]  Yong Deng,et al.  A new fuzzy dempster MCDM method and its application in supplier selection , 2011, Expert Syst. Appl..

[51]  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.

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

[53]  Francisco Herrera,et al.  Computing with Words in Decision support Systems: An overview on Models and Applications , 2010, Int. J. Comput. Intell. Syst..

[54]  Tien-Chin Wang,et al.  Multi-criteria decision making with fuzzy linguistic preference relations , 2011 .

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

[56]  Jian-qiang Wang,et al.  Multi-criteria semantic dominance: A linguistic decision aiding technique based on incomplete preference information , 2013, Eur. J. Oper. Res..

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

[58]  Jing Wang,et al.  Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems , 2015, Int. J. Comput. Intell. Syst..

[59]  Gloria Bordogna,et al.  A linguistic modeling of consensus in group decision making based on OWA operators , 1997, IEEE Trans. Syst. Man Cybern. Part A.

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