Hesitant triangular multiplicative aggregation operators and their application to multiple attribute group decision making

The hesitant triangular fuzzy set (HTFS) is a generalization of the hesitant fuzzy set, and it permits the membership degree of an element to a set to be represented as several possible triangular fuzzy numbers. However, we find that the HTFS uses the symmetrical 0.1–0.9 scale to express the membership degree information and the results derived by using the traditional hesitant triangular fuzzy aggregation operators based on hesitant triangular fuzzy sets are inconsistent with our intuition in some situations. To overcome this issue, we use the unsymmetrical 1–9 scale to express the membership degree information instead of the symmetrical 0.1–0.9 scale in the HTFS, and then a new concept is introduced, which we call the hesitant triangular multiplicative set reflecting our intuition more objectively. Then, we discuss their operational laws and some desirable properties. Based on these operational laws, we develop a series of hesitant triangular multiplicative aggregation operators for aggregating hesitant triangular multiplicative information and then apply them to present an approach to multiple attribute group decision making under hesitant triangular multiplicative environments. Finally, several practical examples are provided to demonstrate the validity and effectiveness of the developed aggregation operators and decision making approach.

[1]  Zeshui Xu,et al.  Preference Relations Based on Intuitionistic Multiplicative Information , 2013, IEEE Transactions on Fuzzy Systems.

[2]  R. Yager.  On a general class of fuzzy connectives , 1980 .

[3]  Intensitas,et al.  Analytical Hierarchy Process , 2017 .

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

[5]  Zeshui Xu,et al.  Compatibility measures and consensus models for group decision making with intuitionistic multiplicative preference relations , 2013, Appl. Soft Comput..

[6]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[7]  Zeshui Xu,et al.  Interval-valued hesitant preference relations and their applications to group decision making , 2013, Knowl. Based Syst..

[8]  W. Pedrycz,et al.  A fuzzy extension of Saaty's priority theory , 1983 .

[9]  Yuan Xue-hai,et al.  Fuzzy Number Intuitionistic Fuzzy Set , 2007 .

[10]  Ronald R. Yager,et al.  Generalized OWA Aggregation Operators , 2004, Fuzzy Optim. Decis. Mak..

[11]  J. Mendel.  Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions , 2001 .

[12]  E. Lee,et al.  Comparison of fuzzy numbers based on the probability measure of fuzzy events , 1988 .

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

[14]  Jing-Shing Yao,et al.  Fuzzy critical path method based on signed distance ranking of fuzzy numbers , 2000, IEEE Trans. Syst. Man Cybern. Part A.

[15]  Madan M. Gupta,et al.  Fuzzy mathematical models in engineering and management science , 1988 .

[16]  Ronald R. Yager,et al.  A context-dependent method for ordering fuzzy numbers using probabilities , 2001, Inf. Sci..

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

[18]  Na Chen,et al.  Some Hesitant Fuzzy Aggregation Operators with Their Application in Group Decision Making , 2011, Group Decision and Negotiation.

[19]  Zeshui Xu,et al.  Aggregation and decision making using intuitionistic multiplicative triangular fuzzy information , 2014 .

[20]  R. Yager,et al.  On ranking fuzzy numbers using valuations , 1999 .

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

[22]  Vicenç Torra,et al.  Knowledge-based validation: Synthesis of diagnoses through synthesis of relations , 2000, Fuzzy Sets Syst..

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

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

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

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

[27]  Guiwu Wei,et al.  Induced hesitant interval-valued fuzzy Einstein aggregation operators and their application to multiple attribute decision making , 2013, J. Intell. Fuzzy Syst..

[28]  Hai Wang,et al.  Generalized hesitant fuzzy sets and their application in decision support system , 2013, Knowl. Based Syst..

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

[30]  Yejun Xu,et al.  Group decision making under hesitant fuzzy environment with application to personnel evaluation , 2013, Knowl. Based Syst..

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

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

[33]  Tien-Chin Wang,et al.  Developing a fuzzy TOPSIS approach based on subjective weights and objective weights , 2009, Expert Syst. Appl..

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

[35]  Francisco Herrera,et al.  A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets , 2013, Inf. Sci..

[36]  Guiwu Wei,et al.  Hesitant triangular fuzzy information aggregation based on Einstein operations and their application to multiple attribute decision making , 2014, Expert Syst. Appl..

[37]  Madan M. Gupta,et al.  Introduction to Fuzzy Arithmetic , 1991 .

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

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

[40]  Zeshui Xu,et al.  Hesitant fuzzy Bonferroni means for multi-criteria decision making , 2013, J. Oper. Res. Soc..

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

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

[43]  Guiwu Wei,et al.  Hesitant triangular fuzzy information aggregation in multiple attribute decision making , 2014, J. Intell. Fuzzy Syst..

[44]  Guiwu Wei,et al.  Approaches to hesitant fuzzy multiple attribute decision making with incomplete weight information , 2014, J. Intell. Fuzzy Syst..