The Linguistic Interval-Valued Intuitionistic Fuzzy Aggregation Operators Based on Extended Hamacher T-Norm and S-Norm and Their Application

Linguistic interval-valued intuitionistic fuzzy sets, as an extension of interval-valued intuitionistic fuzzy sets, have strong practical value in the management of complex uncertainty system with qualitative evaluation information. This study focuses on the development of several linguistic interval-valued intuitionistic fuzzy Hamacher (LIVIFH) aggregation operators based on the extended Hamacher t-norm and s-norm. First, the extended Hamacher t-norm and s-norm, which are applicable to linguistic information environment, are applied to define the linguistic interval-valued intuitionistic fuzzy Hamacher operational laws. Second, based on the proposed operational laws, this study defines the linguistic interval-valued intuitionistic fuzzy Hamacher weighted average (LIVIFHWA) operator and the linguistic interval-valued intuitionistic fuzzy Hamacher weighted geometric (LIVIFHWG) operator, and then investigates their properties. Furthermore, the degeneracy and monotonicity of the proposed operators with respect to the adjustable parameter are explored. Finally, a multiple attribute group decision-making (MAGDM) approach is developed based on the proposed LIVIFH aggregation operators, and then this approach is applied to a supplier selection problem. Parameter analysis indicates that the adjustable parameter in the proposed LIVIFH aggregation operators could reflect the attitudes of decision makers. The LIVIFHWA operator would be more appropriate to optimistic decision makers, and the LIVIFHWG operator to pessimistic decision makers. In addition, as the adjustable parameter increasing, both attitudes tend to be neutral. The proposed method is also compared with two other approaches to show its feasibility and efficiency.

[1]  Peide Liu,et al.  A New Decision-Making Method Based on Interval-Valued Linguistic Intuitionistic Fuzzy Information , 2018, Cognitive Computation.

[2]  Mustafa Batuhan Ayhan,et al.  A two stage approach for supplier selection problem in multi-item/multi-supplier environment with quantity discounts , 2015, Comput. Ind. Eng..

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

[4]  Peide Liu,et al.  Linguistic Intuitionistic Fuzzy Hamy Mean Operators and Their Application to Multiple-Attribute Group Decision Making , 2019, IEEE Access.

[5]  Fanyong Meng,et al.  Linguistic Intuitionistic Fuzzy Group Decision Making Based on Aggregation Operators , 2018, International Journal of Fuzzy Systems.

[6]  Zhen Zhang,et al.  Managing Multigranular Linguistic Distribution Assessments in Large-Scale Multiattribute Group Decision Making , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[7]  Peide Liu,et al.  A Multiple Attribute Group Decision-making Method Based on the Partitioned Bonferroni Mean of Linguistic Intuitionistic Fuzzy Numbers , 2019, Cognitive Computation.

[8]  Peide Liu,et al.  Power average operators of linguistic intuitionistic fuzzy numbers and their application to multiple-attribute decision making , 2017, J. Intell. Fuzzy Syst..

[9]  Guiwu Wei,et al.  Pythagorean hesitant fuzzy Hamacher aggregation operators and their application to multiple attribute decision making , 2018, Int. J. Intell. Syst..

[10]  Zhibin Wu,et al.  Possibility Distribution-Based Approach for MAGDM With Hesitant Fuzzy Linguistic Information , 2016, IEEE Transactions on Cybernetics.

[11]  Xi Liu,et al.  Using New Version of Extended $t$ -Norms and $s$ -Norms for Aggregating Interval Linguistic Labels , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

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

[13]  Huimin Zhang,et al.  Linguistic Intuitionistic Fuzzy Sets and Application in MAGDM , 2014, J. Appl. Math..

[14]  Zeshui Xu,et al.  Hesitant Fuzzy Linguistic Consensus Model Based on Trust-Recommendation Mechanism for Hospital Expert Consultation , 2019, IEEE Transactions on Fuzzy Systems.

[15]  Xiaohong Chen,et al.  Hesitant fuzzy Hamacher aggregation operators for multicriteria decision making , 2015, Appl. Soft Comput..

[16]  Zeshui Xu,et al.  Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm , 2012, Knowl. Based Syst..

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

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

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

[20]  Yin-Feng Xu,et al.  Consistency and consensus measures for linguistic preference relations based on distribution assessments , 2014, Inf. Fusion.

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

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

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

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

[25]  Harish Garg,et al.  Linguistic Interval-Valued Atanassov Intuitionistic Fuzzy Sets and Their Applications to Group Decision Making Problems , 2019, IEEE Transactions on Fuzzy Systems.

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

[27]  José M. Merigó,et al.  Partitioned Heronian means based on linguistic intuitionistic fuzzy numbers for dealing with multi-attribute group decision making , 2018, Appl. Soft Comput..

[28]  Jian-qiang Wang,et al.  A linguistic intuitionistic multi-criteria decision-making method based on the Frank Heronian mean operator and its application in evaluating coal mine safety , 2018, Int. J. Mach. Learn. Cybern..