2-Tuple Linguistic Hesitant Fuzzy Aggregation Operators and Its Application to Multi-Attribute Decision Making

Abstract

In this paper, a new class of uncertain linguistic variables called 2-tuple linguistic hesitant fuzzy sets (2-TLHFSs) is defined, which can express complex multi-attribute decision-making problems as well as reflect decision makers' hesitancy, uncertainty and inconsistency. Besides, it can avoid information and precision losing in aggregation process. Firstly, several new closed operational laws based on Einstein t-norm and t-conorm are defined over 2-TLHFSs, which can overcome granularity and logical problems of existing operational laws. Based on the new operational laws, 2-tuple linguistic hesitant fuzzy Einstein weighted averaging (2-TLHFEWA) operator and 2-tuple linguistic hesitant fuzzy Einstein weighted geometric (2-TLHFEWG) operator are proposed, and some of their properties are investigated. Then, a new model method based on similarity to ideal solution is proposed to determine weights of attribute, which takes both subjective and objective factors into consideration. Finally, a linguistic hesitant fuzzy multi-attribute decision making procedure is developed by means of 2-TLHFEWA and 2-TLHFEWG operators. An example is given to illustrate the practicality and efficiency of the proposed approach.

Intuitionistic linguistic multi-attribute decision making algorithm based on integrated distance measure

“…The OWA operator (Yager, 1988) presents a useful tool to infuse information that reflects the characteristic attitudes of decision makers. Due to its flexibility, the OWA operator has been the focus of many theoretical studies and is used in empirical applications of MADM problems (Merig o, Gil-Lafuente, Yu, & Llopis-Albert, 2018;Tan, Jia, & Chen, 2017;Wei, Gao, & Wei, 2018;Wei & Wang, 2017;Yager, Kacprzyk, & Beliakov, 2011;Yu, 2016;Zhou, Merig o, Chen, & Liu, 2016). Specifically, the OWA operator aggregates the ordered arguments in the following manner:…”