Informatica

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.

The 2-tuple linguistic computational model is an important tool to deal with linguistic information. To extend the application of hesitant fuzzy linguistic term sets and avoid information loss, this paper introduces hesitant fuzzy 2-tuple linguistic term sets that are expressed by using several symbolic numbers in $[0\mathrm{,}1]$. Considering the order relationship between hesitant fuzzy 2-tuple linguistic term sets, measures of expected value and variance are defined. Meanwhile, several induced generalized hesitant fuzzy 2-tuple linguistic aggregation operators are defined, by which the comprehensive attribute values of alternatives can be obtained. Then, models for the optimal weight vector on a decision maker set, on an attribute set and on their ordered sets are constructed, respectively. Furthermore, an approach to multi-granularity group decision making with hesitant fuzzy linguistic information is developed. Finally, an example is selected to illustrate the feasibility and practicality of the proposed procedure.

With respect to multi-attribute decision making under uncertain linguistic environment, a new interval-valued 2-tuple linguistic representation model is introduced. To deal with the situation where the elements in a set are interdependent, several generalized interval-valued 2-tuple linguistic correlated aggregation operators are defined. It is worth pointing out that some interval-valued 2-tuple linguistic operators based on additive measures are special cases of our operators. Meanwhile, several special cases and desirable properties are discussed. Furthermore, models based on the correlation coefficient are constructed, by which the optimal weight vector can be obtained. Moreover, an approach to multi-attribute group decision making with uncertain linguistic information is developed. Finally, an example is selected to show the effectivity and feasibility of the developed procedure.