Intuitionistic fuzzy geometric aggregation operators based on einstein operations

Abstract

Intuitionistic fuzzy information aggregation plays an important part in Atanassov's intuitionistic fuzzy set theory, which has emerged to be a new research direction receiving more and more attention in recent years. In this paper, we first introduce some operations on intuitionistic fuzzy sets, such as Einstein sum, Einstein product, Einstein exponentiation, etc., and further develop some new geometric aggregation operators, such as the intuitionistic fuzzy Einstein weighted geometric operator and the intuitionistic fuzzy Einstein ordered weighted geometric operator, which extend the weighted geometric (WG) operator and the ordered weighted geometric (OWG) operator to accommodate the environment in which the given arguments are intuitionistic fuzzy values. We also establish some desirable properties of these operators, such as commutativity, idempotency and monotonicity, and give some numerical examples to illustrate the developed aggregation operators. In addition, we compare the proposed operators with the existing intuitionistic fuzzy geometric operators and get the corresponding relations. Finally, we apply the intuitionistic fuzzy Einstein weighted geometric operator to deal with multiple attribute decision making under intuitionistic fuzzy environments. C 2011 Wiley Periodicals, Inc.

Prioritized averaging/geometric aggregation operators under the intuitionistic fuzzy soft set environment

“…To demonstrate the e ectiveness of the proposed approach as compared to the existing ones for MCDM, an analysis has been conducted by using di erent operators as proposed by various researchers [5][6][7][8]12]. So, the grades corresponding to di erent parameters of each candidate are aggregated by geometric operator corresponding to the weight vector (0:2; 0:2; 0:2; 0:2; 0:2) T and their aggregated results are summarized in Table 6.…”

“…So, the grades corresponding to di erent parameters of each candidate are aggregated by geometric operator corresponding to the weight vector (0:2; 0:2; 0:2; 0:2; 0:2) T and their aggregated results are summarized in Table 6. By using these aggregated values, the di erent approaches as proposed by various authors [5][6][7][8]12] have been applied to it and their score values as well as ranking of each candidate are computed and tabulated in Table 7. Table 7.…”

“…For instance, Xu [5], Xu and Yager [6] developed weighted averaging and geometric aggregation operators under IFS environment. Wang and Liu [7,8] investigated these aggregation operators by using Einstein operations. Garg [9] presented a generalized intuitionistic fuzzy interactive geometric aggregation operators using Einstein t-norm and tconorm operations.…”

Interval-valued Pythagorean fuzzy Einstein hybrid weighted averaging aggregation operator and their application to group decision making

“…After the successful and positive applications of intuitionistic fuzzy set, aggregation operators become more interesting topic for research. Thus, many scholars in [3][4][5][6][7][8][9][10][11][12][13][14][15][16] developed several aggregation operators for group decision making using intuitionistic fuzzy information.…”

The Application of TOPSIS Method to Group Decision Making based on Similarity Measures under Interval-valued Intuitionistic Fuzzy Settings

“…In [6], Li et al presented a MCDM approach by combining the quality function with the technique for order preference by similarity to an ideal solution (TOPSIS) method [7]under intuitionistic fuzzy environments. Pei and Zheng [8] present a new approach to multi-attribute decision making problems in intuitionistic fuzzy environment, in which the evaluated values (in the form of intervals) of the same alternative with different attributes are considered as one unified entity, Wang and Zhang [9]presented a MCDM method based on IFSs with incomplete certain information on weights.Wang and Liu [10] presented some intuitionistic fuzzy geometric aggregation operators based on Einstein operations for multiattribute decision making. Wu and Zhang [11] proposed a MCDM method based on intuitionistic weighted entropy measures.…”