Generalized intuitionistic fuzzy Bonferroni means

Abstract

Intuitionistic fuzzy set is a widely used tool to express the membership, nonmembership, and hesitancy information of an element to a set. To aggregate the intuitionistic fuzzy information, a lot of aggregation techniques have been developed, especially, the ones which reflect the correlations of the aggregated arguments are the hot research topics, among which Bonferroni mean (BM) is an important aggregation technique. However, the classical BM ignores some aggregation information and the weight vector of the aggregated arguments. In this paper, we introduce the generalized weighted BM and the generalized intuitionistic fuzzy weighted BM, both of which focus on the group opinion. Paying more attention to the individual opinions, we further define the generalized weighted Bonferroni geometric mean and the generalized intuitionistic fuzzy weighted Bonferroni geometric mean. Various families of the existing operators can be obtained when the parameters of the developed aggregation techniques are assigned different values. Finally, we propose an approach to multicriteria decision making on the basis of the proposed aggregation techniques and an example is also given to illustrate our results. C 2011 Wiley Periodicals, Inc.

Some Generalized Pythagorean Fuzzy Bonferroni Mean Aggregation Operators with Their Application to Multiattribute Group Decision-Making

“…Nevertheless, Xia et al [38] highlighted that the GBM introduced by Beliakov et al [37] has a drawback. Therefore, Xia et al [38] introduced a new form of GBM. In the new GBM, the weights of the arguments are also considered.…”

“…However, BM and HM can only consider the interrelationship between any two arguments. Beliakov et al [37] introduced the generalized Bonferroni mean (GBM) to overcome the drawback of BM; GBM has also been extended to IFSs [38]. However, to the best of our knowledge, no research has been conducted on GBM in the Pythagorean fuzzy environment.…”

2-Dimension Uncertain Linguistic Generalized Normalized Weighted Geometric Bonferroni Mean and Its Application in Multiple Attribute Decision Making

“…W = (w 1 ; w 2 ; ; w n ) T is the weight vector of a i (i = 1; 2; ; n), where w i represents the importance degree of a i , satisfying w i > 0, P n i=1 w i = 1. If: WBM p;q (a 1 ; a 2 ; ; a n ) De nition 8 [46]. Let p; q; r 0, and a i (i = 1; 2; ; n) be a collection of nonnegative numbers.…”

“…Let W = ( 1 n ; 1 n ; ; 1 n ) T ; then: 2DULNWGBM p;q (ŝ 1 ;ŝ 2 ; ;ŝ n ) = 2DULGBM p;q (ŝ 1 ;ŝ 2 ; ;ŝ n ): (46) Proof. Since W = ( 1 n ; 1 n ; ; 1 n ) T , according to Eq.…”

“…We can note that the BM operators extended above do not have the characteristic of reducibility. To overcome this shortcoming, Xia et al [46] developed the extended BM, GBM, GWBM, and GWGBM operators, which had reducibility, and further extended them to IFS. However, these operators only considered the relationships between individual attributes and the other ones.…”