Some Interval-Valued Pythagorean Fuzzy Einstein Weighted Averaging Aggregation Operators and Their Application to Group Decision Making

Abstract

<jats:title>Abstract</jats:title><jats:p>In this paper, we introduce the notion of Einstein aggregation operators, such as the interval-valued Pythagorean fuzzy Einstein weighted averaging aggregation operator and the interval-valued Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. We also discuss some desirable properties, such as idempotency, boundedness, commutativity, and monotonicity. The main advantage of using the proposed operators is that these operators give a more complete view of the problem to the decision makers. These operators provide more accurate and precise results as compared the existing method. Finally, we apply these operators to deal with multiple-attribute group decision making under interval-valued Pythagorean fuzzy information. For this, we construct an algorithm for multiple-attribute group decision making. Lastly, we also construct a numerical example for multiple-attribute group decision making.</jats:p>

Evaluation of Investment Policy Based on Multi-Attribute Decision-Making Using Interval Valued T-Spherical Fuzzy Aggregation Operators

“…Note that these IVPyFWA and IWPyFWG operators are the same as those proposed by Rehman et al [41,42]. (7) If we use q = 2, s l = s u = s, i l = i u = i = 0, and d l = d u = d, then the weighted averaging and the weighted geometric aggregation operators of the PyFSs are obtained and are given as:…”

“…For PyFSs, Rahman et al [39] and Peng and Yang [40] developed the Pythagorean fuzzy WA and WG aggregation operators. The WA and WG aggregation tools for IVPyFSs [41,42] were formulated and the recent advancement on the theory of the aggregation of PyFSs and IVPyFSs, alongside their applications in MADM, are discussed [43][44][45][46][47]. The MADM and aggregation theory of hesitant fuzzy sets (HFSs) and bipolar-valued HFSs have also been developed [48][49][50].…”

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

“…Definition 6 [32] Let λ j ( j = 1, 2, 3, ..., n) be a collection of IVPFVs, then IVPFEOWA operator can be defined as:…”

“…Thus in [29] Peng and Yang introduced the concept of interval-valued Pythagorean fuzzy set. Rahman et al [30][31][32][33] introduced many aggregation operators using interval-valued Pythagorean fuzzy numbers and applied them to multi-attribute group decision making.…”

“…Moreover, we introduce some of their basic properties such as idempotency, boundedness and monotonicity. This motivation comes from [32], in which the authors introduced the notion of IVPFEWA operator and IVPFEOWA operator and applied them to group decision making. But in this paper we introduce the notion of IVPFEHWA operator, which is the generalization of the above mention operators.…”