New Approaches to Pythagorean Fuzzy Averaging Aggregation Operators

Rahman, Khaista

doi:10.11648/j.ml.20170302.12

Cited by 18 publications

(21 citation statements)

References 4 publications

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“…Strengthening the concept of IFSs, Yager suggests Pythagorean FSs, which somehow enlarge the space of positive membership and negative membership by introducing some new condition such that

0 \leq P 2 (x) + N 2 (x) \leq 1

. Pythagorean FSs have been explored by many researchers …”

Section: Introductionmentioning

confidence: 99%

Spherical aggregation operators and their application in multiattribute group decision-making

2018

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“…Strengthening the concept of IFSs, Yager suggests Pythagorean FSs, which somehow enlarge the space of positive membership and negative membership by introducing some new condition such that

0 \leq P 2 (x) + N 2 (x) \leq 1

. Pythagorean FSs have been explored by many researchers …”

Section: Introductionmentioning

confidence: 99%

Spherical aggregation operators and their application in multiattribute group decision-making

2018

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“…Note that these PyFWA and PyFWG operators are the same as those proposed by Rahman et al and Peng and Yang [39,40]. This type of MADM problem can easily be solved by placing q = 1, s l = s u = s, i l = i u = i, and d l = d u = d into the proposed IVTSFWA operator, i.e., by using Equation (15).…”

Section: Consequences Of the Proposed Work And A Comparative Studymentioning

confidence: 99%

“…The basic operations for two PyFSs were proposed in the following definition: Definition 3. [39,40] For PyFSs A, B and for λ > 0, we have:…”

Section: Definition 2 [22]mentioning

confidence: 99%

“…Some other useful tools in the aggregation of IFSs and IVIFSs, along with their applications, were also constructed [33][34][35][36][37][38]. 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].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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Expressing the measure of uncertainty, in terms of an interval instead of a crisp number, provides improved results in fuzzy mathematics. Several such concepts are established, including the interval-valued fuzzy set, the interval-valued intuitionistic fuzzy set, and the interval-valued picture fuzzy set. The goal of this article is to enhance the T-spherical fuzzy set (TSFS) by introducing the interval-valued TSFS (IVTSFS), which describes the uncertainty measure in terms of the membership, abstinence, non-membership, and the refusal degree. The novelty of the IVTSFS over the pre-existing fuzzy structures is analyzed. The basic operations are proposed for IVTSFSs and their properties are investigated. Two aggregation operators for IVTSFSs are developed, including weighted averaging and weighted geometric operators, and their validity is examined using the induction method. Several consequences of new operators, along with their comparative studies, are elaborated. A multi-attribute decision-making method in the context of IVTSFSs is developed, followed by a brief numerical example where the selection of the best policy, among a list of investment policies of a multinational company, is to be evaluated. The advantages of using the framework of IVTSFSs are described theoretically and numerically, hence showing the limitations of pre-existing aggregation operators.

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“…Like intuitionistic fuzzy aggregation operators, Pythagorean fuzzy aggregation operators are also become an interesting and important area for research, after the advent of Pythagorean fuzzy set theory. Several researchers in [19][20][21][22][23][24][25][26][27][28] introduced many aggregation operators for decision using Pythagorean fuzzy information.…”

Section: Introductionmentioning

confidence: 99%

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

Rahman

Abdullah

Ali

et al. 2018

Complex Intell. Syst.

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The objective of the present work is divided into two folds. Firstly, interval-valued Pythagorean fuzzy Einstein hybrid weighted averaging aggregation operator has been introduced along with their several properties, namely idempotency, boundedness and monotonicity. Secondly, we apply the proposed operator to deal with multi-attribute group decision-making problem under Pythagorean fuzzy information. For this, we construct an algorithm for multi-attribute group decision making. At the last, we construct a numerical example for multi-attribute group decision making. The main advantage of using the proposed operator is that this operator provides more accurate and precise results is compared to the existing methods.

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New Approaches to Pythagorean Fuzzy Averaging Aggregation Operators

Abstract: In this paper, we present two Pythagorean fuzzy averaging aggregation operators such as, Pythagorean fuzzy weighted averaging (PFWA) operator, Pythagorean fuzzy ordered weighted averaging (PFOWA) operator and also introduce some of their basic properties.

Cited by 18 publications

References 4 publications

Spherical aggregation operators and their application in multiattribute group decision-making

Spherical aggregation operators and their application in multiattribute group decision-making

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

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

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