Approaches to Multi-Attribute Group Decision Making Based on Induced Interval-Valued Pythagorean Fuzzy Einstein Aggregation Operator

Interval-valued Pythagorean fuzzy set is one of the successful extensions of the interval-valued intuitionistic fuzzy set for handling the uncertainties in the data. Under this environment, in this paper, we introduce the notion of induced interval-valued Pythagorean fuzzy Einstein ordered weighted averaging (I-IVPFEOWA) aggregation operator. Some of its desirable properties namely, idempotency, boundedness, commutatively, monotonicity have also been proved. The main advantage of using the proposed operator is that this operator gives a more complete view of the problem to the decision-makers. The method proposed in this paper provides more general, more accurate and precise results as compared to the existing methods. Therefore this method play a vital role in real world problems. Finally, we apply the proposed operator to deal with multi-attribute group decision- making problems under interval-valued Pythagorean fuzzy information. The approach has been illustrated with a numerical example from the field of the decision-making problems to show the validity, practicality and effectiveness of the new approach.

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Pythagorean Fuzzy Einstein Hybrid Averaging Aggregation Operator and its Application to Multiple-Attribute Group Decision Making

Journal of Intelligent Systems ◽

10.1515/jisys-2018-0071 ◽

2018 ◽

Vol 29 (1) ◽

pp. 736-752 ◽

Cited By ~ 4

Author(s):

Khaista Rahman ◽

Saleem Abdullah ◽

Asad Ali ◽

Fazli Amin

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Fuzzy Set ◽

Group Decision ◽

Intuitionistic Fuzzy Set ◽

Vital Role ◽

Aggregation Operator ◽

Weighted Averaging ◽

Pythagorean Fuzzy Set ◽

Multiple Attribute

Abstract Pythagorean fuzzy set is one of the successful extensions of the intuitionistic fuzzy set for handling uncertainties in information. Under this environment, in this paper, we introduce the notion of Pythagorean fuzzy Einstein hybrid averaging (PFEHA) aggregation operator along with some of its properties, namely idempotency, boundedness, and monotonicity. PFEHA aggregation operator is the generalization of Pythagorean fuzzy Einstein weighted averaging aggregation operator and Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. The operator proposed in this paper provides more accurate and precise results as compared to the existing operators. Therefore, this method plays a vital role in real-world problems. Finally, we applied the proposed operator and method to multiple-attribute group decision making.

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Some Improved q-Rung Orthopair Fuzzy Aggregation Operators and Their Applications to Multiattribute Group Decision-Making

Mathematical Problems in Engineering ◽

10.1155/2019/2036728 ◽

2019 ◽

Vol 2019 ◽

pp. 1-18 ◽

Cited By ~ 4

Author(s):

Lei Xu ◽

Yi Liu ◽

Haobin Liu

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Fuzzy Set ◽

Group Decision ◽

Intuitionistic Fuzzy Set ◽

Aggregation Operator ◽

Aggregation Operators ◽

Weighted Averaging ◽

Pythagorean Fuzzy Set ◽

Fuzzy Aggregation

As a generalization of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS), q-rung orthopair fuzzy set (q-ROFS) is a new concept in describing complex fuzzy uncertainty information. The present work focuses on the multiattribute group decision-making (MAGDM) approach under the q-rung orthopair fuzzy information. To begin with, some drawbacks of the existing MAGDM methods based on aggregation operators (AOs) are firstly analyzed. In addition, some improved operational laws put forward to overcome the drawbacks along with some properties of the operational law are proved. Thirdly, we put forward the improved q-rung orthopair fuzzy-weighted averaging (q-IROFWA) aggregation operator and improved q-rung orthopair fuzzy-weighted power averaging (q-IROFWPA) aggregation operator and present some of their properties. Then, based on the q-IROFWA operator and q-IROFWPA operator, we proposed a new method to deal with MAGDM problems under the fuzzy environment. Finally, some numerical examples are provided to illustrate the feasibility and validity of the proposed method.

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The Maximizing Deviation Method Based on Interval-Valued Pythagorean Fuzzy Weighted Aggregating Operator for Multiple Criteria Group Decision Analysis

Discrete Dynamics in Nature and Society ◽

10.1155/2015/746572 ◽

2015 ◽

Vol 2015 ◽

pp. 1-15 ◽

Cited By ~ 32

Author(s):

Wei Liang ◽

Xiaolu Zhang ◽

Manfeng Liu

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Fuzzy Set ◽

Group Decision ◽

Intuitionistic Fuzzy Set ◽

Pythagorean Fuzzy Set ◽

Intuitionistic Fuzzy ◽

Maximizing Deviation Method ◽

Interval Valued ◽

Deviation Method

As a new extension of Pythagorean fuzzy set (also called Atanassov’s intuitionistic fuzzy set of second type), interval-valued Pythagorean fuzzy set which is parallel to Atanassov’s interval-valued intuitionistic fuzzy set has recently been developed to model imprecise and ambiguous information in practical group decision making problems. The aim of this paper is to put forward a novel decision making method for handling multiple criteria group decision making problems within interval-valued Pythagorean fuzzy environment based on interval-valued Pythagorean fuzzy numbers (IVPFNs). There are three key issues being addressed in this approach. The first is to introduce an interval-valued Pythagorean fuzzy weighted arithmetic averaging (IVPF-WAA) operator to aggregate the decision data in order to get the overall preference values of alternatives. Some desirable properties of the IVPF-WAA operator are also investigated. Based on the idea of the maximizing deviation method, the second is to establish an optimization model for determining the weights of criteria for each expert. The third is to construct a minimizing consistency optimal model to derive the weights of criteria for the group. Finally, an illustrating example is given to verify the proposed approach.

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

Journal of Intelligent Systems ◽

10.1515/jisys-2017-0212 ◽

2018 ◽

Vol 29 (1) ◽

pp. 393-408 ◽

Cited By ~ 11

Author(s):

Khaista Rahman ◽

Saleem Abdullah ◽

Muhammad Sajjad Ali Khan

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Aggregation Operator ◽

Aggregation Operators ◽

Decision Makers ◽

Weighted Averaging ◽

Fuzzy Information ◽

Multiple Attribute ◽

Interval Valued

Abstract 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.

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INTERVAL-VALUED INTUITIONISTIC FUZZY ORDERED PRECISE WEIGHTED AGGREGATION OPERATOR AND ITS APPLICATION IN GROUP DECISION MAKING

Technological and Economic Development of Economy ◽

10.3846/20294913.2013.869516 ◽

2014 ◽

Vol 20 (4) ◽

pp. 648-672 ◽

Cited By ~ 13

Author(s):

Wei Zhou ◽

Jian Min He

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Scale Invariance ◽

Group Decision ◽

Aggregation Operator ◽

Aggregation Operators ◽

Weighted Averaging ◽

Intuitionistic Fuzzy ◽

Fuzzy Aggregation ◽

Interval Valued

An important research topic related to the theory and application of the interval-valued intuitionistic fuzzy weighted aggregation operators is how to determine their associated weights. In this paper, we propose a precise weight-determined (PWD) method of the monotonicity and scale-invariance, just based on the new score and accuracy functions of interval-valued intuitionistic fuzzy number (IIFN). Since the monotonicity and scale-invariance, the PWD method may be a precise and objective approach to calculate the weights of IIFN and interval-valued intuitionistic fuzzy aggregation operator, and a more suitable approach to distinguish different decision makers (DMs) and experts in group decision making. Based on the PWD method, we develop two new interval-valued intuitionistic fuzzy aggregation operators, i.e. interval-valued intuitionistic fuzzy ordered precise weighted averaging (IIFOPWA) operator and interval-valued intuitionistic fuzzy ordered precise weighted geometric (IIFOPWG) operator, and study their desirable properties in detail. Finally, we provide an illustrative example.

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

Complexity ◽

10.1155/2017/5937376 ◽

2017 ◽

Vol 2017 ◽

pp. 1-16 ◽

Cited By ~ 39

Author(s):

Runtong Zhang ◽

Jun Wang ◽

Xiaomin Zhu ◽

Meimei Xia ◽

Ming Yu

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Fuzzy Set ◽

Group Decision ◽

Geometric Mean ◽

Intuitionistic Fuzzy Set ◽

Aggregation Operators ◽

Pythagorean Fuzzy Set ◽

Bonferroni Mean ◽

Novel Approach

The Pythagorean fuzzy set as an extension of the intuitionistic fuzzy set characterized by membership and nonmembership degrees has been introduced recently. Accordingly, the square sum of the membership and nonmembership degrees is a maximum of one. The Pythagorean fuzzy set has been previously applied to multiattribute group decision-making. This study develops a few aggregation operators for fusing the Pythagorean fuzzy information, and a novel approach to decision-making is introduced based on the proposed operators. First, we extend the generalized Bonferroni mean to the Pythagorean fuzzy environment and introduce the generalized Pythagorean fuzzy Bonferroni mean and the generalized Pythagorean fuzzy Bonferroni geometric mean. Second, a new generalization of the Bonferroni mean, namely, the dual generalized Bonferroni mean, is proposed by considering the shortcomings of the generalized Bonferroni mean. Furthermore, we investigate the dual generalized Bonferroni mean in the Pythagorean fuzzy sets and introduce the dual generalized Pythagorean fuzzy Bonferroni mean and dual generalized Pythagorean fuzzy Bonferroni geometric mean. Third, a novel approach to multiattribute group decision-making based on proposed operators is proposed. Lastly, a numerical instance is provided to illustrate the validity of the new approach.

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Multi-criteria group decision making with Pythagorean fuzzy soft topology

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-190854 ◽

2020 ◽

Vol 39 (5) ◽

pp. 6703-6720

Author(s):

Muhammad Riaz ◽

Khalid Naeem ◽

Muhammad Aslam ◽

Deeba Afzal ◽

Fuad Ali Ahmed Almahdi ◽

...

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Fuzzy Set ◽

Real World ◽

Group Decision ◽

Intuitionistic Fuzzy Set ◽

Soft Set ◽

Fuzzy Soft Set ◽

Pythagorean Fuzzy Set ◽

Soft Topology

Pythagorean fuzzy set (PFS) introduced by Yager (2013) is the extension of intuitionistic fuzzy set (IFS) introduced by Atanassov (1983). PFS is also known as IFS of type-2. Pythagorean fuzzy soft set (PFSS), introduced by Peng et al. (2015) and later studied by Guleria and Bajaj (2019) and Naeem et al. (2019), are very helpful in representing vague information that occurs in real world circumstances. In this article, we introduce the notion of Pythagorean fuzzy soft topology (PFS-topology) defined on Pythagorean fuzzy soft set (PFSS). We define PFS-basis, PFS-subspace, PFS-interior, PFS-closure and boundary of PFSS. We introduce Pythagorean fuzzy soft separation axioms, Pythagorean fuzzy soft regular and normal spaces. Furthermore, we present an application of PFSSs to multiple criteria group decision making (MCGDM) using choice value method in the real world problems which yields the optimum results for investment in the stock exchange. We also render an application of PFS-topology in medical diagnosis using TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution). The applications are accompanied by Algorithms, flow charts and statistical diagrams.

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