Series of Aggregation Operators for Picture Fuzzy Environments and Their Applications

2020 ◽  
pp. 328-351
Author(s):  
Saleem Abdullah ◽  
Shahzaib Ashraf
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Number ◽  
Group Decision ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Previous Model ◽  
Weighted Averaging ◽  
Fuzzy Information

The main objective of the chapter is to introduce a series of picture fuzzy weighted averaging and geometric aggregation operators by using t-norm and t-conorm. In this chapter, they discussed generalized form of weighted averaging and geometric aggregation operator for picture fuzzy information. Further, the proposed aggregation operators of picture fuzzy number are applied to multi-attribute group decision making problems. To implement the proposed models, they provide some numerical applications of group decision making problems. Also compared with previous model, they conclude that the proposed technique is more effective and reliable.

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

2018 ◽  
Vol 29 (1) ◽  
pp. 393-408 ◽  
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.

scholarly journals Interval-Valued Hesitant Fuzzy Multiattribute Group Decision Making Based on Improved Hamacher Aggregation Operators and Continuous Entropy

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Jun Liu ◽  
Ning Zhou ◽  
Li-Hua Zhuang ◽  
Ning Li ◽  
Fei-Fei Jin
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Information Aggregation ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Ordered Weighted Averaging ◽  
Cowa Operator ◽  
Interval Valued

Under the interval-valued hesitant fuzzy information environment, we investigate a multiattribute group decision making (MAGDM) method with continuous entropy weights and improved Hamacher information aggregation operators. Firstly, we introduce the axiomatic definition of entropy for interval-valued hesitant fuzzy elements (IVHFEs) and construct a continuous entropy formula on the basis of the continuous ordered weighted averaging (COWA) operator. Then, based on the Hamachert-norm andt-conorm, the adjusted operational laws for IVHFEs are defined. In order to aggregate interval-valued hesitant fuzzy information, some new improved interval-valued hesitant fuzzy Hamacher aggregation operators are investigated, including the improved interval-valued hesitant fuzzy Hamacher ordered weighted averaging (I-IVHFHOWA) operator and the improved interval-valued hesitant fuzzy Hamacher ordered weighted geometric (I-IVHFHOWG) operator, the desirable properties of which are discussed. In addition, the relationship among these proposed operators is analyzed in detail. Applying the continuous entropy and the proposed operators, an approach to MAGDM is developed. Finally, a numerical example for emergency operating center (EOC) selection is provided, and comparative analyses with existing methods are performed to demonstrate that the proposed approach is both valid and practical to deal with group decision making problems.

scholarly journals Archimedean Muirhead Aggregation Operators of q-Rung Orthopair Fuzzy Numbers for Multicriteria Group Decision Making

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-33 ◽  
Author(s):  
Yuchu Qin ◽  
Xiaolan Cui ◽  
Meifa Huang ◽  
Yanru Zhong ◽  
Zhemin Tang ◽  
...  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Number ◽  
Group Decision ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Intuitionistic Fuzzy Number ◽  
Fuzzy Information ◽  
Qualitative And Quantitative ◽  
Multicriteria Group Decision Making

q-Rung orthopair fuzzy number (qROFN) is a flexible and superior fuzzy information description tool which can provide stronger expressiveness than intuitionistic fuzzy number and Pythagorean fuzzy number. Muirhead mean (MM) operator and its dual form geometric MM (GMM) operator are two all-in-one aggregation operators for capturing the interrelationships of the aggregated arguments because they are applicable in the cases in which all arguments are independent of each other, there are interrelationships between any two arguments, and there are interrelationships among any three or more arguments. Archimedean T-norm and T-conorm (ATT) are superior operations that can generate general and versatile operational rules to aggregate arguments. To take advantage of qROFN, MM operator, GMM operator, and ATT in multicriteria group decision making (MCGDM), an Archimedean MM operator, a weighted Archimedean MM operator, an Archimedean GMM operator, and a weighted Archimedean GMM operator for aggregating qROFNs are presented to solve the MCGDM problems based on qROFNs in this paper. The properties of these operators are explored and their specific cases are discussed. On the basis of the presented operators, a method for solving the MCGDM problems based on qROFNs is proposed. The effectiveness of the proposed method is demonstrated via a numerical example, a set of experiments, and qualitative and quantitative comparisons. The demonstration results suggest that the proposed method has satisfying generality and flexibility at aggregating q-rung orthopair fuzzy information and capturing the interrelationships of criteria and the attitudes of decision makers and is feasible and effective for solving the MCGDM problems based on qROFNs.

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

2014 ◽  
Vol 20 (4) ◽  
pp. 648-672 ◽  
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.

scholarly journals Solution of multi-criteria group decision making problem based on picture linguistic informations

2019 ◽  
Vol 8 (1-2) ◽  
pp. 1-11 ◽  
Author(s):  
Muhammad Qiyas ◽  
Saleem Abdullah ◽  
Shahzaib Ashraf
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Multiple Attribute ◽  
Decision Making Problem ◽  
Linguistic Term ◽  
Score Index

The aim of this paper is applying the linguistic term and linguistic variables to picture fuzzy information. In this article the multiple attribute group decision making is considered. First we develop the picture linguistic averaging aggregation operators based on new operation on picture fuzzy information. For the (MCGDM) problems with picture linguistic information, we define a score index and accuracy index of (PLNs), and prefer a technique to the correlation among the two (PLNs). Simultaneously, some operation laws for (PLNs) are defined and the related properties are studied. Further, some aggregation operators are developed: picture linguistic weighted averaging (PLWA), picture linguistic ordered weighted averaging (PLOWA), picture linguistic hybrid averaging (PLHA) operators

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

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
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.

scholarly journals Triangular Cubic Hesitant Fuzzy Einstein Hybrid Weighted Averaging Operator and Its Application to Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 658 ◽  
Author(s):  
Aliya Fahmi ◽  
Fazli Amin ◽  
Florentin Smarandache ◽  
Madad Khan ◽  
Nasruddin Hassan
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Linguistic Information ◽  
Ordered Weighted Averaging ◽  
Averaging Operator ◽  
Multiple Attribute ◽  
The Relationship

In this paper, triangular cubic hesitant fuzzy Einstein weighted averaging (TCHFEWA) operator, triangular cubic hesitant fuzzy Einstein ordered weighted averaging (TCHFEOWA) operator and triangular cubic hesitant fuzzy Einstein hybrid weighted averaging (TCHFEHWA) operator are proposed. An approach to multiple attribute group decision making with linguistic information is developed based on the TCHFEWA and the TCHFEHWA operators. Furthermore, we establish various properties of these operators and derive the relationship between the proposed operators and the existing aggregation operators. Finally, a numerical example is provided to demonstrate the application of the established approach.

scholarly journals Group Decision Making Based on Triangular Neutrosophic Cubic Fuzzy Einstein Hybrid Weighted Averaging Operators

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 180 ◽  
Author(s):  
Aliya Fahmi ◽  
Fazli Amin ◽  
Madad Khan ◽  
Florentin Smarandache
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Averaging Operators ◽  
Ordered Weighted Averaging ◽  
Multiple Attribute

In this paper, a new concept of the triangular neutrosophic cubic fuzzy numbers (TNCFNs), their score and accuracy functions are introduced. Based on TNCFNs, some new Einstein aggregation operators, such as the triangular neutrosophic cubic fuzzy Einstein weighted averaging (TNCFEWA), triangular neutrosophic cubic fuzzy Einstein ordered weighted averaging (TNCFEOWA) and triangular neutrosophic cubic fuzzy Einstein hybrid weighted averaging (TNCFEHWA) operators are developed. Furthermore, their application to multiple-attribute decision-making with triangular neutrosophic cubic fuzzy (TNCF) information is discussed. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

scholarly journals FUCOM-MARCOS based Group Decision-making using Dombi Power Aggregation of Dual Probabilistic Linguistic Information

2021 ◽  
Author(s):  
Abhijit Saha ◽  
Arunodaya Raj Mishra ◽  
Pratibha Rani
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Average Operator ◽  
Sensitivity Assessment ◽  
Probabilistic Linguistic Term Sets ◽  
The Stability ◽  
System Selection

Abstract The dual probabilistic linguistic (DPL) term sets are considered superior to probabilistic linguistic term sets. The power average operator can lessen the effects of the extreme assessing data from some decision-makers with prejudice. Further, the Dombi operators are quite flexible with the general parameter during the aggregation process. Moreover, based on deviation from the maximum consistency by the exclusion of the concern of the redundancy of the comparisons made in criteria pairs, FUCOM (full consistency method) is utilized as a subjective criteria weight computing model. Besides, MARCOS (Measurements alternatives and ranking according to compromise solution) method is based on the determination of utility degrees according to the distance from anti-ideal and ideal solutions and their aggregations. In this study, we combine the merits of power average operator, Dombi operator, FUCOM technique and MARCOS for dealing with multi-criteria group decision-making (MCGDM) problems under a DPL setting where rank of the alternatives are obtained through MARCOS method. For aggregating decision-experts preferences, we propose two types of operators, namely- DPL Dombi power weighted averaging and DPL Dombi power weighted geometric aggregation operators. We discuss the elegant properties of these proposed aggregation operators. We provide a case study regarding open source software learning management system selection to focus the practicability and usefulness of the proposed approach. Furthermore, we perform a sensitivity assessment on diverse criteria weight sets in order to test the stability of our developed intriguing approach. To this effect, we also provide a comparison between our approach with various extant methods.

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