A further investigation on q-rung orthopair fuzzy Einstein aggregation operators

2021 ◽  
pp. 1-19
Author(s):  
Wen Sheng
Keyword(s):  
Aggregation Operators ◽  
Weighted Averaging ◽  
Agricultural Product ◽  
Traceability System ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Shift Invariance ◽  
Algebraic Operations ◽  
Einstein Operations ◽  
Important Branch

Aggregation of q-rung orthopair fuzzy information serves as an important branch of the q-rung orthopair fuzzy set theory, where operations on q-rung orthopair fuzzy values (q-ROFVs) play a crucial role. Recently, aggregation operators on q-ROFVs were established by employing the Einstein operations rather than the algebraic operations. In this paper, we give a further investigation on operations and aggregation operators for q-ROFVs based on the Einstein operational laws. We present the operational principles of Einstein operations over q-ROFVs and compare them with those built on the algebraic operations. The properties of the q-rung orthopair fuzzy Einstein weighted averaging (q-ROFEWA) operator and q-rung orthopair fuzzy Einstein weighted geometric (q-ROFEWG) operator are investigated in detail, such as idempotency, monotonicity, boundedness, shift-invariance and homogeneity. Then, the developed operators are applied to multiattribute decision making problems under the q-rung orthopair fuzzy environment. Finally, an example for selecting the design scheme for a blockchain-based agricultural product traceability system is presented to illustrate the feasibility and effectiveness of the proposed methods.

scholarly journals Some Aggregation Operators Based on Einstein Operations under Interval-Valued Dual Hesitant Fuzzy Setting and Their Application

2014 ◽  
Vol 2014 ◽  
pp. 1-21 ◽  
Author(s):  
Wenkai Zhang ◽  
Xia Li ◽  
Yanbing Ju
Keyword(s):  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Operator Interval ◽  
Multiple Attribute ◽  
Einstein Operations ◽  
The Relationship ◽  
Interval Valued

We investigate the multiple attribute decision making (MADM) problems in which attribute values take the form of interval-valued dual hesitant fuzzy information. Firstly, some operational laws for interval-valued dual hesitation fuzzy elements (IVDHFEs) based on Einstein operations are developed. Then we develop some aggregation operators based on Einstein operations: the interval-valued dual hesitant fuzzy Einstein weighted averaging (IVDHFEWA) operator, interval-valued dual hesitant fuzzy Einstein ordered weighted averaging (IVDHFEOWA) operator, interval-valued dual hesitant fuzzy Einstein hybrid averaging (IVDHFEHA) operator, interval-valued dual hesitant fuzzy Einstein weighted geometric (IVDHFEWG) operator, interval-valued dual hesitant fuzzy Einstein ordered weighted geometric (IVDHFEOWG) operator, and interval-valued dual hesitant fuzzy Einstein hybrid geometric (IVDHFEHG) operator. Furthermore, we discuss some desirable properties of these operators, and investigate the relationship between the developed operators and the existing ones. Based on the IVDHFEWA operator, an approach to MADM problems is proposed under the interval-valued dual hesitant fuzzy environment. Finally, a numerical example is given to show the application of the developed method, and a comparison analysis is conducted to demonstrate the effectiveness of the proposed approach.

scholarly journals A New Ranking Methodology for Pythagorean Trapezoidal Uncertain Linguistic Fuzzy Sets Based on Einstein Operations

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 440 ◽  
Author(s):  
Arshad Khan ◽  
Saleem Abdullah ◽  
Muhammad Shakeel ◽  
Faisal Khan ◽  
Noor Amin ◽  
...  
Keyword(s):  
Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Decision Making Process ◽  
Ordered Weighted Averaging ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Fuzzy Aggregation ◽  
Einstein Operations

In this article, we proposed new Pythagorean trapezoidal uncertain linguistic fuzzy aggregation information—namely, the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein weighted averaging (PTULFEWA) operator, the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein ordered weighted averaging (PTULFEOWA) operator, and the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein hybrid weighted averaging (PTULFEHWA) operator—using the Einstein operational laws. We studied some important properties of the suggested aggregation operators and showed that the PTULFEHWA is more general than the other proposed operators, which simplifies these aggregation operators. Furthermore, we presented a multiple attribute group decision making (MADM) process for the proposed aggregation operators under the Pythagorean trapezoidal uncertain linguistic fuzzy (PTULF) environment. A numerical example was constructed to determine the effectiveness and practicality of the proposed approach. Lastly, a comparative analysis was performed of the presented approach with existing approaches to show that the proposed method is consistent and provides more information that may be useful for complex problems in the decision-making process.

scholarly journals Complex T-Spherical Fuzzy Aggregation Operators with Application to Multi-Attribute Decision Making

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1311 ◽  
Author(s):  
Zeeshan Ali ◽  
Tahir Mahmood ◽  
Miin-Shen Yang
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
The Novel ◽  
Fuzzy Environment ◽  
Novel Approach ◽  
Operational Laws ◽  
Comparison Results ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making

In this paper, the novel approach of complex T-spherical fuzzy sets (CTSFSs) and their operational laws are explored and also verified with the help of examples. CTSFS composes the grade of truth, abstinence, and falsity with a condition that the sum of q-power of the real part (also for imaginary part) of the truth, abstinence, and falsity grades cannot be exceeded from a unit interval. Additionally, to examine the interrelationships among the complex T-spherical fuzzy numbers (CTSFNs), we propose two aggregation operators, called complex T-spherical fuzzy weighted averaging (CTSFWA) and complex T-spherical fuzzy weighted geometric (CTSFWG) operators. A multi-attribute decision making (MADM) problem is resolved based on CTSFNs by using the proposed CTSFWA and CTSFWG operators. To examine the proficiency and reliability of the explored works, we use an example to make comparisons between the proposed operators and some existing operators. Based on the comparison results, the proposed CTSFWA and CTSFWG operators are well suited in the fuzzy environment with legitimacy and prevalence by contrasting other existing operators.

More on Dombi operations and Dombi aggregation operators for q-rung orthopair fuzzy values

2020 ◽  
Vol 39 (3) ◽  
pp. 3715-3735
Author(s):  
Wen Sheng Du
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fundamental Properties ◽  
Fuzzy Environment ◽  
Investment Companies ◽  
Special Cases ◽  
Shift Invariance ◽  
Definition Of ◽  
Dombi Operations

Dombi operations which include the Dombi product and Dombi sum are special cases of t-norms and t-conorms besides the algebraic operations. Recently, operations and aggregation operators for q-rung orthopair fuzzy values (q-ROFVs) based on Dombi operations were proposed. In this paper, we further discuss some additional issues relating to Dombi operations and Dombi aggregation operators of q-ROFVs. First, we give a reasonable explanation for the definition of the Dombi scalar multiplication and Dombi exponentiation which are constructed respectively by the Dombi sum and Dombi product over q-ROFVs, and then investigate the fundamental properties of these operations. Subsequently, the shift-invariance and homogeneity properties of the q-rung orthopair fuzzy Dombi weighted averaging/geometric operators are analyzed. And the boundedness of aforementioned aggregation operators are precisely characterized with respect to the parameter in Dombi operations. Finally, a method for multiattribute decision making is proposed by utilizing the developed operators under the q-rung orthopair fuzzy environment and an example of the selection of investment companies is given to illustrate the detailed decision making process.

scholarly journals Approach to Multi-Attribute Decision-Making Methods for Performance Evaluation Process Using Interval-Valued T-Spherical Fuzzy Hamacher Aggregation Information

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 145
Author(s):  
Yun Jin ◽  
Zareena Kousar ◽  
Kifayat Ullah ◽  
Tahir Mahmood ◽  
Nimet Yapici Pehlivan ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Evaluation Process ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Membership Degree ◽  
Operational Laws ◽  
Multi Attribute Decision Making ◽  
Interval Valued ◽  
Do So

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

An approach for supplier selection problem based on picture cubic fuzzy aggregation operators

2021 ◽  
Vol 40 (5) ◽  
pp. 10145-10162
Author(s):  
Ahmad Bakr Khoshaim ◽  
Muhammad Qiyas ◽  
Saleem Abdullah ◽  
Muhammad Naeem ◽  
Muneeza
Keyword(s):  
Supply Chain ◽  
Supply Chain Management ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Numerical Application ◽  
Chain Management ◽  
Fuzzy Environment ◽  
Picture Fuzzy Set ◽  
Fuzzy Aggregation ◽  
Fuzzy Order

This article is an advanced approach to picture fuzzy set through the application of cubic set theory. For instance, we establish the idea of the picture cubic fuzzy sets (PCFSs) theory and define several operations for PCFS. Also, presented some weighted aggregation operators under picture cubic fuzzy information, so called picture cubic fuzzy weighted averaging (PCFWA) operator, picture cubic fuzzy order weighted averaging (PCFOWA) operator, picture cubic fuzzy weighted geometric (PCFWG) operator, and picture cubic fuzzy order weighted geometric (PCFOWG) operator. Further, we study their fundamental properties and showed the relationship among these aggregation operators. In order to determine the feasibility and practicality of the mentioned new technique, we developed multi-attribute group decision -making algorithm with picture cubic fuzzy environment. Further, the developed method applied to supply chain management and for implementation, consider numerical application of supply chain management. Compared the developed approach with other preexisting aggregation operators, and we concluded that the defined technique is better, reliable and effective.

New Einstein Hybrid Aggregation Operators for Intuitionistic Fuzzy Sets and Applications in Multi-Criteria Decision-Making

2019 ◽  
pp. 252-283
Author(s):  
Bhagawati Prasad Joshi ◽  
Abhay Kumar
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Decision Maker ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Decision Making Processes

The fusion of multidimensional intuitionistic fuzzy information plays an important part in decision making processes under an intuitionistic fuzzy environment. In this chapter, it is observed that existing intuitionistic fuzzy Einstein hybrid aggregation operators do not follow the idempotency and boundedness. This leads to sometimes illogical and even absurd results to the decision maker. Hence, some new intuitionistic fuzzy Einstein hybrid aggregation operators such as the new intuitionistic fuzzy Einstein hybrid weighted averaging (IFEHWA) and the new intuitionistic fuzzy Einstein hybrid weighted geometric (IFEHWG) were developed. The new IFEHWA and IFEHWG operators can weigh the arguments as well as their ordered positions the same as the intuitionistic fuzzy Einstein hybrid aggregation operators do. Further, it is validated that the defined operators are idempotent, bounded, monotonic and commutative. Then, based on the developed approach, a multi-criteria decision-making (MCDM) procedure is given. Finally, a numerical example is conducted to demonstrate the proposed method effectively.

scholarly journals Extensions of Dombi Aggregation Operators for Decision Making under m-Polar Fuzzy Information

2020 ◽  
Vol 2020 ◽  
pp. 1-20 ◽  
Author(s):  
Muhammad Akram ◽  
Naveed Yaqoob ◽  
Ghous Ali ◽  
Wathek Chammam
Keyword(s):  
Decision Making ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Ordered Weighted Averaging ◽  
Fuzzy Environment ◽  
Proposed Model ◽  
Electre I ◽  
Geometric Operator

An m-polar fuzzy set is a powerful mathematical model to analyze multipolar, multiattribute, and multi-index data. The m-polar fuzzy sets have appeared as a useful tool to portray uncertainty in multiattribute decision making. The purpose of this article is to analyze the aggregation operators under the m-polar fuzzy environment with the help of Dombi norm operations. In this article, we develop some averaging and geometric aggregation operators using Dombi t-norm and t-conorm to handle uncertainty in m-polar fuzzy (mF, henceforth) information, which are mF Dombi weighted averaging (mFDWA) operator, mF Dombi ordered weighted averaging (mFDOWA) operator, mF Dombi hybrid averaging (mFDHA) operator, mF Dombi weighted geometric (mFDWG) operator, mF Dombi weighted ordered geometric operator, and mF Dombi hybrid geometric (mFDHG) operator. We investigate properties, namely, idempotency, monotonicity, and boundedness, for the proposed operators. Moreover, we give an algorithm to solve multicriteria decision-making issues which involve mF information with mFDWA and mFDWG operators. To prove the validity and feasibility of the proposed model, we solve two numerical examples with our proposed models and give comparison with mF-ELECTRE-I approach (Akram et al. 2019) and mF Hamacher aggregation operators (Waseem et al. 2019). Finally, we check the effectiveness of the developed operators by a validity test.

scholarly journals A Novel Multiple Attribute Satisfaction Evaluation Approach with Hesitant Intuitionistic Linguistic Fuzzy Information

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Shanghong Yang ◽  
Zhuo Sun ◽  
Yanbing Ju ◽  
Chengya Qiao
Keyword(s):  
Weighted Average ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Evaluation Approach ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Satisfaction Evaluation ◽  
Attribute Satisfaction

This paper investigates the multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant intuitionistic linguistic fuzzy element (HILFE). Firstly, motivated by the idea of intuitionistic linguistic variables (ILVs) and hesitant fuzzy elements (HFEs), the concept, operational laws, and comparison laws of HILFE are defined. Then, some aggregation operators are developed for aggregating the hesitant intuitionistic linguistic fuzzy information, such as hesitant intuitionistic linguistic fuzzy weighted aggregation operators, hesitant intuitionistic linguistic fuzzy ordered weighted aggregation operators, and generalized hesitant intuitionistic linguistic fuzzy weighted aggregation operators. Moreover, some desirable properties of these operators and the relationships between them are discussed. Based on the hesitant intuitionistic linguistic fuzzy weighted average (HILFWA) operator and the hesitant intuitionistic linguistic fuzzy weighted geometric (HILFWG) operator, an approach for evaluating satisfaction degree is proposed under hesitant intuitionistic linguistic fuzzy environment. Finally, a practical example of satisfaction evaluation for milk products is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness.

scholarly journals Decision Support System For Energy Source Selection Based On Credibility Fuzzy Information.

2021 ◽  
Author(s):  
Saleem Abdullah ◽  
Muhammad Yahya
Keyword(s):  
Energy Source ◽  
Decision Making ◽  
Decision Support ◽  
Support System ◽  
Fuzzy Numbers ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Source Selection ◽  
Operational Laws

Abstract This main objective of this work is to define some new operations of credibility fuzzy numbers using Hamacher t-norm and t-conorm. These operation are more generalized operation for credibility fuzzy numnbers, we apply these operations to aggregation operators for credibility fuzzy numbers. Furthermore, using the basic operational laws of Hamacher t-norm and t-conorm, we develop a series of credibility fuzzy Hamacher aggregation operators like credibility fuzzy Hamacher weighted averaging (CFHWA) and credibility fuzzy Hamacher geometric (CFHWG) aggregation operators. we also explained some of the proposed Hamacher aggregation operators properties like commutativity, idempotency and monotonicity. In order to validate the proposed Hamacher aggregation operators for credibility fuzzy numbers, we develop general algorithm for decision making technique under credibility fuzzy numbers and using these operators. The proposed algorithm is apply to electricity crises in Pakistan problems. Finally a comparison with other existing methods is done to check the accuracy and validation of the proposed methods. At rest the proposed method is verified by other well known methods.

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