scholarly journals Linguistic Neutrosophic Numbers Einstein Operator and Its Application in Decision Making

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 389 ◽  
Author(s):  
Fan ◽  
Feng ◽  
Hu
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Aggregation Operators ◽  
The Other ◽  
Linguistic Variable ◽  
Average Operator ◽  
Einstein Operation ◽  
Neutrosophic Number ◽  
Linguistic Neutrosophic Numbers ◽  
Einstein Product

Linguistic neutrosophic numbers (LNNs) include single-value neutrosophic numbers and linguistic variable numbers, which have been proposed by Fang and Ye. In this paper, we define the linguistic neutrosophic number Einstein sum, linguistic neutrosophic number Einstein product, and linguistic neutrosophic number Einstein exponentiation operations based on the Einstein operation. Then, we analyze some of the relationships between these operations. For LNN aggregation problems, we put forward two kinds of LNN aggregation operators, one is the LNN Einstein weighted average operator and the other is the LNN Einstein geometry (LNNEWG) operator. Then we present a method for solving decision-making problems based on LNNEWA and LNNEWG operators in the linguistic neutrosophic environment. Finally, we apply an example to verify the feasibility of these two methods.

Pythagorean Hesitant Fuzzy Hamacher Aggregation Operators in Multiple-Attribute Decision Making

2017 ◽  
Vol 28 (5) ◽  
pp. 759-776 ◽  
Author(s):  
Guiwu Wei ◽  
Mao Lu
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Average Operator ◽  
Multiple Attribute ◽  
Fuzzy Aggregation ◽  
Ordered Weighted Average ◽  
Algebraic Operations ◽  
Geometric Operator

Abstract The Hamacher product is a t-norm and the Hamacher sum is a t-conorm. They are good alternatives to the algebraic product and the algebraic sum, respectively. Nevertheless, it seems that most of the existing hesitant fuzzy aggregation operators are based on algebraic operations. In this paper, we utilize Hamacher operations to develop some Pythagorean hesitant fuzzy aggregation operators: Pythagorean hesitant fuzzy Hamacher weighted average operator, Pythagorean hesitant fuzzy Hamacher weighted geometric operator, Pythagorean hesitant fuzzy Hamacher ordered weighted average operator, Pythagorean hesitant fuzzy Hamacher ordered weighted geometric operator, Pythagorean hesitant fuzzy Hamacher hybrid average operator, and Pythagorean hesitant fuzzy Hamacher hybrid geometric operator. The prominent characteristics of these proposed operators are studied. Then, we utilize these operators to develop some approaches for solving the Pythagorean hesitant fuzzy multiple-attribute decision-making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

scholarly journals Decision Method of Probabilistic Hesitant Fuzzy Information Based on Hamacher Aggregation Operators and MULTIMOORA

2020 ◽  
Vol 38 (6) ◽  
pp. 1361-1369
Author(s):  
Yahui Zhu ◽  
Li Gao
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Multiple Perspectives ◽  
Average Operator ◽  
Decision Method ◽  
Geometric Average ◽  
Multi Attribute Decision Making ◽  
Multimoora Method

Aiming at solving the problem of probability hesitation fuzzy multi-attribute decision making, a new decision-making method of probability hesitation fuzzy multi-attribute is proposed in this paper, based on Hamacher operations and MULTIMOORA method. Firstly, probability hesitation fuzzy Hamacher operations are defined, including sum, product, scalar multiplication and exponentiation, and their properties are studied. On this basis, probability hesitation fuzzy Hamacher weighted average operator and probability hesitation fuzzy Hamacher weighted geometric average operator are proposed, and their properties are also studied. Secondly, alternative from multiple perspectives are chosen and compared by using the MULTIMOORA method. Finally, the effectiveness and feasibility of the decision-making method are verified by an example.

scholarly journals A Hybrid Method for Complex Pythagorean Fuzzy Decision Making

2021 ◽  
Vol 2021 ◽  
pp. 1-23
Author(s):  
Muhammad Akram ◽  
Samirah Alsulami ◽  
Kiran Zahid
Keyword(s):  
Decision Making ◽  
Uncertain Data ◽  
Fuzzy Model ◽  
Weighted Average ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Decision Making ◽  
Average Operator ◽  
Fuzzy Aggregation ◽  
Selection Of

This article takes advantage of advancements in two different fields in order to produce a novel decision-making framework. First, we contribute to the theory of aggregation operators, which are mappings that combine large amounts of data into more advantageous forms. They are extensively used in different settings from classical to fuzzy set theory alike. Secondly, we expand the literature on complex Pythagorean fuzzy model, which has an edge over other models due to its ability to handle uncertain data of periodic nature. We propose some aggregation operators for complex Pythagorean fuzzy numbers that depend on the Hamacher t-norm and t-conorm, namely, the complex Pythagorean fuzzy Hamacher weighted average operator, the complex Pythagorean fuzzy Hamacher ordered weighted average operator, and the complex Pythagorean fuzzy Hamacher hybrid average operator. We explore some properties of these operators inclusive of idempotency, monotonicity, and boundedness. Then, the operators are applied to multicriteria decision-making problems under the complex Pythagorean fuzzy environment. Furthermore, we present an algorithm along with a flow chart, and we demonstrate their applicability with the assistance of two numerical examples (selection of most favorable country for immigrants and selection of the best programming language). We investigate the adequacy of this algorithm by conducting a comparative study with the case of complex intuitionistic fuzzy aggregation operators.

scholarly journals Multi-Attribute Decision-Making Based on m-Polar Fuzzy Hamacher Aggregation Operators

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1498 ◽  
Author(s):  
Neha Waseem ◽  
Muhammad Akram ◽  
José Carlos R. Alcantud
Keyword(s):  
Decision Making ◽  
Waste Treatment ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Average Operator ◽  
Electre I ◽  
Multi Attribute Decision Making ◽  
Algorithmic Model ◽  
Geometric Operator ◽  
Health Care Waste

In this paper, we introduce certain aggregation operators, namely, the m-polar fuzzy (mF) Hamacher weighted average operator, mF Hamacher ordered weighted average (mFHOWA) operator, mF Hamacher hybrid average (mFHHA) operator, mF Hamacher weighted geometric (mFHWG) operator, mF Hamacher weighted ordered geometric operator, and mF Hamacher hybrid geometric (mFHHG) operator. We discuss some properties of these operators, inclusive of their ability to implement both symmetric and asymmetric treatments of the items. We develop an algorithmic model to solve multi-attribute decision-making (MADM) problems in mF environment using mF Hamacher weighted average operator (mFHWA) and mFHWG operators. They can compensate for the possible asymmetric roles of the attributes that describe the problem. In the end, to prove the validity and feasibility of the proposed work, we give applications for selecting the most affected country regarding human trafficking, selecting health care waste treatment methods and selecting the best company for investment. We also solve practical MADM problems by using ELECTRE-I method, and give a comparative analysis.

scholarly journals A Novel Multi-Criteria Group Decision-Making Approach Based on Bonferroni and Heronian Mean Operators under Hesitant 2-Tuple Linguistic Environment

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1489
Author(s):  
Shahzad Faizi ◽  
Wojciech Sałabun ◽  
Nisbha Shaheen ◽  
Atiq ur Rehman ◽  
Jarosław Wątróbski
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Geometric Bonferroni Mean ◽  
The Individual ◽  
Heronian Mean

Ambiguous and uncertain facts can be handled using a hesitant 2-tuple linguistic set (H2TLS), an important expansion of the 2-tuple linguistic set. The vagueness and uncertainty of data can be grabbed by using aggregation operators. Therefore, aggregation operators play an important role in computational processes to merge the information provided by decision makers (DMs). Furthermore, the aggregation operator is a potential mechanism for merging multisource data which is synonymous with cooperative preference. The aggregation operators need to be studied and analyzed from various perspectives to represent complex choice situations more readily and capture the diverse experiences of DMs. In this manuscript, we propose some valuable operational laws for H2TLS. These new operational laws work through the individual aggregation of linguistic words and the collection of translation parameters. We introduced a hesitant 2-tuple linguistic weighted average (H2TLWA) operator to solve multi-criteria group decision-making (MCGDM) problems. We also define hesitant 2-tuple linguistic Bonferroni mean (H2TLBM) operator, hesitant 2-tuple linguistic geometric Bonferroni mean (H2TLGBM) operator, hesitant 2-tuple linguistic Heronian mean (H2TLHM) operator, and a hesitant 2-tuple linguistic geometric Heronian mean (H2TLGHM) operator based on the novel operational laws proposed in this paper. We define the aggregation operators for addition, subtraction, multiplication, division, scalar multiplication, power and complement with their respective properties. An application example and comparison analysis were examined to show the usefulness and practicality of the work.

scholarly journals METHODS FOR PROBABILISTIC DECISION MAKING WITH LINGUISTIC INFORMATION

2014 ◽  
Vol 20 (2) ◽  
pp. 193-209 ◽  
Author(s):  
Guiwu Wei ◽  
Xiaofei Zhao
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Uncertain Information ◽  
Owa Operator ◽  
Linguistic Information ◽  
Probabilistic Information ◽  
Ordered Weighted Average ◽  
Linguistic Labels ◽  
Selection Of

With respect to decision making problems by using probabilities, immediate probabilities and information that can be represented with linguistic labels, some new decision analysis are proposed. Firstly, we shall develop three new aggregation operators: generalized probabilistic 2-tuple weighted average (GP-2TWA) operator, generalized probabilistic 2-tuple ordered weighted average (GP-2TOWA) operator and generalized immediate probabilistic 2-tuple ordered weighted average (GIP-2TOWA) operator. These operators use the weighted average (WA) operator, the ordered weighted average (OWA) operator, linguistic information, probabilistic information and immediate probabilistic information. They are quite useful because they can assess the uncertain information within the problem by using both linguistic labels and the probabilistic information that considers the attitudinal character of the decision maker. In these approaches, alternative appraisal values are calculated by the aggregation of 2-tuple linguistic information. Thus, the ranking of alternative or selection of the most desirable alternative(s) is obtained by the comparison of 2-tuple linguistic information. Finally, we give an illustrative example about selection of strategies to verify the developed approach and to demonstrate its feasibility and practicality.

Pythagorean probabilistic hesitant fuzzy aggregation operators and their application in decision-making

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Bushra Batool ◽  
Saleem Abdullah ◽  
Shahzaib Ashraf ◽  
Mumtaz Ahmad
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Content Type ◽  
Operational Laws ◽  
Fuzzy Aggregation ◽  
Emergency Decision Making ◽  
Emergency Decision ◽  
Established Technique

PurposeThis is mainly because the restrictive condition of intuitionistic hesitant fuzzy number (IHFN) is relaxed by the membership functions of Pythagorean probabilistic hesitant fuzzy number (PyPHFN), so the range of domain value of PyPHFN is greatly expanded. The paper aims to develop a novel decision-making technique based on aggregation operators under PyPHFNs. For this, the authors propose Algebraic operational laws using algebraic norm for PyPHFNs. Furthermore, a list of aggregation operators, namely Pythagorean probabilistic hesitant fuzzy weighted average (PyPHFWA) operator, Pythagorean probabilistic hesitant fuzzy weighted geometric (PyPHFWG) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted average (PyPHFOWA) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted geometric (PyPHFOWG) operator, Pythagorean probabilistic hesitant fuzzy hybrid weighted average (PyPHFHWA) operator and Pythagorean probabilistic hesitant fuzzy hybrid weighted geometric (PyPHFHWG) operator, are proposed based on the defined algebraic operational laws. Also, interesting properties of these aggregation operators are discussed in detail.Design/methodology/approachPyPHFN is not only a generalization of the traditional IHFN, but also a more effective tool to deal with uncertain multi-attribute decision-making problems.FindingsIn addition, the authors design the algorithm to handle the uncertainty in emergency decision-making issues. At last, a numerical case study of coronavirus disease 2019 (COVID-19) as an emergency decision-making is introduced to show the implementation and validity of the established technique. Besides, the comparison of the existing and the proposed technique is established to show the effectiveness and validity of the established technique.Originality/valuePaper is original and not submitted elsewhere.

scholarly journals Hybrid Weighted Arithmetic and Geometric Aggregation Operator of Neutrosophic Cubic Sets for MADM

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 278 ◽  
Author(s):  
Lilian Shi ◽  
Yue Yuan
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Arithmetic Average ◽  
Weighted Arithmetic ◽  
Geometric Average ◽  
Multi Attribute Decision Making

Neutrosophic cubic sets (NCSs) can express complex multi-attribute decision-making (MADM) problems with its interval and single-valued neutrosophic numbers simultaneously. The weighted arithmetic average (WAA) and geometric average (WGA) operators are common aggregation operators for handling MADM problems. However, the neutrosophic cubic weighted arithmetic average (NCWAA) and neutrosophic cubic geometric weighted average (NCWGA) operators may result in some unreasonable aggregated values in some cases. In order to overcome the drawbacks of the NCWAA and NCWGA, this paper developed a new neutrosophic cubic hybrid weighted arithmetic and geometric aggregation (NCHWAGA) operator and investigates its suitability and effectiveness. Then, we established a MADM method based on the NCHWAGA operator. Finally, a MADM problem with neutrosophic cubic information was provided to illustrate the application and effectiveness of the proposed method.

scholarly journals Analysis of Decision Support System Based on 2-Tuple Spherical Fuzzy Linguistic Aggregation Information

2019 ◽  
Vol 10 (1) ◽  
pp. 276
Author(s):  
Saleem Abdullah ◽  
Omar Barukab ◽  
Muhammad Qiyas ◽  
Muhammad Arif ◽  
Sher Afzal Khan
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Comparison Analysis ◽  
Practical Application ◽  
Multiple Attribute ◽  
Ordered Weighted Average ◽  
Selection For ◽  
Fuzzy Linguistic

The aim of this paper is to propose the 2-tuple spherical fuzzy linguistic aggregation operators and a decision-making approach to deal with uncertainties in the form of 2-tuple spherical fuzzy linguistic sets. 2-tuple spherical fuzzy linguistic operators have more flexibility than general fuzzy set. We proposed a numbers of aggregation operators, namely 2-tuple spherical fuzzy linguistic weighted average, 2-tuple spherical fuzzy linguistic ordered weighted average, 2-tuple spherical fuzzy linguistic hybrid average, 2-tuple spherical fuzzy linguistic weighted geometric, 2-tuple spherical fuzzy linguistic ordered geometric, and 2-tuple spherical fuzzy linguistic hybrid geometric operators. The distinguishing feature of these proposed operators is studied. At that point, we have used these operators to design a model to deal with multiple attribute decision-making issues under the 2-tuple spherical fuzzy linguistic information. Then, a practical application for best company selection for feeds is given to prove the introduced technique and to show its practicability and effectiveness. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantage of our method. Results indicate that the proposed method is suitable and effective for decision making problems.

Model for Multiple Attribute Decision Making Based on Picture 2-Tuple Linguistic Power Aggregation Operators

2019 ◽  
Vol 11 (1) ◽  
pp. 35-65 ◽  
Author(s):  
Guiwu Wei
Keyword(s):  
Decision Making ◽  
Enterprise Resource Planning ◽  
Weighted Average ◽  
Resource Planning ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Erp System ◽  
Multiple Attribute ◽  
Linguistic Power ◽  
System Selection

In this article, the authors investigate the multiple attribute decision making problems with picture 2-tuple linguistic information. The utilized power average and power geometric operations used to develop some picture 2-tuple linguistic power aggregation operators: picture 2-tuple linguistic power weighted average (P2TLPWA) operator, picture 2-tuple linguistic power weighted geometric (P2TLPWG) operator, picture 2-tuple linguistic power ordered weighted average (P2TLPOWA) operator, picture 2-tuple linguistic power ordered weighted geometric (P2TLPOWG) operator, picture 2-tuple linguistic power hybrid average (P2TLPHA) operator and picture 2-tuple linguistic power hybrid geometric (P2TLPHG) operator. The prominent characteristic of these proposed operators is studied. This article has utilized these operators to develop some approaches to solve the picture 2-tuple linguistic multiple attribute decision making problems. Finally, a practical example for enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

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