scholarly journals Simplified neutrosophic linguistic normalized weighted bonferroni mean operator and its application to multi-criteria decision-making problems

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3339-3360 ◽  
Author(s):  
Zhang-Peng Tian ◽  
Jing Wang ◽  
Hong-Yu Zhang ◽  
Xiao-Hong Chen ◽  
Jian-Qiang Wang
Keyword(s):  
Decision Making ◽  
Comparison Method ◽  
Multi Criteria Decision Making ◽  
Comparison Analysis ◽  
Scale Functions ◽  
Bonferroni Mean ◽  
Special Cases

The main purpose of this paper is to provide a method of multi-criteria decision-making that combines simplified neutrosophic linguistic sets and normalized Bonferroni mean operator to address the situations where the criterion values take the form of simplified neutrosophic linguistic numbers and the criterion weights are known. Firstly, the new operations and comparison method for simplified neutrosophic linguistic numbers are defined and some linguistic scale functions are employed. Subsequently, a Bonferroni mean operator and a normalized weighted Bonferroni mean operator of simplified neutrosophic linguistic numbers are developed, in which some desirable characteristics and special cases with respect to the parameters p and q in Bonferroni mean operator are studied. Then, based on the simplified neutrosophic linguistic normalized weighted Bonferroni mean operator, a multi-criteria decision-making approach is proposed. Finally, an illustrative example is given and a comparison analysis is conducted between the proposed approach and other existing method to demonstrate the effectiveness and feasibility of the developed approach.

Complex q-rung orthopair fuzzy Schweizer–Sklar Muirhead mean aggregation operators and their application in multi-criteria decision-making

2021 ◽  
pp. 1-23
Author(s):  
Peide Liu ◽  
Tahir Mahmood ◽  
Zeeshan Ali
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Imaginary Part ◽  
Fuzzy Set ◽  
Score Function ◽  
Aggregation Operators ◽  
Unit Interval ◽  
Multi Criteria Decision Making ◽  
Accuracy Function ◽  
Special Cases

Complex q-rung orthopair fuzzy set (CQROFS) is a proficient technique to describe awkward and complicated information by the truth and falsity grades with a condition that the sum of the q-powers of the real part and imaginary part is in unit interval. Further, Schweizer–Sklar (SS) operations are more flexible to aggregate the information, and the Muirhead mean (MM) operator can examine the interrelationships among the attributes, and it is more proficient and more generalized than many aggregation operators to cope with awkward and inconsistence information in realistic decision issues. The objectives of this manuscript are to explore the SS operators based on CQROFS and to study their score function, accuracy function, and their relationships. Further, based on these operators, some MM operators based on PFS, called complex q-rung orthopair fuzzy MM (CQROFMM) operator, complex q-rung orthopair fuzzy weighted MM (CQROFWMM) operator, and their special cases are presented. Additionally, the multi-criteria decision making (MCDM) approach is developed by using the explored operators based on CQROFS. Finally, the advantages and comparative analysis are also discussed.

scholarly journals Generalized Fuzzy Soft Power Bonferroni Mean Operators and Their Application in Decision Making

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 810
Author(s):  
Zitai Xu ◽  
Chunfang Chen ◽  
Yutao Yang
Keyword(s):  
Decision Making ◽  
Soft Power ◽  
Original Data ◽  
Decision Makers ◽  
Decision Making Process ◽  
Software Selection ◽  
Decision Method ◽  
Bonferroni Mean ◽  
Special Cases ◽  
Multi Attribute Decision Making

In decision-making process, decision-makers may make different decisions because of their different experiences and knowledge. The abnormal preference value given by the biased decision-maker (the value that is too large or too small in the original data) may affect the decision result. To make the decision fair and objective, this paper combines the advantages of the power average (PA) operator and the Bonferroni mean (BM) operator to define the generalized fuzzy soft power Bonferroni mean (GFSPBM) operator and the generalized fuzzy soft weighted power Bonferroni mean (GFSWPBM) operator. The new operator not only considers the overall balance between data and information but also considers the possible interrelationships between attributes. The excellent properties and special cases of these ensemble operators are studied. On this basis, the idea of the bidirectional projection method based on the GFSWPBM operator is introduced, and a multi-attribute decision-making method, with a correlation between attributes, is proposed. The decision method proposed in this paper is applied to a software selection problem and compared to the existing methods to verify the effectiveness and feasibility of the proposed method.

scholarly journals Logarithmic Hybrid Aggregation Operators Based on Single Valued Neutrosophic Sets and Their Applications in Decision Support Systems

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 364 ◽  
Author(s):  
Shahzaib Ashraf ◽  
Saleem Abdullah ◽  
Florentin Smarandache ◽  
Noor Amin
Keyword(s):  
Decision Making ◽  
Decision Process ◽  
Aggregation Operators ◽  
Decision Making Process ◽  
Practical Case ◽  
Multi Criteria Decision Making ◽  
Comparison Analysis ◽  
Negative Interaction ◽  
Positive Interaction ◽  
Neutrosophic Sets

Recently, neutrosophic sets are found to be more general and useful to express incomplete, indeterminate and inconsistent information. The purpose of this paper is to introduce new aggregation operators based on logarithmic operations and to develop a multi-criteria decision-making approach to study the interaction between the input argument under the single valued neutrosophic (SVN) environment. The main advantage of the proposed operator is that it can deal with the situations of the positive interaction, negative interaction or non-interaction among the criteria, during decision-making process. In this paper, we also defined some logarithmic operational rules on SVN sets, then we propose the single valued neutrosophic hybrid aggregation operators as a tool for multi-criteria decision-making (MCDM) under the neutrosophic environment and discussd some properties. Finally, the detailed decision-making steps for the single valued neutrosophic MCDM problems were developed, and a practical case was given to check the created approach and to illustrate its validity and superiority. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantages of our proposed method. Results indicate that the proposed method is suitable and effective for decision process to evaluate their best alternative.

scholarly journals TOPSIS Method Based on Complex Spherical Fuzzy Sets with Bonferroni Mean Operators

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1739
Author(s):  
Zeeshan Ali ◽  
Tahir Mahmood ◽  
Miin-Shen Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Unit Interval ◽  
Polar Coordinates ◽  
Topsis Method ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Special Cases ◽  
Order Preference ◽  
Multi Attribute Decision Making

The theory of complex spherical fuzzy sets (CSFSs) is a mixture of two theories, i.e., complex fuzzy sets (CFSs) and spherical fuzzy sets (SFSs), to cope with uncertain and unreliable information in realistic decision-making situations. CSFSs contain three grades in the form of polar coordinates, e.g., truth, abstinence, and falsity, belonging to a unit disc in a complex plane, with a condition that the sum of squares of the real part of the truth, abstinence, and falsity grades is not exceeded by a unit interval. In this paper, we first consider some properties and their operational laws of CSFSs. Additionally, based on CSFSs, the complex spherical fuzzy Bonferroni mean (CSFBM) and complex spherical fuzzy weighted Bonferroni mean (CSFWBM) operators are proposed. The special cases of the proposed operators are also discussed. A multi-attribute decision making (MADM) problem was chosen to be resolved based on the proposed CSFBM and CSFWBM operators. We then propose the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method based on CSFSs (CSFS-TOPSIS). An application example is given to delineate the proposed methods and a close examination is undertaken. The advantages and comparative analysis of the proposed approaches are also presented.

scholarly journals Multiattribute Group Decision-Making Based on Linguistic Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Aggregation Operators

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-24 ◽  
Author(s):  
Mingwei Lin ◽  
Jiuhan Wei ◽  
Zeshui Xu ◽  
Riqing Chen
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Bonferroni Mean ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Special Cases ◽  
Geometric Bonferroni Mean ◽  
Decision Making Model ◽  
Pythagorean Fuzzy Numbers

The partitioned Bonferroni mean (PBM) operator can efficiently aggregate inputs, which are divided into parts based on their interrelationships. To date, it has not been used to aggregate linguistic Pythagorean fuzzy numbers (LPFNs). In this paper, we extend the PBM operator and partitioned geometric Bonferroni mean (PGBM) operator to the linguistic Pythagorean fuzzy sets (LPFSs) and use them to develop a novel multiattribute group decision-making model under the linguistic Pythagorean fuzzy environment. We first define some novel operational laws for LPFNs, which take into consideration the interactions between the membership degree (MD) and nonmembership degree (NMD) from two different LPFNs. Based on these novel operational laws, we put forward the interaction PBM (LPFIPBM) operator, the weighted interaction PBM (LPFWIPBM) operator, the interaction PGBM (LPFIPGBM) operator, and the weighted interaction PGBM (LPFWIPGBM) operator. Then, we study some properties of these proposed operators and discuss their special cases. Based on the proposed LPFWIPBM and LPFWIPGBM operators, a novel multiattribute group decision-making model is developed to process the linguistic Pythagorean fuzzy information. Finally, some illustrative examples are introduced to compare our proposed methods with the existing ones.

scholarly journals Application of Dual Hesitant Fuzzy Geometric Bonferroni Mean Operators in Deciding an Energy Policy for the Society

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Raja Noshad Jamil ◽  
Tabasam Rashid
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Energy Policy ◽  
Multicriteria Decision Making ◽  
Hesitant Fuzzy Sets ◽  
Multicriteria Decision ◽  
Bonferroni Mean ◽  
Special Cases ◽  
Geometric Bonferroni Mean

Dual hesitant fuzzy geometric Bonferroni mean is defined for dual hesitant fuzzy sets. Different properties of dual hesitant fuzzy geometric Bonferroni mean are discussed. Some special cases are studied in detail for dual hesitant fuzzy geometric Bonferroni mean. In addition, dual hesitant fuzzy weighted geometric Bonferroni mean and dual hesitant fuzzy Choquet geometric Bonferroni mean are proposed. A multicriteria decision-making method is discussed to find the best alternative among different alternatives by using proposed aggregated operators and an illustrated example is also given to understand our proposal.

scholarly journals Hesitant Fuzzy Linguistic Multicriteria Decision-Making Method Based on Generalized Prioritized Aggregation Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Jia-ting Wu ◽  
Jian-qiang Wang ◽  
Jing Wang ◽  
Hong-yu Zhang ◽  
Xiao-hong Chen
Keyword(s):  
Decision Making ◽  
Multicriteria Decision Making ◽  
Comparison Method ◽  
Aggregation Operator ◽  
New Approach ◽  
Multicriteria Decision ◽  
Scale Functions ◽  
Prioritized Aggregation Operator ◽  
Prioritized Aggregation Operators ◽  
Fuzzy Linguistic

Based on linguistic term sets and hesitant fuzzy sets, the concept of hesitant fuzzy linguistic sets was introduced. The focus of this paper is the multicriteria decision-making (MCDM) problems in which the criteria are in different priority levels and the criteria values take the form of hesitant fuzzy linguistic numbers (HFLNs). A new approach to solving these problems is proposed, which is based on the generalized prioritized aggregation operator of HFLNs. Firstly, the new operations and comparison method for HFLNs are provided and some linguistic scale functions are applied. Subsequently, two prioritized aggregation operators and a generalized prioritized aggregation operator of HFLNs are developed and applied to MCDM problems. Finally, an illustrative example is given to illustrate the effectiveness and feasibility of the proposed method, which are then compared to the existing approach.

Novel Multi-criteria Decision-making Approaches Based on Hesitant Fuzzy Sets and Prospect Theory

2016 ◽  
Vol 15 (03) ◽  
pp. 621-643 ◽  
Author(s):  
Juan-Juan Peng ◽  
Jian-Qiang Wang ◽  
Xiao-Hui Wu
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Prospect Theory ◽  
Hausdorff Distance ◽  
Comparison Method ◽  
Distance Measures ◽  
Preference Ranking ◽  
Multi Criteria Decision Making ◽  
The Novel ◽  
Hesitant Fuzzy Sets

Hesitant fuzzy sets (HFSs), an extension of fuzzy sets, are considered to be useful in solving decision making problems where decision makers are unable to choose between several values when expressing their preferences. The purpose of this paper is to develop two hesitant fuzzy multi-criteria decision making (MCDM) methods based on prospect theory (PT). First, the novel component-wise ordering method for two hesitant fuzzy numbers (HFNs) is defined; however, this method does not consider the length of the two HFNs. Second, by utilizing the directed Hausdorff distance between two imprecise point sets, the generalized hesitant Hausdorff distance is developed, which overcomes the shortcomings of the existing distance measures. Third, based on the proposed comparison method and distance, as well as PT, the extended TODIM and Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE) approaches are developed in order to solve MCDM problems with hesitant fuzzy information. Finally, a practical example is provided to illustrate the pragmatism and effectiveness of the proposed approaches. Sensitivity and comparison analyses are also conducted using the same example. The findings indicate that the proposed methods do not require complicated computation procedures, yet still yield a reasonable and credible solution.

scholarly journals Multiple attribute group decision-making based on interval-valued q-rung orthopair uncertain linguistic power Muirhead mean operators and linguistic scale functions

PLoS ONE ◽  
2021 ◽  
Vol 16 (10) ◽  
pp. e0258772
Author(s):  
Yuan Xu ◽  
Shifeng Liu ◽  
Jun Wang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Comparison Method ◽  
Model Framework ◽  
Scale Functions ◽  
Multiple Attribute ◽  
Definition Of ◽  
Magdm Problems ◽  
Interval Valued

Fuzzy set theory and its extended form have been widely used in multiple-attribute group decision-making (MAGDM) problems, among which the interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs) got a lot of attention for its ability of capturing information denoted by interval values. Based on the previous studies, to find a better solution for fusing qualitative quantization information with fuzzy numbers, we propose a novel definition of interval-valued q-rung orthopair uncertain linguistic sets (IVq-ROULSs) based on the linguistic scale functions, as well as its corresponding properties, such as operational rules and the comparison method. Furthermore, we utilize the power Muirhead mean operators to construct the information fusion method, and provide a variety of aggregation operators based on the proposed information description environment. A model framework is constructed for solving the MAGDM problem utilizing the proposed method. Finally, we illustrate the performance of the new method and investigate its advantages and superiorities through comparative analysis.

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