scholarly journals Multicriteria Decision Making Based on Archimedean Bonferroni Mean Operators of Hesitant Fermatean 2-Tuple Linguistic Terms

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-19 ◽  
Author(s):  
Huijuan Wang ◽  
Xin Wang ◽  
Lidong Wang
Keyword(s):  
Decision Making ◽  
Multicriteria Decision Making ◽  
Decision Makers ◽  
Linguistic Terms ◽  
Fundamental Properties ◽  
Bonferroni Mean ◽  
Special Cases ◽  
Geometric Bonferroni Mean ◽  
Parameter Values ◽  
Uncertainty Information

The study is concerned with the representation and aggregation of complex uncertainty information. First, the concept of hesitant Fermatean 2-tuple linguistic sets (HF2TLSs) is introduced for characterizing an individual’s imprecision preferences and assessing information by combining 2-tuple linguistic terms and Fermatean fuzzy sets. The advantage of hesitant Fermatean 2-tuple linguistic information is that it can handle higher levels of uncertainty and express the decision-makers’ hesitancy. Second, we extend Bonferroni mean (BM) operators under the background of HF2TLSs for the sake of their application in information fusion and decision making. The Archimedean t-norm and s-norm- (ATS-) based hesitant Fermatean 2-tuple linguistic weighted Bonferroni mean (A-HF2TLWBM) operator and the ATS-based hesitant Fermatean 2-tuple linguistic weighted geometric Bonferroni mean (A-HF2TLWGBM) operator are developed by considering the interrelationship between any two variables. The main benefit of the proposed operators is that these operators deliver more complete and flexible results compared to existing methods. Moreover, some fundamental properties and special cases are examined by adjusting parameter values. Finally, an approach is designed as a support for handling decision making problems, and an example regarding investment selection is provided to demonstrate the practicality of the designed method with a detailed discussion of parameter influence and comparisons with the existing methods.

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 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 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.

Intuitionistic Fuzzy Power Geometric Bonferroni Means and Their Application to Multiple Attribute Group Decision Making

2015 ◽  
Vol 23 (02) ◽  
pp. 285-315 ◽  
Author(s):  
Yingdong He ◽  
Zhen He ◽  
Chao Jin ◽  
Huayou Chen
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Bonferroni Mean ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Geometric Average ◽  
Multiple Attribute ◽  
Special Cases ◽  
Geometric Bonferroni Mean

The geometric Bonferroni mean (GBM) can capture the interrelationships between input arguments, which is an important generalization of Bonferroni mean (BM). In this paper, we combine geometric Bonferroni mean (GBM) with the power geometric average (PGA) operator under intuitionistic fuzzy environment and present the intuitionistic fuzzy geometric power Bonferroni mean (IFPGBM) and the weighted intuitionistic fuzzy power geometric Bonferroni mean (WIFPGBM). The desirable properties of these new extensions of Bonferroni mean and their special cases are investigated. We list the detailed steps of multiple attribute group decision making with the developed IFPGBM or WIFPGBM, and give a comparison of the new extensions of Bonferroni mean by this paper with the corresponding existing intuitionistic fuzzy Bonferroni means. Finally, examples are illustrated to show the validity and feasibility of the new approaches.

scholarly journals Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Operators and Their Application in Multiple-Attribute Decision-Making

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-25 ◽  
Author(s):  
Wei Yang ◽  
Jiarong Shi ◽  
Yong Liu ◽  
Yongfeng Pang ◽  
Ruiyue Lin
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Investment Company ◽  
Pythagorean Fuzzy Set ◽  
Bonferroni Mean ◽  
Multiple Attribute ◽  
Special Cases ◽  
Geometric Bonferroni Mean

The aim of this paper is to develop partitioned Pythagorean fuzzy interaction Bonferroni mean operators based on the Pythagorean fuzzy set, Bonferroni mean, and interaction between membership and nonmembership. Several new aggregation operators are developed including the Pythagorean fuzzy interaction partitioned Bonferroni mean (PFIPBM) operator, the Pythagorean fuzzy weighted interaction partitioned Bonferroni mean (PFWIPBM) operator, the Pythagorean fuzzy interaction partitioned geometric Bonferroni mean (PFIPGBM) operator, and the Pythagorean fuzzy weighted interaction partitioned geometric Bonferroni mean (PFWIPGBM) operator. Some main properties and some special particular cases of the new operators are studied. Many existing operators are the special cases of new aggregation operators. Moreover, a multiple-attribute decision-making method based on the proposed operator has been developed and the investment company selection problem is presented to illustrate feasibility and practical advantages of the new method.

A Multi-Criteria Decision-Making Method Based on Heronian Mean Operators Under a Linguistic Hesitant Fuzzy Environment

2015 ◽  
Vol 32 (05) ◽  
pp. 1550035 ◽  
Author(s):  
Su-Min Yu ◽  
Huan Zhou ◽  
Xiao-Hong Chen ◽  
Jian-Qiang Wang
Keyword(s):  
Decision Making ◽  
Decision Makers ◽  
Fuzzy Arithmetic ◽  
New Order ◽  
Comparison Analysis ◽  
Weighted Arithmetic ◽  
Fuzzy Environment ◽  
Special Cases ◽  
Parameter Values ◽  
Heronian Mean

Linguistic hesitant fuzzy sets (LHFSs) are a very useful and appropriate means of expressing preferences of decision-makers; moreover their basic operations and comparison methods have been defined and applied to the solving of MCDM problems. However, there are a number of limitations in the related studies. In this paper, using information from existing studies, several new operations and a new order relationship are defined; moreover four linguistic hesitant fuzzy Heronian mean operators are proposed: the linguistic hesitant fuzzy arithmetic Heronian mean (LHFAHM) operator; the linguistic hesitant fuzzy weighted arithmetic Heronian mean (LHFWAHM) operator; the linguistic hesitant fuzzy geometric Heronian mean (LHFGHM) operator; and the linguistic hesitant fuzzy weighted geometric Heronian mean (LHFWGHM) operator. Furthermore, some useful and desirable properties of these operators are analyzed in some special cases, with respect to the different parameter values in these operators, are discussed. Additionally, an approach based on the LHFWAHM and LHFWGHM operators for solving MCDM problems is proposed. Finally, an illustrative example is provided to verify the validity and feasibility of the proposed approaches, and a comparison analysis is also presented to demonstrate the influences of different parameters on the results of decision-making.

scholarly journals Q-INDETERMINATE CORRELATION COEFFICIENT BETWEEN SIMPLIFIED NEUTROSOPHIC INDETERMINATE SETS AND ITS MULTICRITERIA DECISION-MAKING METHOD

2021 ◽  
Vol 27 (6) ◽  
pp. 404-411
Author(s):  
Shigui Du ◽  
Jun Ye ◽  
Rui Yong ◽  
Fangwei Zhang
Keyword(s):  
Decision Making ◽  
Correlation Coefficients ◽  
Multicriteria Decision Making ◽  
Decision Makers ◽  
Open Pit ◽  
Neutrosophic Set ◽  
Multicriteria Decision ◽  
Simplified Neutrosophic Set ◽  
Uncertainty Information ◽  
Slope Design

Owing to the indeterminacy, incompleteness, and inconsistency of decision makers’ arguments/cognitions regarding complicated decision-making problems, the truth, falsity, and indeterminacy degrees given by decision makers may imply the partial certainty and partial uncertainty information. In this case, a simplified neutrosophic set (SNS) cannot express the uncertainty degrees of the truth, falsity, indeterminacy arguments. To depict the hybrid information of SNS and neutrosophic (indeterminate) numbers (NNs) together, this study presents a simplified neutrosophic indeterminate set (SNIS) to describe the uncertainty degrees of the truth, falsity, indeterminacy, and then based on the de-neutrosophication technology using the parameterized SNSs of SNISs we introduce the q-indeterminate correlation coefficients of SNISs with a parameter q ∈ [0, 1]. Next, a simplified neutrosophic indeterminate multicriteria decision-making method using the qindeterminate correlation coefficients of SNISs is established along with decision makers’ risk attitudes, such as the small risk for q = 0, the moderate risk for q = 0.5, and the large risk for q = 1, to carry out multicriteria decision-making problems in SNIS setting. Eventually, the proposed decision-making approach is applied in an example of selecting a satisfactory slope design scheme for an open pit mine to indicate the practicality and flexibility in SNIS setting.

Multi-Valued Neutrosophic Number Bonferroni Mean Operators with their Applications in Multiple Attribute Group Decision Making

2016 ◽  
Vol 15 (05) ◽  
pp. 1181-1210 ◽  
Author(s):  
Peide Liu ◽  
Lili Zhang ◽  
Xi Liu ◽  
Peng Wang
Keyword(s):  
Decision Making ◽  
Group Decision ◽  
Comparison Method ◽  
Aggregation Operator ◽  
Neutrosophic Set ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Geometric Bonferroni Mean ◽  
Parameter Values

Bonferroni mean (BM) is a very useful aggregation operator, which can consider the correlations between the aggregated arguments and the multi-valued neutrosophic set can be much more convenient to denote the incomplete, indeterminate and inconsistent information, in this paper, we applied the Bonferroni mean to the multi-valued neutrosophic set, and proposed some Bonferroni mean operators of multi-valued neutrosophic numbers (MVNNs). First, we gave some operational laws and a comparison method of MVNNs, then we presented the weighted Bonferroni mean (WBM) operator and weighted geometric Bonferroni mean (WGBM) operator. Further, we proposed the multi-valued neutrosophic weighted Bonferroni mean (MVNWBM) operator and the multi-valued neutrosophic weighted geometric Bonferroni mean (MVNWGBM) operator and some properties of them are also investigated. Finally, the decision making methods are developed based on MVNWGBM operator and MVNWBM operator, and an example about investment selection is given to illustrate the applications of the developed methods and the influence of different parameter values on the decision-making results.

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