Multiple Criteria Decision Making Approach with Multivalued Neutrosophic Linguistic Normalized Weighted Bonferroni Mean Hamacher Operator

Li, Baolin; Wang, Juanru; Yang, Lihua; Li, Xuetao

doi:10.1155/2018/2432167

Cited by 9 publications

(18 citation statements)

References 48 publications

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“…A great number of extended Hamacher aggregation operators based on different fuzzy number situations have been developed [ 37 , 38 , 39 ]. Recently, Garg et al [ 40 ] extended Hamacher t-norm and t-conorm with interval intuitionistic fuzzy numbers to deal with multi-criteria decision making problems; Gao et al [ 41 ] presented some Hamacher prioritized operators for aggregating dual hesitant bipolar fuzzy numbers; Wu et al [ 42 ] combined Hamacher aggregation operators with single-valued neutrosophic 2-tuple linguistic numbers; Li et al [ 43 ] defined the multivalued neutrosophic linguistic normalized weighted Bonferroni mean Hamacher operators; Tang and Meng [ 44 ] discussed the Hamacher aggregation operators under linguistic intuitionistic fuzzy environment. Nevertheless, the Hamacher aggregation operators have not been extended to LNNs so far.…”

Section: Introductionmentioning

confidence: 99%

Linguistic neutrosophic Hamacher aggregation operators and the application in evaluating land reclamation schemes for mines

Liang¹,

Zhao²,

Luo³

2018

PLoS ONE

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Land reclamation has become a significant way for the improvement of ecological environment in mining areas. When selecting the optimal land reclamation scheme, LNNs (linguistic neutrosophic numbers) are suitable to describe the complex fuzzy evaluation information through linguistic truth, indeterminacy and falsity membership degrees. Furthermore, the Hamacher aggregation operators are good tools to handle multi-criteria decision making problems. Accordingly, the aim of this paper is to extend Hamacher aggregation operators with LNNs and then build a decision making framework for evaluating land reclamation schemes in mining areas. First, new operational laws of LNNs based on Hamacher t-norm and t-conorm are defined. Then, several linguistic neutrosophic Hamacher aggregation operators, including the linguistic neutrosophic Hamacher weighted mean aggregation operators and linguistic neutrosophic Hamacher hybrid weighted mean aggregation operators are developed. Meanwhile, their desirable properties are proved. Thereafter, a method for decision making with linguistic neutrosophic information based on these operators is proposed to deal with complex decision problems. At last, the validity of this method is confirmed by an illustrative example of evaluating the land reclamation schemes in mining areas. In addition, the impact of the parameter in extended Hamacher aggregation operators is discussed. The merits of the proposed method are also highlighted by comparing with other decision making methods. The results show that the proposed linguistic neutrosophic Hamacher aggregation operators have great flexibility and advantages, and can provide powerful ways for the evaluation of land reclamation schemes.

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Section: Introductionmentioning

confidence: 99%

Linguistic neutrosophic Hamacher aggregation operators and the application in evaluating land reclamation schemes for mines

Liang¹,

Zhao²,

Luo³

2018

PLoS ONE

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“…From Table 7, we can find that the optimal vendor is always A 3 , while the worst vendor is A 1 or A 3 , and the ranking orders are slightly different between the method proposed by Li et al [25] and the method proposed in this manuscript. If the aggregating operator based on Algebraic operations developed by Li et al [25] is used, when p = q = 1, the ranking is A 3 A 4 A 2 A 5 A 1 . Obviously, the optimal vendor is A 3 , and the worst vendor is A 1 .…”

Section: Comparison Analysismentioning

confidence: 72%

“…To reveal the merits of the novel approach, we perform a comparative analysis between our method and the existing methods [25], [31]. In this part, the method developed by Li et al [25] is applied to settle the same example with multiple-valued picture fuzzy linguistic information in this manuscript. The comparative results are presented in Table 7.…”

Section: Comparison Analysismentioning

confidence: 99%

Multiple-Valued Picture Fuzzy Linguistic Set Based on Generalized Heronian Mean Operators and Their Applications in Multiple Attribute Decision Making

Yang

2020

IEEE Access

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To better express and handle the increasing complicated fuzzy decision making information, we firstly put forward the concept of multiple-valued picture fuzzy linguistic set (MVPFLS), which is motivated by the advantages of hesitant fuzzy set (HFS), linguistic term set (LTS), and picture fuzzy set (PFS). First, the concepts concerning MVPFLS and the multiple-valued picture fuzzy linguistic element (MVPFLE) are proposed. Second, the operating rules of MVPFLEs on account of linguistic scale functions (LSFs) are given, and the compared functions for MVPFLE are also defined. Third, the traditional generalized Heronian mean (HM) operators capturing the correlation among attributes are extended to multiple-valued picture fuzzy linguistic environment, namely, the multiple-valued picture fuzzy linguistic generalized weighted Heronian mean (MVPFLGWHM) aggregating operator and the multiple-valued picture fuzzy linguistic generalized weighted geometric Heronian mean (MVPFLGWGHM) aggregating operator are proposed, their interesting characteristics and some particular instances are also given. Fourth, the method utilizing the proposed aggregating operators to settle multiple attribute decision making (MADM) issues is provided. Eventually, a practical instance is employed to validate the powerfulness of the new approach, and the sensitivity analysis is performed along with comparative analysis. INDEX TERMS Multiple-valued picture fuzzy linguistic set, Heronian operator, multiple attribute decision making.

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“…In FS theory, t-conorm (T * ) and t-norm (T) are very important to the generalization of intersection or union of fuzzy sets [34,42,46,[55][56][57][58][59][60][61].…”

Section: Hamacher T-norm and Hamacher T-conormmentioning

confidence: 99%

Some Normal Intuitionistic Fuzzy Heronian Mean Operators Using Hamacher Operation and Their Application

Zhang

Kong

2018

Symmetry

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Hamacher operation is a generalization of the algebraic and Einstein operation and expresses a family of binary operation in the unit interval [0,1]. Heronian mean can deal with correlations of different criteria or input arguments and does not bring out repeated calculation. The normal intuitionistic fuzzy numbers (NIFNs) can depict normal distribution information in practical decision making. A decision-making problem was researched under the NIFN environment in this study, and a new multi-criteria group decision-making (MCGDM) approach is herein introduced on the basis of Hamacher operation. Firstly, according to Hamacher operation, some operational laws of NIFNs are presented. Secondly, it is noted that Heronian mean not only takes into account mutuality between the attribute values once, but also considers the correlation between input argument and itself. Therefore, in order to aggregate NIFN information, we developed some operators and studied their properties. These operators include Hamacher Heronian mean (NIFHHM), Hamacher weighted Heronian mean (NIFHWHM), Hamacher geometric Heronian mean (NIFHGHM), and Hamacher weighted geometric Heronian mean (NIFHWGHM). Furthermore, we applied the proposed operators to the MCGDM problem and developed a new MCGDM approach. The characteristics of this new approach are that: (1) it is suitable for making a decision under the NIFN environment and it is more reasonable for aggregating the normal distribution data; (2) it utilizes Hamacher operation to provide an effective and powerful MCGDM algorithm and to make more reliable and more flexible decisions under the NIFN circumstance; (3) it uses the Heronian mean operator to deal with interrelations between the attributes or input arguments, and it does not bring about repeated calculation. Therefore, the proposed method can describe the interaction of the different criteria or input arguments and offer some reasonable and reliable MCGDM aggregation operators, which can open avenues for decision making and broaden perspectives of the decision experts. Lastly, an application is given for showing the effectiveness and feasibility of the approach presented in this paper.

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Multiple Criteria Decision Making Approach with Multivalued Neutrosophic Linguistic Normalized Weighted Bonferroni Mean Hamacher Operator

Cited by 9 publications

References 48 publications

Linguistic neutrosophic Hamacher aggregation operators and the application in evaluating land reclamation schemes for mines

Linguistic neutrosophic Hamacher aggregation operators and the application in evaluating land reclamation schemes for mines

Multiple-Valued Picture Fuzzy Linguistic Set Based on Generalized Heronian Mean Operators and Their Applications in Multiple Attribute Decision Making

Some Normal Intuitionistic Fuzzy Heronian Mean Operators Using Hamacher Operation and Their Application

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