Bonferroni Mean Operators of Linguistic Neutrosophic Numbers and Their Multiple Attribute Group Decision-Making Methods

Fan, Changxing; Ye, Jun; Hu, Keli; Fan, En

doi:10.3390/info8030107

Cited by 37 publications

(42 citation statements)

References 18 publications

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“…He et al [33] proposed two interval-valued hesitant fuzzy power BM operators by combining the BM with the power average operator. Fan et al [34] presented linguistic neutrosophic numbers (LNNs) and a normalized weighted BM operator by merging the LNN and BM operator. Besides, the BM operator has also been extended to other fuzzy environment to aggregate various fuzzy information [35,36], such as hesitant fuzzy sets and linguistic intuitionistic fuzzy numbers.…”

Section: Bonferroni Meanmentioning

confidence: 99%

Risk Assessment for Failure Mode and Effects Analysis Using the Bonferroni Mean and TODIM Method

et al. 2019

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As a safety and reliability analysis technique, failure mode and effects analysis (FMEA) has been used extensively in several industries for the identification and elimination of known and potential failures. However, some shortcomings associated with the FMEA method have limited its applicability. This study aims at presenting a comprehensive FMEA model that could efficiently handle the preference interdependence and psychological behavior of experts in the process of failure modes ranking. In this model, a linguistic variable expressed by the interval-valued Pythagorean fuzzy number (IVPFN) is utilized by experts to provide preference information with regard to failure modes’ evaluation and risk factors’ weight. Then, to depict the interdependent relationships between experts’ preferences, the Bonferroni mean operator is extended to IVPFN to aggregate the experts’ preference. Subsequently, an extended TODIM approach in which the dominance degree of failure modes is calculated by grey relational analysis is utilized to determine the risk priority of failure modes. Finally, a practical example concerning the risk assessment of a nuclear reheat valve system is provided to demonstrate the effectiveness and feasibility of the presented method. In addition, a sensitivity analysis and comparison analysis are conducted, and the results show that the preference interdependence and psychological behavior of experts have an important effect on the risk priority of failure modes.

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Section: Bonferroni Meanmentioning

confidence: 99%

Risk Assessment for Failure Mode and Effects Analysis Using the Bonferroni Mean and TODIM Method

et al. 2019

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“…Liu and Li [28] proposed the normal neutrosophic GBM operator and the normal neutrosophic weighted GBM operator, and also investigate their properties and special cases. In addition, the GBM operator has also been introduced into other fuzzy environments to fuse various fuzzy information [29][30][31][32], such as Pythagorean fuzzy sets, interval-valued intuitionistic fuzzy sets, Pythagorean 2-tuple linguistic sets, and linguistic neutrosophic sets.…”

Section: Aggregation Experts'preferencesmentioning

confidence: 99%

Failure Mode and Effects Analysis Considering Consensus and Preferences Interdependence

Zhu

Wang

2018

Algorithms

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Failure mode and effects analysis is an effective and powerful risk evaluation technique in the field of risk management, and it has been extensively used in various industries for identifying and decreasing known and potential failure modes in systems, processes, products, and services. Traditionally, a risk priority number is applied to capture the ranking order of failure modes in failure mode and effects analysis. However, this method has several drawbacks and deficiencies, which need to be improved for enhancing its application capability. For instance, this method ignores the consensus-reaching process and the correlations among the experts' preferences. Therefore, the aim of this study was to present a new risk priority method to determine the risk priority of failure modes under an interval-valued Pythagorean fuzzy environment, which combines the extended Geometric Bonferroni mean operator, a consensus-reaching process, and an improved Multi-Attributive Border Approximation area Comparison approach. Finally, a case study concerning product development is described to demonstrate the feasibility and effectiveness of the proposed method. The results show that the risk priority of failure modes obtained by the proposed method is more reasonable in practical application compared with other failure mode and effects analysis methods.Algorithms 2018, 11, 34 2 of 24 of limitations. Numerous alternative methods have been presented in the literature to handle some of these drawbacks [2], which could explain why focusing on these shortcomings can improve the performance of traditional FMEA. However, many practical application cases have suggested that the ranking results determined by these alternative methods are not reliable and suffer from drawbacks in some situations. The main reasons are the assumption that the experts' preferences are independent and the team of experts have reached a consensus before aggregating the experts' preferences. Therefore, it is worth studying the problem of how to determine effectively the risk priority of failure modes without considering these two assumptions.It is very important for an FMEA team to adopt a suitable aggregation method to aggregate the experts' preferences into a collective evaluation matrix before determining the failure modes ranking. Many aggregation methods that assume that experts' preferences are independent have been applied to aggregate the experts' preferences. In practice, the FMEA team experts come from different departments or industries, and their subjective preferences, which are often influenced by social, power, knowledge, and other factors, usually indicate some interdependent characteristics. On the one hand, the geometric Bonferroni mean (GBM) initially proposed by Xia et al. [9] is an efficient operator to deal with the aggregation of interdependent arguments. The GBM operator has a prominent characteristic that can easily capture the interrelationships among input arguments [9]. Therefore, it is significant to integrate the experts' preferences...

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“…In order to overcome the insufficiency of SVNLSs, Fang and Ye (2017) gave the concept of LNN by means of LVs and SVNNs; which is characterized by expressing the TD, ID and FD with three LVs rather than exact values. Further, Fan, Ye, Hu, and Fan (2017) developed a LNN normalized weighted BM (LNNNWBM) operator and a LNN normalized weighted geometric BM (LNNNWGBM) operator for group decision. Liang, Zhao, and Wu (2017) proposed a TOPSIS model with LNNs in mining project investment.…”

Section: Introductionmentioning

confidence: 99%

Bidirectional projection measure of linguistic neutrosophic numbers and their application to multi-criteria group decision making

Лю

You

2019

Computers & Industrial Engineering

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A B S T R A C TLinguistic neutrosophic numbers (LNNs) are an effective tool in describing the incomplete and indeterminate evaluation information by using three linguistic variables (LVs) to denote the truth-degree (TD), indeterminacydegree (ID), and falsity-degree (FD), and the bidirectional projection measure has some advantages in dealing with multi-criteria group decision making (MCGDM) problems because it can consider both the distance and the included angle, but more importantly, it considers the bidirectional projection between each alternative and the ideal solution. In this paper, we define a new distance measure between two linguistic neutrosophic sets (LNSs), and build a model based on the maximum deviation to obtain fuzzy measure, further, we develop the bidirectional projection-based MCGDM method with LNNs in which a weight model based on fuzzy measure is proposed where the weights of evaluation criteria is partial unknown and the interactions among criteria are considered. Finally, we use some examples to verify the effectiveness of the proposed approach and demonstrate its advantages by comparing with some existing methods.

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Bonferroni Mean Operators of Linguistic Neutrosophic Numbers and Their Multiple Attribute Group Decision-Making Methods

Cited by 37 publications

References 18 publications

Risk Assessment for Failure Mode and Effects Analysis Using the Bonferroni Mean and TODIM Method

Risk Assessment for Failure Mode and Effects Analysis Using the Bonferroni Mean and TODIM Method

Failure Mode and Effects Analysis Considering Consensus and Preferences Interdependence

Bidirectional projection measure of linguistic neutrosophic numbers and their application to multi-criteria group decision making

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