Normal Distribution Fuzzy Sets

Lv, Zehua; Chen, Chuanbo; Li, Wenhai

doi:10.1007/978-3-540-71441-5_31

Cited by 8 publications

(4 citation statements)

References 25 publications

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“…Fuzzy sets and fuzzy logic have since been widely employed to handle uncertainty issues in daily life [ 61 , 62 ]. Scholars have successively optimized fuzzy sets [ 63 , 64 ], such as Fuzzy Sets of Type-2 [ 65 ], standard fuzzy sets [ 66 ], hesitant fuzzy sets [ 67 ], interval-valued intuitionistic fuzzy values [ 20 ], and complex Pythagorean fuzzy sets [ 48 ]. In conjunction with MCDM techniques like AHP, ANP, DEA, and TOPSIS, fuzzy set theory and its extension have been used to solve supplier selection decision-making problems [ 68 , 69 ].…”

Section: Literature Reviewmentioning

confidence: 99%

Sustainable supplier selection based on VIKOR with single-valued neutrosophic sets

Luo,

Wang,

Yang

et al. 2023

PLoS ONE

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Considering economic, environmental, and social issues, the sustainability of the supply chain has drawn considerable attention due to societal and environmental changes within the supply chain network. The strategic study of the entire supply chain process and maximizing an organization’s competitive advantage depend heavily on supplier selection based on sustainable indicators. Selecting sustainable suppliers for the supply chain is challenging since it is a multi-criteria decision-making (MCDM) problem with significant uncertainty in the decision-making process. This study uses the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) technique and single-valued neutrosophic sets (SVNS) to deal with the challenge of choosing a sustainable supplier with insufficient information. This method reduces the influence of personal experience and preference on the final evaluation results and the problem of excessive individual regret caused by factor correlation and improves the consistency of evaluation results. Finally, the method’s success and adaptability are demonstrated by sensitivity analysis and additional comparison analysis, and the benefits and drawbacks of the suggested framework are examined. Compared to other approaches, it can assist decision-makers in communicating fuzzy and uncertain information, offering a perspective and approach for MCDM in the face of such situations, and helping them select suppliers of high caliber and who practice sustainable business practices.

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Section: Literature Reviewmentioning

confidence: 99%

Sustainable supplier selection based on VIKOR with single-valued neutrosophic sets

Luo,

Wang,

Yang

et al. 2023

PLoS ONE

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“…Step 3: By utilizing the NIFWGA operator as defined in Eq. (22), to aggregate the given information β i j , j = 1, 2, 3, 4 of the Table 2, the collective values β i 's of each alternative V i are obtained as…”

Section: When Evaluations Are Taken In Nifnsmentioning

confidence: 99%

“…Yang and Ko [20] defined the normal fuzzy number to express the uncertainties in the data while Li et al [21] compares them with the triangular or trapezoidal fuzzy numbers. Prompted by this fuzzy number, Lv et al [22] presented the concept of normal distribution fuzzy sets (NFSs) and a method to display the membership degrees in an IFSs by a series of normal distribution functions with parameters a (expected values) and σ (variance), and denoted as NFS(a, σ ). The normal fuzzy numbers (NFNs) have broadly used and several advantages such as all the physical aspects and production activities are well represented by such numbers; the higher derivative of the normal membership function is continuous.…”

Section: Introductionmentioning

confidence: 99%

New ranking method for normal intuitionistic sets under crisp, interval environments and its applications to multiple attribute decision making process

Garg

2020

Complex Intell. Syst.

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The aim of this paper is to present novel algorithms for solving the multiple attribute decision-making problems under the normal intuitionistic fuzzy set environment. Normal intuitionistic and interval-valued intuitionistic sets are the essential mechanisms for influencing the decision-making queries with anonymous and indeterminant data by engaging a degree of membership and non-membership of normal distribution data in quantitative terms. Holding these features in mind and united the idea of hesitation degree, this paper presents some improved score functions to rank the normal intuitionistic and interval-valued intuitionistic sets. The advantage of these proposed functions is to overwhelm the weakness of the existing functions and will aid to rank the given objects in a more consistent way. The numerous salient features of the proposed functions are studied. Later, we develop two new algorithms for interval-valued as well as crisp numbers based on the proposed functions to solve multiple attribute decision-making problems. The given approaches have been confirmed with numerical examples and the advantages, as well as comparative analysis, are furnished to shows its influence over existing approaches.

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“…Example5.1 Suppose that there are 10 candidate securities whose returns are described as fuzzy triangular or fuzzy normally distributed variables (32) , as listed in Table 5, the last column lists the proportion of the existing capital investment in each security. The transaction cost for each security depends on the trade volume in Tables 3 and 4, where we designate the value intervals of transaction in proportion as well as transaction cost rates γ .…”

Section: Ten Securities Portfolio Problemmentioning

confidence: 99%

A Fuzzy Multi-Objective Portfolio Selection Model with Piecewise Linear Transaction Costs

Wang

Watada

2014

IEEJ Trans.EIS

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In this paper, we studied a multi-objective portfolio selection problem with piecewise linear transaction costs in a fuzzy environment. Transaction costs are expenses incurred when buying or selling securities and they are a burden on investors who frequently make trades to balance their portfolio. To better evaluate portfolio performance with transaction costs, this paper extends a previous study to a new model called fuzzy multi-objective portfolio selection model with piecewise linear transaction costs. A fuzzy simulation-based particle swarm optimization algorithm is designed to solve the model considering investors' individual risk attitude. In addition, several numerical examples are provided to illustrate the effectiveness of this model and algorithm. A conclusion is drawn at the end of this paper.

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Normal Distribution Fuzzy Sets

Cited by 8 publications

References 25 publications

Sustainable supplier selection based on VIKOR with single-valued neutrosophic sets

Sustainable supplier selection based on VIKOR with single-valued neutrosophic sets

New ranking method for normal intuitionistic sets under crisp, interval environments and its applications to multiple attribute decision making process

A Fuzzy Multi-Objective Portfolio Selection Model with Piecewise Linear Transaction Costs

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