Existence and uniqueness for the construction of fuzzy sets from a solidly nested family

Wu, Chong

doi:10.1007/s10700-014-9190-4

Cited by 3 publications

(2 citation statements)

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“…However, RPN has some shortcomings especially in transforming linguistic variable and considering the difference of weight about risk factors. Therefore, lots of methods are proposed to improve FMEA, such as evidence theory [23][24][25], expert system [26,27], uncertainty measure [28], hybrid approaches [29], fuzzy set theory [30,31], and so on [32].…”

Section: Introductionmentioning

confidence: 99%

Risk Evaluation in Failure Mode and Effects Analysis Using Fuzzy Measure and Fuzzy Integral

2017

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Failure mode and effects analysis (FMEA) is a popular and useful approach applied to examine potential failures in different products, designs, processes, and services. As a vital index, the risk priority number (RPN) can determine the risk priorities of failure modes by some risk factors such as occurrence (O), severity (S), and detection (D). However, in FMEA, the traditional risk priority number approach has some shortcomings, especially in setting the weight of risk factors. This paper presents an improved risk priority number approach based on a fuzzy measure and fuzzy integral. A fuzzy measure is used to reflect the importance of the individual indicators and the indicator set and a fuzzy integral is a nonlinear function defined on the basis of fuzzy measure. The weights of risk factors given by domain experts are seen as fuzzy densities to generate a λ-fuzzy measure which can reflect the weights' difference and relevance about risk factors. Then, the Choquet integral is used to fuse every value of risk factors about failure modes so as to obtain the comprehensive evaluation result. The result can reflect the comprehensive risk level, so it has a definite physical significance. Finally, an illustrative example and a comparison with another approach are given to show the effectiveness of the proposed approach in the paper.

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Section: Introductionmentioning

confidence: 99%

Risk Evaluation in Failure Mode and Effects Analysis Using Fuzzy Measure and Fuzzy Integral

2017

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“…Thus, the concept of a fuzzy set can actually be regarded from various alternative points of view, as functional equations (see [6,5]), nested families of sets and nested topologies (see [1,7,20]) or representable total preorders (see [12,6]) among others. In addition, in [8] the concept of a weightable quasi-metric was shown to be closely related to some classical functional equations, of which some were also intimately linked to the denition of a fuzzy set of a universe as proved in [6,5].…”

Section: Introductionmentioning

confidence: 99%

Weightable quasi-metrics related to fuzzy sets

Campión¹,

Catalán²,

Induráin³

et al. 2017

HJMS

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Generating fuzzy sets from the families of sets

2021

IFS

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The main purpose of this paper is to establish a mechanical procedure to determine the membership functions using the data collected from the economic and engineering problems. Determining the membership functions from the collected data may depend on the subjective viewpoint of decision makers. The mechanical procedure proposed in this paper can get rid of the subjective bias of decision makers. The concept of solid families is also proposed by regarding the sets in a family to be continuously varied. The desired fuzzy sets will be generated in the sense that its α-level sets will be identical to the sets of the original family. In order to achieve this purpose, any arbitrary families will be rearranged as the nested families by applying some suitable functions to the original families that are formulated from the collected data.

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Existence and uniqueness for the construction of fuzzy sets from a solidly nested family

Cited by 3 publications

References 20 publications

Risk Evaluation in Failure Mode and Effects Analysis Using Fuzzy Measure and Fuzzy Integral

Risk Evaluation in Failure Mode and Effects Analysis Using Fuzzy Measure and Fuzzy Integral

Weightable quasi-metrics related to fuzzy sets

Generating fuzzy sets from the families of sets

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