Logarithmic Similarity Measure between Interval-Valued Fuzzy Sets and Its Fault Diagnosis Method

Abstract

Fault diagnosis is an important task for the normal operation and maintenance of equipment. In many real situations, the diagnosis data cannot provide deterministic values and are usually imprecise or uncertain. Thus, interval-valued fuzzy sets (IVFSs) are very suitable for expressing imprecise or uncertain fault information in real problems. However, existing literature scarcely deals with fault diagnosis problems, such as gasoline engines and steam turbines with IVFSs. However, the similarity measure is one of the important tools in fault diagnoses. Therefore, this paper proposes a new similarity measure of IVFSs based on logarithmic function and its fault diagnosis method for the first time. By the logarithmic similarity measure between the fault knowledge and some diagnosis-testing samples with interval-valued fuzzy information and its relation indices, we can determine the fault type and ranking order of faults corresponding to the relation indices. Then, the misfire fault diagnosis of the gasoline engine and the vibrational fault diagnosis of a turbine are presented to demonstrate the simplicity and effectiveness of the proposed diagnosis method. The fault diagnosis results of gasoline engine and steam turbine show that the proposed diagnosis method not only gives the main fault types of the gasoline engine and steam turbine but also provides useful information for multi-fault analyses and predicting future fault trends. Hence, the logarithmic similarity measure and its fault diagnosis method are main contributions in this study and they provide a useful new way for the fault diagnosis with interval-valued fuzzy information.

Extended TOPSIS method for multi-criteria group decision-making problems under cubic intuitionistic fuzzy environment

“…In order to compare the serformances of the proposed approach with respect to the existing approaches [21,25,30,33,34,40] under the CFSs, IVIFSs, IFSs, and interval-valued FSs environments, an analysis has been conducted. To apply these existing approaches to the considered data, rst, the rating values of CIFNs are converted into these numbers by taking the rating corresponding to IFNs as zero.…”

“…Garg and Arora [29] extended the Li [28] approach to the interval-valued intuitionistic fuzzy soft set environment. Lu and Ye [30] developed logarithm similarity measures to solve the problems under interval-valued fuzzy set environment. Garg and Kumar [31] presented new similarity measures for IFSs based on the connection number of the set pair analysis.…”

Significance of TOPSIS approach to MADM in computing exponential divergence measures for pythagorean fuzzy sets

“…The similarity measures of the IFSs and PFSs are broadly used in various disciplines, comparable to the pattern identification (Peng and Garg, 2019), the clinical finding (Son and Phong, 2016), decision-making (Zhang et al, 2019). However, Lu and Ye (2018) offered similarity measure of IVFSs on log function. Agheli et al 2021 recently proposed a method for calculating Pythagorean similar measure for two Pythagorean fuzzy value by making use of T-norm and S-norm.…”

Similarity between interval-valued fuzzy sets taking into account the width of the intervals and admissible orders

“…In this way, they may improve the numerical results of applications, as can be seen in [1,2,3,5,6,7,17,18,28,36]. Since many applications of fuzzy sets make use of similarity measures [8,10,11,30] (see also the recent works [15,16]) in order to determine the degree of resemblance between fuzzy sets, interval-valued similarities have become also an object of interest for some authors [19,25,31,42].…”