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Fuzzy number

About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.


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Proceedings ArticleDOI
01 Jan 1993
TL;DR: An automatic fuzzy system design method that uses a genetic algorithm and integrates three design stages that was applied to the classic inverted-pendulum control problem and has been shown to be practical through a comparison with another method.
Abstract: The authors propose an automatic fuzzy system design method that uses a genetic algorithm and integrates three design stages. The method determines membership functions, the number of fuzzy rules, and the rule-consequent parameters at the same time. Because these design stages may not be independent, it is important to consider them simultaneously to obtain optimal fuzzy systems. The method includes a genetic algorithm and a penalty strategy that favors systems with fewer rules. The method was applied to the classic inverted-pendulum control problem and has been shown to be practical through a comparison with another method. >

419 citations

Journal ArticleDOI
TL;DR: The proposed fuzzy risk analysis method is more flexible and more intelligent than the existing methods due to the fact that it considers the degrees of confidence of decisionmakers' opinions.
Abstract: In this paper, we present a new method for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. Firstly, we present a method called the simple center of gravity method (SCGM) to calculate the center-of-gravity (COG) points of generalized fuzzy numbers. Then, we use the SCGM to propose a new method to measure the degree of similarity between generalized fuzzy numbers. The proposed similarity measure uses the SCGM to calculate the COG points of trapezoidal or triangular generalized fuzzy numbers and then to calculate the degree of similarity between generalized fuzzy numbers. We also prove some properties of the proposed similarity measure and use an example to compare the proposed method with the existing similarity measures. The proposed similarity measure can overcome the drawbacks of the existing methods. We also apply the proposed similarity measure to develop a new method to deal with fuzzy risk analysis problems. The proposed fuzzy risk analysis method is more flexible and more intelligent than the existing methods due to the fact that it considers the degrees of confidence of decisionmakers' opinions.

418 citations

Journal ArticleDOI
TL;DR: The similarity between fuzzy systems and mathematical approximation is discussed and an idea to improve approximation accuracy is suggested based on uniform approximation bounds.
Abstract: In this paper, the approximation properties of MIMO fuzzy systems generated by the product inference are discussed. We first give an analysis of fuzzy basic functions (FBF's) and present several properties of FBF's. Based on these properties of FBF's, we obtain several basic approximation properties of fuzzy systems: 1) basic approximation property which reveals the basic approximation mechanism of fuzzy systems; 2) uniform approximation bounds which give the uniform approximation bounds between the desired (control or decision) functions and fuzzy systems; 3) uniform convergent property which shows that fuzzy systems with defined approximation accuracy can always be obtained by dividing the input space into finer fuzzy regions; and 4) universal approximation property which shows that fuzzy systems are universal approximators and extends some previous results on this aspect. The similarity between fuzzy systems and mathematical approximation is discussed and an idea to improve approximation accuracy is suggested based on uniform approximation bounds. >

418 citations

Journal ArticleDOI
TL;DR: A supplier evaluation approach based on the analytic network process (ANP) and the technique for order performance by similarity to ideal solution (TOPSIS) methods to help a telecommunication company in the GSM sector in Turkey under the fuzzy environment where the vagueness and subjectivity are handled with linguistic terms parameterized by triangular fuzzy numbers.
Abstract: With the globalization and the emergence of the extended enterprise of interdependent organizations, there has been a steady increase in the outsourcing of parts and services. This has led firms to give more importance to the purchasing function and its associated decisions. Since these decisions require a long term investment for the telecommunication industry especially and affect the strategic positioning of the companies in the sector, the selection of the proper supplier is one of the most important problems. Supplier selection is a multi-criteria problem which includes both tangible and intangible factors. This paper develops a supplier evaluation approach based on the analytic network process (ANP) and the technique for order performance by similarity to ideal solution (TOPSIS) methods to help a telecommunication company in the GSM sector in Turkey under the fuzzy environment where the vagueness and subjectivity are handled with linguistic terms parameterized by triangular fuzzy numbers. Contrary to conventional Fuzzy ANP (FANP) methodology in the literature, we use triangular fuzzy numbers in all pairwise comparison matrices in the FANP. Hence, criteria weights are calculated as the triangular fuzzy numbers and then these fuzzy criteria weights are inserted to the fuzzy TOPSIS methodology to rank the alternatives. This approach is demonstrated with a real world case study involving six main evaluation criteria that the company has determined to choose the most appropriate supplier. The study was followed by the sensitivity analyses of the results.

417 citations

Journal ArticleDOI
TL;DR: A fuzzy TOPSIS based methodology is applied to solve the solid waste transshipment site selection problem in Istanbul, Turkey and the criteria weights are calculated by using the AHP.

417 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023202
2022446
2021696
2020649
2019653
2018733