Topic
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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TL;DR: Six methods are described that represent different alternatives in the fuzzy modeling process and how they can be integrated with a genetic algorithms to obtain a first approximation to the fuzzy rules without any assumption about the structure of the data.
Abstract: This paper presents different approaches to the problem of fuzzy rules extraction by using fuzzy clustering as the main tool. Within these approaches we describe six methods that represent different alternatives in the fuzzy modeling process and how they can be integrated with a genetic algorithms. These approaches attempt to obtain a first approximation to the fuzzy rules without any assumption about the structure of the data. Because the main objective is to obtain an approximation, the methods we propose must be as simple as possible, but also, they must have a great approximative capacity and in that way we work directly with fuzzy sets induced in the variables input space. The methods are applied to four examples and the errors obtained are specified in the different cases.
169 citations
TL;DR: This work has shown that a fuzzy analytical hierarchy process (FAHP) is an effective risk assessment method in which a questionnaire is used to collect experts’ responses, but determining fuzzy numbers and estimates is difficult.
Abstract: A fuzzy analytical hierarchy process (FAHP) is an effective risk assessment method in which a questionnaire is used to collect experts’ responses. However, determining fuzzy numbers and est...
169 citations
TL;DR: In this paper, the authors proposed an approximate approach for ranking fuzzy numbers based on the left and right dominance of one fuzzy number over the other, which is useful in ranking the fuzzy numbers when membership functions cannot be acquired.
Abstract: This study presents an approximate approach for ranking fuzzy numbers based on the left and right dominance. The proposed approach only requires a few left and right spreads at some α-levels of fuzzy numbers to determine the respective dominance of one fuzzy number over the other. The total dominance is then determined by combining the left and right dominance based on a decision maker's optimistic perspectives. Such a dominance is useful in ranking the fuzzy numbers when membership functions cannot be acquired. The approach proposed herein is relatively simple in terms of computational efforts and is efficient when ranking a large quantity of fuzzy numbers. By using a few left and right spreads, two groups of examples demonstrate the accuracy and applicability of the proposed approach.
169 citations
TL;DR: This notion provides a useful framework to compare different concepts of fuzzy random variables, using methods of general topology and drawing on results from topological measure theory and the theory of analytic spaces.
168 citations
TL;DR: This work improves Hong and Lee's general learning method by first selecting relevant attributes and building appropriate initial membership functions, which effectively induces membership functions and fuzzy if-then rules.
168 citations