Abstract
Fuzzy equations were solved by using different standard methods. One of the well-known methods is the method of -cut. The method of superimposition of sets has been used to define arithmetic operations of fuzzy numbers. In this article, it has been shown that the fuzzy equation AX B , where A, X, B are fuzzy numbers can be solved by using the method of superimposition of sets. It has also been shown that the method gives same result as the method of -cut.
Highlights
Fuzzy equations were investigated by Dubois and Prade [1]
Fuzzy equations were solved by using different standard methods
Mazarbhuiya et al [12] defined the arithmetic operations viz. addition and subtraction of fuzzy numbers with out using the method of -cuts i.e. using a method called superimposition of sets introduced by Baruah [13]
Summary
Fuzzy equations were investigated by Dubois and Prade [1]. Sanchez [2] put forward a solution of fuzzy equation by using extended operations. Various researchers have proposed different methods for solving the fuzzy equations [see e.g. Buckley [3], Wasowski [4], Biacino and Lettieri [5]. After this a lot research papers have appeared proposing solutions of various types of fuzzy equations viz. Klir and Yuan [11] solved the fuzzy equations A X B where A, X and B are fuzzy numbers, by using the method of -cut.
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