Solution of fuzzy equations with extended operations |
| |
Authors: | Elie Sanchez |
| |
Institution: | Service Universitaire de Biomathématiques, Faculté de Médecine, Marseille, France |
| |
Abstract: | Assuming that 1 is any operation defined on a product set X × Y and taking values on a set Z, it can be extended to fuzzy sets by means of Zadeh's extension principle. Given a fuzzy subset C of Z, it is here shown how to solve the equation (or ) when a fuzzy subset A of X (or a fuzzy subset B of Y) is given. The methodology we provide includes, as a special case, the resolution of fuzzy arithmetical operations, i.e. when 1 stands for +, ?, × or ÷, extended to fuzzy numbers (fuzzy subsets of the real line). The paper is illustrated with several examples in fuzzy arithmetic. |
| |
Keywords: | Fuzzy equations Extension principle Fuzzy arithmetic |
本文献已被 ScienceDirect 等数据库收录! |
|