Algebraic analysis of fuzzy systems
نویسندگان
چکیده
In this paper, we have developed an algebraic theory, suitable for the analysis of fuzzy systems. We have used the notions of semiring and semimodule, introduced the notion of semilinear space and gave numerous examples of them and defined also the notions of linear dependence and independence. Then, we have shown that the composition operation, which plays an essential role in the analysis of fuzzy systems because of its role in the compositional rule of inference, can be interpreted as a homomorphism between special semimodules. Consequently, this operation is, in a certain sense, a linear operation. This property formally explains why fuzzy systems are attractive for the applications.
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ورودعنوان ژورنال:
- Fuzzy Sets and Systems
دوره 158 شماره
صفحات -
تاریخ انتشار 2007