Semilinear Spaces - Basic Structures for Fuzzy Systems∗
نویسنده
چکیده
The notion of a linear space is generalized to the case where the underlying algebra is a commutative monoid and the set of scalars is a semiring reduct of a BL-algebra or an MValgebra. The notions of linear dependence and independence are also introduced and necessary and sufficient conditions when vectors form a basis of a semi-linear space are given. A linear mapping between two semilinear spaces is defined and considered in the case when it is represented by a fuzzy relation. An example of a fuzzy system which can be characterized by fuzzy IF-THEN rules is modeled using the respective linear mapping.
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