FUZZY INNER PRODUCT-SPACES

The N-Euclidean space M(I) is a fuzzy pseudo-normed algebra, whose underlying set is the smallest real vector space including all nonnegative fuzzy real numbers. We introduce axioms for a fuzzy inner product, on a unitary M(I)-module, with values in M(I). We establish the fuzzy Schwarz inequality for fuzzy inner products. We introduce the Cartesian product of fuzzy inner product spaces and investigate the relations between their underlying topologies. We conclude the research by supplying two interesting examples of fuzzy inner product spaces.