Generalized Triangular Norms Based Product and Similarity of Fuzzy Sets

This paper first generalizes the definitions of inner product and outer product of fuzzy sets by replacing the lattice operators with triangular norms in the existing definitions, and then discusses their new properties. Based on the new definitions and the obtained results, lattice similarity, which is the original model of the axiomatic definition relevant to the similarity of fuzzy sets, is re-examined and some new perspectives are presented.