Fuzzy relational products in information processing: classical products and new products

This paper summarizes and compares different fuzzy relational products. First, the classical circle product is discussed. Then, another set of classical products, triangle subproduct, triangle superproduct, and square product are revisited for both harsh and soft versions. Afterward, two new fuzzy relational products developed by the authors, namely similarity product and star product are described. These new products have been developed from practical viewpoints of certain applications for which the semantics of the classical products has proven inadequate. The products' definitions and semantics are given, and compared with those of the classical ones where appropriate.