A family of similarity and star products: new additions to fuzzy relational products

In this paper, a family of new fuzzy relational products is presented. This new family of products is based on the Similarity product and the Star product previously defined by the author and his colleagues. The products have been developed from practical viewpoints arisen in certain applications for which the semantics of the classical fuzzy relational products has proven somewhat inadequate. These two products are further extended here. The definitions and semantics of the two products together with those of their respective variations are elaborated. Suggestions on the products' potential application are also discussed. These new additions together with the classical fuzzy relational products would certainly contribute greatly to our ability to manipulate and process information with uncertainty by means of fuzzy relations.