Relational compositions in Fuzzy Class Theory

We present a method for mass proofs of theorems of certain forms in a formal theory of fuzzy relations and classes. The method is based on formal identification of fuzzy classes and inner truth values with certain fuzzy relations, which allows transferring basic properties of sup-T and inf-R compositions to a family of more than 30 composition-related operations, including sup-T and inf-R images, pre-images, Cartesian products, domains, ranges, resizes, inclusion, height, plinth, etc. Besides yielding a large number of theorems on fuzzy relations as simple corollaries of a few basic principles, the method provides a systematization of the family of relational notions and generates a simple equational calculus for proving elementary identities between them, thus trivializing a large part of the theory of fuzzy relations. (C) 2008 Elsevier B.V. All rights reserved.