Resolution of composite fuzzy relation equations based on Archimedean triangular norms

Lately, the sup-t-norm composition of fuzzy relations has been used instead of the well-known max-min. Thus, there is a need for methods of studying a nd solving sup-t-norm fuzzy relation equations (t is any t-norm). In this p aper, the solution existence problem is first studied and solvability crite ria for composite fuzzy relation equations of any t-norm are given. Then, a methodology for solving fuzzy relation equations based on sup-t compositio n, where t is an Archimedean t-norm, is proposed. This resolution method is simpler and faster than those proposed for covering all the continuous t-n orms. The result is important, since, as is shown in the paper, the only co ntinuous t-norm. that is not Archimedean is the "minimum". (C) 2001 Elsevie r Science B.V. All rights reserved.