Fuzzy arithmetics for fuzzy n-poles: When is interactivity irrelevant?

Abstract

We consider binary operations on fuzzy quantities whose interaction is specified by means of a joint possibility distribution. When and to what extent is this interaction relevant? We discuss the problem and tackle it in the case of fuzzy quantities with a finite support, called below fuzzy n-poles. We give a criterion for total irrelevance, once the two fuzzy operands are specified. We argue that fuzzy arithmetics should take inspiration from the arithmetics of random variables rather than crisp arithmetics, so as to get rid of notational inconsistencies. © 2012 Springer-Verlag Berlin Heidelberg.