Algebraic aspects of fuzzy systems

In performing complex tasks, very often, we recur to rules. In following rules we can recognize the general paradigm "given a condition do an action". We can code, in a given formal language, the above paradigm as a conditional statement like "if A then B", where A forms a conditional part, while B is the action part of the rule. In such a way, we can formalize knowledge based system and rule based system, in some formal language. When such rule based systems face with imprecise phenomena, it seems natural to use the formalism of fuzzy set theory. We refer to them as fuzzy rule based system