A method for generalized fuzzy rough sets and application to fuzzy control systems

Zadeh fuzzy set is defined with single fuzzy membership for incomplete information. Fuzzy set with two fuzzy membership functions "True" and "False" will give more information than the single fuzzy membership function. Zadeh and Mamdani fuzzy conditional inferences need to know both "Precedent part" and "Consequent part". In many applications like Medical diagnosis, Business intelligence and Control systems, the consequent part may not be known. In this paper, fuzzy conditional inference is studied when consequent part is not known. Generalized fuzzy logic with two membership function is studied for Rough sets. Fuzzy Certainty Factor(FCF ) is studied as the difference of "True " and "False" to eliminate the conflict of evidence The fuzzy control system is given as an application.