Approximations on intuitionistic fuzzy predicate calculus through rough computing

Abstract

In 1986, Attansov introduced the intuitionistic fuzzy set which is the generalized approach of fuzzy set model introduced by Zadeh. Considering the importance of these two theories, various hybridizations with the available mathematical tools have been derived and they are in practice. Related to the concept of rough sets, the hybridized work of Nakamura, Dubois and Prade are noteworthy. In 2005, G. Ganesan et al., have introduced the concept of thresholds in Rough Fuzzy Hybridizations. Later, in 2008, G. Ganesan et al, derived a naïve approach on approximating the connectives in fuzzy predicate calculus through rough sets. This concept was developed by introducing a threshold on the membership of the arguments in the fuzzy predicates. This work yielded the Two way approximations for the fuzzy connectives. In this work, it is noticed that the complement and the negation of the predicates are found in a unique way, whereas in case of intuitionistic fuzziness, the complement and the negation are to be found in two different ways namely membership based and non membership based. Using this concept, in this paper, we introduce Two way approach on Intuitionistic Fuzzy Logic. Also, in this paper, we derive Two way approximations on each intuitionistic fuzzy connectives using rough sets.