Intuitionistic fuzzy (⊗,N)-general regular languages and their minimization implementation

We firstly give the notion of intuitionistic fuzzy (⊗,N)-general regular languages (IF(⊗,N)-GRLs) under a t-norm ⊗ and a fuzzy negation N and study their properties. The similarities and differences between IF(⊗,N)-GRLs and intuitionistic fuzzy regular languages (IFRLs) are investigated for explaining the existence of intuitionistic fuzzy automata (IFAs) (⊗,N)-recognizing IF(⊗,N)-GRLs. Next, we discuss whether or not the set of IF(⊗,N)-GRLs is closed under the generalized operations shown here. Concretely, the set of IF(⊗,N)-GRLs is closed under the generalized intersection, but not closed under the generalized complement, and the necessary and sufficient condition of closure of that set under the generalized union, the generalized concatenation and the generalized Kleene closure is thought as well. We also deliberate on the Pumping lemma and the Myhill-Nerode theorem in the framework of IF(⊗,N)-GRLs. Finally, we study the minimization implementation of IF(⊗,N)-GRLs, that is, for an IF(⊗,N)-GRL f, if it is (⊗,N)-recognized by a given accessible deterministic intuitionistic fuzzy automaton (DIFA) A, then a polynomial-time algorithm is presented to realize the construction of a minimal DIFA (⊗,N)-recognizing f by using A.