Let $$Q \rightarrow R$$ be a surjective homomorphism of Noetherian rings such that Q is Gorenstein and R as Q-bimodule admits finite resolution by modules which are projective on both sides. We define an adjoint pair functors between the homotopy category totally acyclic R-complexes Q-complexes. This analogous to classical module categories Q. As consequence, we obtain precise notion approximat...

Fuzzy rule bases are built of linguistic, qualitative knowledge. By using fuzzy rules we are able to specify simple models of complex systems. But, we have to pay a price for this simpliication. In general, fuzzy knowledge is gradually incomplete and gradually inconsistent. This paper deals with the detection of such partial gaps of knowledge or local contradictions. In order to do so we introd...