Characterizations of obstinate filters in semihoops

Abstract

In this paper, we consider fundamental properties of obstinate filters in semihoops and give some characterizations of them.  Also, we discuss the relationship between obstinate filters and other types of filters (maximal, implicative, positive implicative, normal and fantastic filters) of semihoops and prove that a filter is an obstinate filter if and only if it is a maximal filter and positive implicative filter.  Finally, we give some characterizations of simple semihoop by obstinate filter and prove that the homomorphic image of obstinate filters are also obstinate filters.  These results will provide a more general algebraic foundation for inference rule in fuzzy logic based on left continuous t-norms.