In the formal and fully graded setting of Fuzzy Class Theory (or higher-order fuzzy logic) we make an initial investigation into basic notions of fuzzy topology. In particular we study graded notions of fuzzy topology regarded as a fuzzy system of open or closed fuzzy sets and as a fuzzy system of fuzzy neighborhoods. We show their basic graded properties and mutual relationships provable in Fu...

Various expanded rough set models based on tolerance relations enlarge the application fields of rough set theory. Through generating tolerance relations to fuzzy tolerance relations and combining with dominance relations, a tolerance class of a fuzzy tolerance relation is further decomposed into a positive fuzzy tolerance class, a negative fuzzy tolerance class and a purely fuzzy tolerance cla...

In this paper we present the ITP/OCL tool, a rewritingbased tool that supports automatic validation of UML class diagrams with respect to OCL constraints. Its implementation is directly based on the equational specification of UML+OCL class diagrams. It is written entirely in Maude making extensive use of its reflective capabilities. We also give notice of the Visual ITP/OCL, a Java graphical i...

We show how higher-order rewriting may be encoded into rst-order rewriting modulo an equational theory E. We obtain a characterization of the class of higher-order rewriting systems which can be encoded by rst-order rewriting modulo an empty theory (that is, E = ;). This class includes of course the-calculus. Our technique does not rely on a particular substitution calculus but on a set of abst...

Based on fuzzy one-class support vector machine (SVM) and least squares (LS) oneclass SVM, we propose an LS fuzzy one-class SVM to deal with the class imbalanced problem. The LS fuzzy one-class SVM applies a fuzzy membership to each sample and attempts to solve the modified primal problem. Hence, we just need to solve a system of linear equations as opposed solving the quadratic programming pro...

We introduce the concept of semantic paramodulation as a \semantic" de nition of paramodulation (in the sense that it applies to any model, not only to the term algebra) within the framework of category-based equational logic (introduced by [8, 9]). This not only generalises the traditional syntactic approaches to paramodulation, but also provides an abstract framework for a uni ed treatment of...

We investigate the representation and complete classes for algebras of partial functions with signature relative complement domain restriction. provide prove correctness a finite equational axiomatisation class representable by functions. As corollary, same equations axiomatise injective For representations, we show that is meet if only it join complete. Then completely precisely atomic algebra...

Abstract We provide a new perspective on extended Priestley duality for large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice operations are each presented as pair partial dual spaces. In enriched environment, equational conditions the algebraic side may more often be rendered first-order particular, we specialize our general results t...