This paper introduces a new class of fuzzy closure operators called implicative closure operators, which generalize some notions of fuzzy closure operators already introduced by different authors. We show that implicative closure operators capture some usual consequence relations used in Approximate Reasoning, like Chakraborty s graded consequence relation, Castro et al. s fuzzy consequence rel...

Let I , H , S , P , Pf be the usual operators on classes of algebras of the same type (Pf for filtered products). The partially ordered monoid generated by the operators H , S , P with respect to composition of operators, I as an identity element, and a natural ordering between operators is described by Pigozzi (Algebra Universalis 2 (1972), 346–353). Let us denote by M = 〈H,S, P 〉 and by Mf = ...

We study the gauge invariant 't Hooft operator in canonical formalism for Yang-Mills theory as well $\mathcal{N} =4 $ super-Yang-Mills with group U(N) $. It is shown that spectrum of labeled by arbitrary irreducible representation same Wilson representation. So it possible to construct a unitary S making two kinds loop operators transformed into each other. S-duality transformation could be rea...

Abstract We study variants of s -numbers in the context multilinear operators. The notion an $$s^{(k)}$$ s ( k ) -scale k -linear operators is defined. In particular, we shall deal with -scales approximation, Gelf...