Finite rank perturbations of a semi-bounded self-adjoint operator A are studied in the scale of Hilbert spaces associated with A. A concept of quasi-boundary value space is used to describe self-adjoint operator realizations of regular and singular perturbations of A by the same formula. As an application the one-dimensional Schrödinger operator with generalized zero-range potential is consider...

In this paper, we have introduced the concept of fuzzy ordered AG-groupoids which is the generalization of fuzzy ordered semigroups first considered by Kehayopulu and Tsingelis (2002). We have studied some important features of a left regular ordered AG-groupoid in terms of fuzzy left ideals, fuzzy right ideals, fuzzy two-sided ideals, fuzzy generalized bi-ideals, fuzzy bi-ideals, fuzzy interio...

The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. Y.B. Jun and S.Z. Song introduced the notion of intuitionistic fuzzy points. In this paper we find some relations between the intuitionistic fuzzy ideals of a semigroup S and the set of all intuitionistic fuzzy points of S. Keywords—Semigroup, Regular(intra-regular) semigroup, In...

We define strict closure space algebras as Boolean algebras augmented with a unary operation Int that satisfies conditions analogous to those of the interior operation from strict closure spaces. We also consider a first order modal logic SCS in which the necessity operator satisfies analogous conditions. Sikorski proved that every interior algebra can be represented as an algebra of subsets of...

The closure of a regular language under a [partial, semi-] commutation I has been extensively studied. We present new advances on two problems of this area: (1) When is the closure of a regular language under [partial, semi-] commutation still regular? (2) Are there any robust classes of languages closed under [partial, semi-] commutation? We show that the class Pol(G) of polynomials of group l...

We consider n-dimensional semi-algebraic spatial databases. We compute in first-order logic extended with a transitive closure operator, a linear spatial database which characterizes the semi-algebraic spatial database up to a homeomorphism. In this way, we generalize our earlier results to semi-algebraic spatial databases in arbitrary dimensions, our earlier results being true for only two dim...

In this paper, extension of the EQ-logic by the ∆connective is introduced. The former is a new kind of many-valued logic which based on EQ-algebra of truth values, i.e. the algebra in which fuzzy equality is the fundamental operation and implication is derived from it. First, we extend the EQ-algebra by the ∆ operation and then introduce axioms and inference rules of EQ∆-logic. We also prove th...

fuzzy logic, 67algebraic semantics, 53approximate reasoning, 6axiomatic extensions of MTL, 56 Bellman, R., 21bipolar possibilistic logic, 93BL logic, 51 canonical chain, 66canonical completeness, 66canonical extension, 83Carnap, R., 3comparative truth, 63compositionality, 29computational complexity, 73core fuzzy logic, 58 De Finetti B., 3degre...