We present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. First, we introduce a hyper BCK-algebra induced by a max-min general fuzzy automaton. Then, we study the properties of this hyper BCK-algebra. Particularly, some theorems and results for hyper BCK-algebra are proved. For example, it is shown that this structure consists of different ty...

First we show that the cosets of a fuzzy ideal μ in a BCK-algebraX form another BCK-algebra  X/μ (called the fuzzy quotient BCK-algebra of X by μ). Also we show thatX/μ is a fuzzy partition of X and we prove several some isomorphism theorems. Moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition P of a commutative BCK-algebra iscompatible, then P is a fuzzy quo...

There is a fundamental asymmetry between algebras and their dual objects, coalgebras, namely that the dual of a coalgebra is an algebra, but the converse is only true in finite dimensions. We prove that there exists a differential graded coalgebra whose continuous dual is the differential graded algebra of differential forms. This coalgebra will be constructed as an explicit subspace of de Rham...

December 22, 1999 Abstract. Suppose A is a hyperfinite von Neumann algebra with a normal faithful normalized trace τ . We prove that if E is a homogeneous Hilbertian subspace of Lp(τ) (1 ≤ p < ∞) such that the norms induced on E by Lp(τ) and L2(τ) are equivalent, then E is completely isomorphic to the subspace of Lp([0, 1]) spanned by Rademacher functions. Consequently, any homogeneous Hilberti...

The present work concerns the algebra of semi-magic square matrices. These can be decomposed into matrices of specific rotational symmetry types, where the square of a matrix of pure type always has a particular type. We examine the converse problem of categorising the square roots of such matrices, observing that roots of either type occur, but only one type is generated by the functional calc...

0. Introduction. In this paper we consider factorizations of finite rank operators through finite-dimensional C∗-algebras. We are interested in factorization norms involving either the completely bounded norm ‖ ‖cb or Haagerup’s decomposable norm ‖ ‖dec (see [11]). Let us denote byMn the C∗-algebra of all n×n matrices with complex entries. Let A and B be two C∗-algebras, and let us consider a f...

This paper aims to present some inequalities for unitarily invariant norms. In section 2, we give a refinement of the Cauchy-Schwarz inequality for matrices. In section 3, we obtain an improvement for the result of Bhatia and Kittaneh [Linear Algebra Appl. 308 (2000) 203-211]. In section 4, we establish an improved Heinz inequality for the Hilbert-Schmidt norm. Finally, we present an inequality...

The paper considers an early approach toward a (fuzzy) set theory with a graded membership predicate and a graded equality relation which had been developed by the German mathematician D. Klaua in 1965. In the context of the mathematical fuzzy logic MTL of left-continuous t-norms we discuss some properties of these graded relations. We compare the simultaneous recursive definitions of these rel...

The eigenvalue problem for an irreducible nonnegative matrix A = a ij ] in the max algebra system is A x = x, where (A x) i = max j (a ij x j) and turns out to be the maximum circuit geometric mean, (A). A power method algorithm is given to compute (A) and eigenvector x. This method generalizes and simpliies an algorithm due to Braker and Olsder. The algorithm is developed by using results on t...