In this paper, the notion of closure operators of matroids  is generalized to fuzzy setting  which is called $M$-fuzzifying closure operators, and some properties of $M$-fuzzifying closure operators are discussed. The $M$-fuzzifying matroid induced by an $M$-fuzzifying closure operator can induce an $M$-fuzzifying closure operator. Finally, the characterizations of $M$-fuzzifying acyclic matroi...

We define a notion of program which is not a computer program but an operator program: a detailed description of actions performed and decisions taken by a human operator (computer user) performing a task to achieve a goal in a simple setting consisting of that user, one or more computers and a work environment. Our definition and notations are based on the program algebra PGA: a small body of ...

Using the notion of a symmetric virtual diagonal for Banach algebra, we prove that algebra is symmetrically amenable if its second dual amenable. We introduce operator amenability in category completely contractive algebras as an analogue algebras. give some equivalent formulations and investigate hereditary properties show locally compact groups to Fourier algebra. Finally, discuss about Jorda...

For a bounded linear operator on Hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎We study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎Also we show that any quasinilpotent operator $T$ has an hypernoncyclic vector‎, ‎and so $T$ has a nontrivial hyperinvariant subspace‎.

In this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. It is shown that it generates the Kolmogorov entropy as a special case. If $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

We consider the bilinear Fourier integral operatorS(f, g)(x) =ZRdZRdei1(x,)ei2(x,)(x, , ) ˆ f()ˆg()d d,on modulation spaces. Our aim is to indicate this operator is well defined onS(Rd) and shall show the relationship between the bilinear operator and BFIO onmodulation spaces.

By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.

As an special intuitionistic fuzzy set defined on the real number set, triangular intuitionistic fuzzy number (TIFN) is a fundamental tool for quantifying an ill-known quantity. In order to model the decision maker's overall preference with mandatory requirements, it is necessary to develop some Bonferroni harmonic mean operators for TIFNs which can be used to effectively intergrate the informa...