We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...

In the present paper, we study some properties of fuzzy norm of linear operators. At first the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is studied.

In this paper, new definitions of $L$-fuzzy closure operator, $L$-fuzzy interior operator, $L$-fuzzy remote neighborhood system, $L$-fuzzy neighborhood system and $L$-fuzzy quasi-coincident neighborhood system are proposed. It is proved that the category of $L$-fuzzy closure spaces, the category of $L$-fuzzy interior spaces, the category of $L$-fuzzy remote neighborhood spaces, the category of ...

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic and geometric aggregation operators with hesitant fuzzy linguistic information. Then, motivated by the idea of traditional arithmetic operation, we have developed some aggregation operators for aggregating hesitant fuzzy linguistic information: hesitant fuzzy linguistic weighted average (...

This paper proposes a new approach based on Bonferroni mean operator and possibility degree to solve fuzzy multi-attribute decision making (FMADM) problems in which the attribute value takes the form of interval type-2 fuzzy numbers. We introduce the concepts of interval possibility mean value and present a new method for calculating the possibility degree of two interval trapezoidal type-2 fuz...

the purpose of this paper is to introduce the concept of l-fuzzybilinear operators. we obtain a decomposition theorem for l-fuzzy bilinearoperators and then prove that a l-fuzzy bilinear operator is the same as apowerset operator for the variable-basis introduced by s.e.rodabaugh (1991).finally we discuss the continuity of l-fuzzy bilinear operators.

in this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. by using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. moreover, we investigate the ...

In some multi-attribute decision making (MADM) problems, various relationships among the decision attributes should be considered. This paper investigates the prioritization relationship of attributes in MADM with trapezoidal intuitionistic fuzzy numbers (TrIFNs). TrIFNs are a special intuitionistic fuzzy set on a real number set and have the better capability to model ill-known quantities. Fir...

In this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. By using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. Also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. Moreover, we investigate the ...

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...