In this paper, the concepts of $L$-concave structures, concave $L$-interior operators and concave $L$-neighborhood systems are introduced. It is shown that the category of $L$-concave spaces and the category of concave $L$-interior spaces are isomorphic, and they are both isomorphic to the category of concave $L$-neighborhood systems whenever $L$ is a completely distributive lattice. Also, it i...

In a previous paper [10] we explored the notion of coherent fuzzy consequence operator. It is well-known that the operator induced by a fuzzy preorder through Zadeh’s compositional rule is always a coherent fuzzy consequence operator. It is also known that the relation induced by a fuzzy consequence operator is a fuzzy preorder if such operator is coherent [7]. Fuzzy closing operators of mathem...

As an extension of the intuitionistic fuzzy set, intuitionistic trapezoidal fuzzy set is an invaluable mathematical theory to express uncertain phenomenon in our real word. In this article, the aggregation methods of the intuitionistic trapezoidal fuzzy information are chief researched. Firstly, the generalized aggregation operator is introduced for aggregating intuitionistic trapezoidal fuzzy ...

Suppose L is a differential operator of order k. Moreover, let u be a function defined and k times continuously differentiable in the closure of a domain Ω of R. Provided the adjoint differential operator possesses a fundamental solution, we shall see that u can be recovered from Lu and the boundary values of u. Strictly speaking, we shall get an integral representation of u in form of the sum ...

Einstein product and Einstein sum are good alternatives to the algebraic product and algebraic sum, respectively. Nevertheless, it seems that in the literature there is little investigation on aggregation techniques using the Einstein operations on IFS for aggregating a collection of intuitionistic fuzzy value (IFV). The induced ordered weighted averaging operator is more suitable for aggregati...

In current PC computing environment, the fuzzy clustering method based on perturbation (FCMBP) is failed when dealing with similar matrices whose orders are higher than tens. The reason is that the traversal process adopted in FCMBP is exponential complexity. This paper treated the process of finding fuzzy equivalent matrices with smallest error from an optimization point of view and proposed a...

In this paper, we present the induced generalized intuitionistic fuzzy ordered weighted averaging (IGIFOWA) operator. It is a new aggregation operator that generalized the IFOWA operator, including all the characteristics of both the generalized IFOWA and the induced IFOWA operators. It provides a very general formulation that includes as special cases a wide range of aggregation operators for ...

With respect to multiple attribute decision making (MADM) problems in which the attribute value takes the form of intuitionistic trapezoidal fuzzy number, a new decision making analysis method is developed. Firstly, some operational laws and expected values of intuitionistic trapezoidal fuzzy numbers, and distance between two intuitionistic trapezoidal fuzzy numbers, are introduced, and the com...

We shall show that B(H) can be represented by the strong closure of the linear span of the compounds of a fixed operator in B(H) and the rank one operators, composed only by the vectors of a certain orthonormal basis of H, in a nest algebra, even, under some assumption, in the radical of a nest algebra. 0. Notations, basic relationships, and introduction Throughout, the nonzero Hilbert space H ...