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In this paper, the definition of fuzzy rough relation on a set will be introduced and then it would be proved that the collection of such relations is closed under different binary compositions such as, algebraic sum, algebraic product etc.…
This paper investigates the solutions of a family of certain linear fuzzy arithmetic equations that involve fuzzy numbers belonging to certain finite-dimensional vector spaces of $\mathbb{R}_{\mathcal{F}}$, called…
We prove an uniform boundedness principle for the Lipschitz seminorm of continuous, monotone, positively homogeneous and subadditive mappings on suitable cones of functions. The result is applicable to several classes of classically…
Bipolar fuzzy relation equations arise as a generalization of fuzzy relation equations considering unknown variables together with their logical connective negations. The occurrence of a variable and the occurrence of its negation…
Let us denote ${\cal V}$, the finite dimensional vector spaces of functions of the form $\psi(x) = p_n(x) + f(x) p_m(x)$ where $p_n(x)$ and $p_m(x)$ are arbitrary polynomials of degree at most $n$ and $m$ in the variable $x$ while $f(x)$…
We solve the fuzzy linear systems in a fuzzy number space $\mathcal{X}$, namely the Gaussian probability density membership function (Gaussian-PDMF) space. The fuzzy linear systems include two types: the semi-fuzzy linear system (SFLS) and…
Fuzzy Neural Networks (FNNs) are effective machine learning models for classification tasks, commonly based on the Takagi-Sugeno-Kang (TSK) fuzzy system. However, when faced with high-dimensional data, especially with noise, FNNs encounter…
Strongly irreducible operators can be considered as building blocks for bounded linear operators on complex separable Hilbert spaces. Many bounded linear operators can be written as direct sums of at most countably many strongly irreducible…
Real and complex norms of a linear operator acting on a normed complexified space are considered. Bounds on the ratio of these norms are given. The real and complex norms are shown to coincide for four classes of operators: 1) real linear…
We establish global regularity of multilinear Fourier integral operators that are associated to nonlinear wave equations on product of $L^p$ spaces by proving endpoint boundedness on suitable products spaces containing combinations of the…
In this article, we give a representation of bounded complex linear operators which preserve idempotent elements on the Fourier algebra of a locally compact group. When such an operator is moreover positive or contractive, we show that the…
The \emph{Continuity Problem} is the question whether effective operators are continuous, where an effective operator $F$ is a function on a space of constructively given objects $x$, defined by mapping construction instructions for $x$ to…
In this paper, we are trying to examine trade offs between fuzzy logic and certain Bayesian networks and we propose to combine their respective advantages into fuzzy certain Bayesian networks (FCBN), a certain Bayesian networks of fuzzy…
In this paper, an optimization model with a linear objective function subjected to a system of fuzzy relation equations (FRE) is studied where the feasible region is defined by the Dombi t-norm. Dombi family of t-norms includes a parametric…
Building upon specific compatibility conditions, we establish fundamental structural results concerning ordering relations for triangular fuzzy numbers. We demonstrate that orders satisfying compatibility with arithmetic operations, MIN-MAX…
This paper discusses a class of uncertain optimization problems, in which unknown parameters are modeled by fuzzy intervals. The membership functions of the fuzzy intervals are interpreted as possibility distributions for the values of the…
In this paper, we introduce a novel fuzzy structure named "fuzzy primal". We study the essential properties and discuss basic operations on it. A fuzzy operator (.)$^\diamond$ on the family of all fuzzy sets is introduced here by applying…
Over past several years, deep learning has achieved huge successes in various applications. However, such a data-driven approach is often criticized for lack of interpretability. Recently, we proposed artificial quadratic neural networks…
The purpose of this survey article is a comprehensive study of operator Lipschitz functions. A continuous function $f$ on the real line ${\Bbb R}$ is called operator Lipschitz if $\|f(A)-f(B)\|\le{\rm const}\|A-B\|$ for arbitrary…
In this paper we first define the category of fuzzy hyper BCK- algebras. After that we show that the category of hyper BCK-algebras has equalizers, coequalizers, products. It is a consequence that this category is complete and hence has…