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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…
In this study, we consider a linear differential equation with fuzzy boundary values. We express the solution of the problem in terms of a fuzzy set of crisp real functions. Each real function from the solution set satisfies differential…
Systems of fuzzy relation equations and inequalities in which an unknown fuzzy relation is on the one side of the equation or inequality are linear systems. They are the most studied ones, and a vast literature on linear systems focuses on…
A major limitation of fuzzy or neuro-fuzzy systems is their failure to deal with high-dimensional datasets. This happens primarily due to the use of T-norm, particularly, product or minimum (or a softer version of it). Thus, there are…
In this paper, we investigate direct solution of FRE and compare their results with expected real consequences. We give an applied example formulated by a FRE problem and show that FRE defined by maximum t-conorm and an arbitrary t-norm can…
The theory of fuzzy mathematics has been proven very effective for defining and solving optimization problems. Fuzzy quadratic programming (FQP) is a consequence of this approach. In this paper, an algorithm has been proposed to solve FQP…
Consider a problem where a set of feasible observations are provided by an expert and a cost function is defined that characterizes which of the observations dominate the others and are hence, preferred. Our goal is to find a set of linear…
In the first part of the two-part series, the model to describe the exact aggregated feasible region (AFR) of multiple types of demand-side resources is derived. Based on a discrete-time unified individual model of heterogeneous resources,…
In regression problems, the use of TSK fuzzy systems is widely extended due to the precision of the obtained models. Moreover, the use of simple linear TSK models is a good choice in many real problems due to the easy understanding of the…
We present a logical framework to represent and reason about fuzzy optimization problems based on fuzzy answer set optimization programming. This is accomplished by allowing fuzzy optimization aggregates, e.g., minimum and maximum in the…
Random fuzzy variables join the modeling of the impreciseness (due to their ``fuzzy part'') and randomness. Statistical samples of such objects are widely used, and their direct, numerically effective generation is therefore necessary.…
The Frank-Wolfe (FW) method is a popular algorithm for solving large-scale convex optimization problems appearing in structured statistical learning. However, the traditional Frank-Wolfe method can only be applied when the feasible region…
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…
Fuzzy relation equations (FRE)are associated with the composition of binary fuzzy relations. In the present work FRE are used as a tool for studying the process of learning a new subject matter by a student class. A classroom application…
Fuzzy Extractor (FE) and Fuzzy Signature (FS) are useful schemes for generating cryptographic keys from fuzzy data such as biometric features. Several techniques have been proposed to implement FE and FS for fuzzy data in an Euclidean…
The purpose of this paper is to study a non-convex fuzzy multi-objective quadratic programming problem, in which both the technological coefficients and resources are fuzzy with nonlinear membership function. A computational procedure to…
Representation learning has emerged as a crucial focus in machine and deep learning, involving the extraction of meaningful and useful features and patterns from the input data, thereby enhancing the performance of various downstream tasks…
The main objective of this paper is to derive the optimality conditions for one type of fuzzy optimization problems. At the beginning, we define a cone of descent direction for fuzzy optimization, and prove that its intersection with the…
In this paper we introduce a technique to produce tighter cutting planes for mixed-integer non-linear programs. Usually, a cutting plane is generated to cut off a specific infeasible point. The underlying idea is to use the infeasible point…
This paper investigates fuzzy nonlinear system equations using an optimization approach. Here, the inner-outer direct search technique is used with fuzzy coefficients and vectors to quantify the uncertain solution. The fuzzy nonlinear…