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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 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…
In this paper, systems of linear differential equations with crisp real coefficients and with initial condition described by a vector of fuzzy numbers are studied. A new method based on the geometric representations of linear…
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…
Determining the reliability of evidence sources is a crucial topic in Dempster-Shafer theory (DST). Previous approaches have addressed high conflicts between evidence sources using discounting methods, but these methods may not ensure the…
Fuzzy rule based classification systems are one of the most popular fuzzy modeling systems used in pattern classification problems. This paper investigates the effect of applying nine different T-norms in fuzzy rule based classification…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
In this paper, notion of p - norm generalized trapezoidal intuitionistic fuzzy numbers is introduced. A new ranking method is introduced for p - norm generalized trapezoidal intuitionistic fuzzy numbers. Also we consider linear programming…
We propose two practical non-convex approaches for learning near-isometric, linear embeddings of finite sets of data points. Given a set of training points $\mathcal{X}$, we consider the secant set $S(\mathcal{X})$ that consists of all…
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…
While approaches to model the progression of fracture have received significant attention, methods to find the solution to the associated nonlinear equations have not. In general, nonlinear solution methods and optimization methods have a…
This preliminary note presents a heuristic for determining rank constrained solutions to linear matrix equations (LME). The method proposed here is based on minimizing a non-convex quadratic functional, which will hence-forth be termed as…
Rule-based models are essential for high-stakes decision-making due to their transparency and interpretability, but their discrete nature creates challenges for optimization and scalability. In this work, we present the Fuzzy Rule-based…
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…
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…
In this article, the piecewise-linear finite element method (FEM) is applied to approximate the solution of time-fractional diffusion equations on bounded convex domains. Standard energy arguments do not provide satisfactory results for…
The low-rank matrix reconstruction (LRMR) approach is widely used in direction-of-arrival (DOA) estimation. As the rank norm penalty in an LRMR is NP-hard to compute, the nuclear norm (or the trace norm for a positive semidefinite (PSD)…
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…
The purpose of this paper is to point to the usefulness of applying a linear mathematical formulation of fuzzy multiple criteria objective decision methods in organising business activities. In this respect fuzzy parameters of linear…
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…