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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…

The novelty of this paper is to construct the explicit combinatorial formula for the number of all distinct fuzzy matrices of finite order, which leads us to invent a new sequence. In order to achieve this new sequence, we analyze the…

This survey describes a class of methods known as "fast direct solvers". These algorithms address the problem of solving a system of linear equations $\boldsymbol{Ax}=\boldsymbol{b}$ arising from the discretization of either an elliptic PDE…

In this paper, We have introduced a new class of sequences of fuzzy numbers defined by using modulus function and generalized weighted mean over the class defined in \cite{OS}. We have proved that this class form a quasilinear complete…

This paper considers the linear objective function optimization with respect to a novel system of fuzzy relation equations, where the fuzzy compositions are defined by the minimum t-norm. It is proved that the feasible solution set is…

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 defuzzification method of WABL is investigated, its properties are analyzed. The WABL method is applied to some fuzzy models. The package of applied programs is worked out on the base of proposed algorithms. The obtained in…

Design of a fuzzy rule based classifier is proposed. The performance of the classifier for multispectral satellite image classification is improved using Dempster- Shafer theory of evidence that exploits information of the neighboring…

In this paper, we introduce a Bayesian abstract fuzzy economy model and we prove the Bayesian fuzzy equilibrium existence. As applications, we prove the existence of the solutions for two types of random quasi-variational inequalities with…

In traditional ELM and its improved versions suffer from the problems of outliers or noises due to overfitting and imbalance due to distribution. We propose a novel hybrid adaptive fuzzy ELM(HA-FELM), which introduces a fuzzy membership…

One of the weaknesses of classical (fuzzy) rough sets is their sensitivity to noise, which is particularly undesirable for machine learning applications. One approach to solve this issue is by making use of fuzzy quantifiers, as done by the…

In this paper we propose a novel approach for learning from data using rule based fuzzy inference systems where the model parameters are estimated using Bayesian inference and Markov Chain Monte Carlo (MCMC) techniques. We show the…

Neuro-Fuzzy Modeling has been applied in a wide variety of fields such as Decision Making, Engineering and Management Sciences etc. In particular, applications of this Modeling technique in Decision Making by involving complex Systems of…

This book gives the basic notions of fuzzy matrix theory and its applications to simple fuzzy models. The approach is non-traditional in order to attract many students to use this methodology in their research. The traditional approach of…

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…

Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems is a fundamental yet challenging problem in many fields of science and engineering. Existing methods face significant obstacles: Gaussian-based filters struggle…

Reliability assessment of distribution system, based on historical data and probabilistic methods, leads to an unreliable estimation of reliability indices since the data for the distribution components are usually inaccurate or…

Accuracy in neural PDE solvers often breaks down not because of limited expressivity, but due to poor optimisation caused by ill-conditioning, especially in multi-fidelity and stiff problems. We study this issue in Physics-Informed Extreme…

Poisson's equation is the canonical elliptic partial differential equation. While there exist fast Poisson solvers for finite difference and finite element methods, fast Poisson solvers for spectral methods have remained elusive. Here, we…

In this work we propose a formal system for fuzzy algebraic reasoning. The sequent calculus we define is based on two kinds of propositions, capturing equality and existence of terms as members of a fuzzy set. We provide a sound semantics…