Direct Methods for Singular Fuzzy Linear Systems Using Generalized Inverses and Its Applications

Abinaya R; Ashish Kumar Nandi

Home/Archive/arXiv

arXiv · 2607.15318

Direct Methods for Singular Fuzzy Linear Systems Using Generalized Inverses and Its Applications

Abinaya R·Ashish Kumar Nandi

View original source ↗Read source document ↗Export metadata ↓

Abstract

Fuzzy matrices provide an effective framework for modeling uncertainty in scientific and engineering problems, particularly fuzzy linear systems. This work transforms a general FLS into a crisp linear system using an embedding approach and reduces it to a standard block structured form via column operations. A direct LU decomposition is developed under suitable range conditions, enabling the computation of minimum norm solutions of rectangular FLS using the generalized inverses. A full rank decomposition is further proposed to compute the Moore Penrose inverse for arbitrary rectangular matrices, and consistency conditions for these inverses are established. A unified framework for obtaining strong fuzzy solutions based on monotonicity and non-negativity constraints are presented. Efficient algorithms based on LU, QR, and SVD decompositions are developed for the block structured matrix. The applicability and computational efficiency of the proposed methods are demonstrated through fuzzy circuit equations and Markov chain processes.

Explore related subjects

math.GM math.RA

Keep this discovery

BibTeX RIS

Abinaya R, Ashish Kumar Nandi. 2026-07-16. Direct Methods for Singular Fuzzy Linear Systems Using Generalized Inverses and Its Applications. https://arxiv.org/abs/2607.15318

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Average Chord Lengths in a Triangle

Let $P$ be a point inside a triangle $T$. We consider the average length of the chords of $T$ through $P$, where the direction of the chord is chosen uniformly. An elementary formula is obtained in terms of the distances from $P$ to the sides and vertices of the triangle. Several classical triangle centers give especially simple specializations. For example, if $I$ is the incenter, then \[ M_T(I)=\frac{2r}{\pi} \log\left(\cot\frac A4\cot\frac B4\cot\frac C4\right). \] Our main result is the sharp inequality \[ M_T(P)\le \frac{p}{\pi\sqrt3}\log(2+\sqrt3), \] valid simultaneously for every triangle of perimeter $p$ and every interior point $P$. Thus, among all such pairs $(T,P)$, the largest possible average chord length occurs only when $T$ is equilateral and $P$ is its center. The proof is an elementary symmetrization argument. We close with brief remarks relating the problem to the radial center of a convex body, the electrostatic potential center of a triangle, and dual quermassintegrals.

math.GM↗

arXiv2026

The decrease in sectional curvature of the Fisher--Rao manifold of beta distributions

In the paper, the author develops a general convexity lemma and applies it to demonstrate the monotonic decrease of a function involving polygamma functions, arising from the sectional curvature of the Fisher--Rao manifold of beta distributions.

math.GM↗

arXiv2026

A Proof of Liu's Conjecture on the Fundamental Triangle Inequality

Let $a,b,c$ be the side lengths of a triangle, and let $R$ and $r$ denote its circumradius and inradius, respectively. We prove a conjecture of Liu stating that \[\sum_{\mathrm{cyc}} \left(\frac{a(b+c-a)}{bc}\right)^k \geq 2+\left(\frac{2r}{R}\right)^k,~~k>1, \] with the reverse inequality for $0<k<1$. The proof reduces the problem to three positive variables with fixed sum and product. We also determine the equality cases.

math.GM↗