Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2607.22616

A Linear alpha-cut intervals based Parsimonious Fuzzy Best-Worst Method with an Application to Warehouse Location Selection

Vikas V. Sharma·Mohit Kumar
View original source ↗Read source document ↗Export metadata ↓

Abstract

To address computational intensity and crisp weight limitations in the alpha-cut intervals based Fuzzy Best-Worst Method (alpha-FBWM), this research proposes the Linear alpha-cut intervals based Fuzzy Best-Worst Method (Linear alpha-FBWM). By reformulating the non-linear optimization into a single linear programming model, the framework directly determines criteria weights as Triangular Fuzzy Numbers (TFNs) to retain uncertainty. To evaluate weight alignment with decision-makers' initial fuzzy preferences, an Ordinal Preference Violation (OPV) metric is introduced based on the prominence effect. Numerical examples demonstrate that Linear alpha-FBWM minimizes logical violations and matches or outperforms the original alpha-FBWM. To efficiently handle large-scale datasets, we extend this into the Linear alpha-cut intervals based Parsimonious Fuzzy Best-Worst Method (Linear alpha-PFBWM), embedding the linear formulation. This model allows initial alternative ratings as fuzzy numbers and computes non-reference alternative priorities via fuzzy interpolation without early defuzzification. The framework is validated using a literature example and a real-world warehouse selection case study involving 20 alternatives across Gujarat for a multinational paint firm. The integrated approach reduced the required expert evaluations from 185 to 20 initial ratings and 35 pairwise comparisons. This 81.08% reduction in pairwise comparisons proves the framework to be an efficient, reliable, and scalable tool for complex industrial decision-making.

Explore related subjects

math.GM

Keep this discovery

BibTeXRIS

Vikas V. Sharma, Mohit Kumar. 2026-06-15. A Linear alpha-cut intervals based Parsimonious Fuzzy Best-Worst Method with an Application to Warehouse Location Selection. https://arxiv.org/abs/2607.22616

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

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↗