Sets of solution-set-invariant coefficient matrices of fuzzy relation equations with max-min composition 1

Abstract

This paper describes a set of solution-set-invariant coefficient matrices of the fuzzy relation equation with max-min composition A ⊙ x = b or ${\bigvee }_{j\in \{1,2,\cdots ,n\}}(a_{\mathit{ij}}\wedge x_j)=b_i\mathrm{for}\mathrm{all}i\in \{1,2,\cdots ,m\}$ with $1\ge b_1\ge b_2\ge \cdots \ge b_m>0.$ An algorithm is given for determining the set scripfontA = {B ∣ {x ∣ B ⊙ x = b} = {x ∣ A ⊙ x = b}} completely.