Sets of solution-set-invariant coefficient matrices of fuzzy relation equations with max-min composition1.

This paper describes a set of solution-set-invariant coefficient matrices of the fuzzy relation equation with max-min composition <italic>A</italic> ⊙ <italic>x</italic> = <italic>b</italic> or ⋁ j ∈ { 1 , 2 , ⋯ , n } ( a ij ∧ x j ) = b i for all i ∈ { 1 , 2 , ⋯ , m } with 1 ≥ b 1 ≥ b 2 ≥ ⋯ ≥ b m > 0. An algorithm is given for determining the set scripfont<italic>A</italic> = {<italic>B</italic> ∣ {<italic>x</italic> ∣ <italic>B</italic> ⊙ <italic>x</italic> = <italic>b</italic>} = {<italic>x</italic> ∣ <italic>A</italic> ⊙ <italic>x</italic> = <italic>b</italic>}} completely. [ABSTRACT FROM AUTHOR]