Abstract
In this Ch. we continue to study the max-min fuzzy relation equation (3.3) defined on finite sets and assuming L to be a linear lattice with universal bounds 0 and 1 but endowed with an additional structure L’ of a complete linear lattice with universal bounds 0’ and 1’, tied to the foregoing one by accurate and reasonable requirements. These are basic preliminaries in order to solve some important optimization problems in the set of solutions of a fuzzy equation. Strictly speaking, introducing a suitable functional which measures the “fuzziness content” of a fuzzy relation, we characterize all the solutions of a max-min composite fuzzy equation possessing the smallest and the greatest value of such fuzziness.
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