Relational algorithms for theoretical and empirical evaluation of systems of fuzzy connectives

Fuzzy relations offer the means for discovering and analyzing structures hidden in business, medical scientific and technological data. A large variety of competing systems of many-valued logic connectives may be used in defining relational computations, each system of connectives extracting a different fuzzy relational structure from the analyzed data. Hence, new methods for comparing the inner structure of relations obtained by different implication operators from the same collection of data are urgently required. In this paper, we describe a mathematical method that can be used for comparative evaluation (meta-analysis) of such results. The method uses constructive theory of generalized morphisms. This makes it possible to express in the unified way (as the relational formulas containing BK-products) not only the relational computations themselves but also the algorithms employed in the meta-analysis of the results generated by these computations