Aggregation of diverse types of fuzzy orders for decision making problems

In this paper, conditions for n-argument functions to preserve diverse types of fuzzy orders during aggregation process are presented. Namely, the following fuzzy orders are studied: total preorder, total order, strict total order, partial preorder, partial order, strict partial order, interval order or semiorder and their preservation in aggregation process along with other connections between input fuzzy relations and the aggregated one are presented. Moreover, dependencies between diverse classes and also among the given class of fuzzy orders are presented. The considered fuzzy orders are compound properties depending in their definitions on arbitrary binary operations on [0, 1], including fuzzy conjunctions and disjunctions (with special cases of triangular norms and triangular conorms). Finally, an application of the obtained result is presented by the given algorithm.