On some properties of the alpha-order and the weight distribution functions
Keywords:
fuzzy set, Fuzzy number, alpha-order, aggregation function,, binary relationAbstract
In this paper, we describe how it can be applied the \(\alpha\)-order to any fuzzy sets in a great class \(\mathscr{C}\) of fuzzy sets. Before that, we introduce the algebraic tools that are underlying to this construction, and we detail the mentioned class of fuzzy sets of the real line that can be ranked by using such fuzzy binary relation. Furthermore, we introduce some new properties both of the weight distribution functions and of the \(\alpha\)-orders. For the sake of completeness, we illustrate all processes by showing examples enough.
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