On interval RO- and (G, O, N)-implications derived from interval overlap and grouping functions

Abstract This paper deals with two sorts of interval fuzzy implications derived from interval overlap and grouping functions, viz., interval R O - and ( G , O , N ) -implications. Firstly, interval R O -implications, preserving the residuation property, are the interval generalization of R O -implications induced by overlap functions. We investigate their properties and their correlations with interval automorphisms. Secondly, interval ( G , O , N ) -operations are generalized from D-operations induced by tuples ( O , G , N ) . We obtain a necessary and sufficient condition for the interval ( G , O , N ) -operation to be an interval fuzzy implication, namely interval ( G , O , N ) -implication. And then, we investigate vital properties and conclusions regarding interval ( G , O , N ) -operations and interval ( G , O , N ) -implications. Finally, we study the intersections between families of interval fuzzy implications, including interval R O -, ( G , N ) -, ( O , G , N ) - and ( G , O , N ) -implications.

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