N-Reciprocity Property for Interval-Valued Fuzzy Relations with an Application to Group Decision Making Problems in Social Networks

In this paper we study interval-valued fuzzy relations. We consider preference relations, i.e. a triplet consisting of strict preference, indifference and incomparability which are defined with the use of a fuzzy negation. We analyze the preservation of the fuzzy negation based reciprocity property of interval-valued fuzzy relations by aggregation functions and by some basic interval-valued fuzzy relations. We use diverse representa-tions of aggregation functions. We also consider the connection between N-reciprocal relations and transitivity properties. We provide a numerical example where the final alternative is chosen with the use of generalized voting method, where admissible linear orders for intervals are applied.