An algorithm for group decision making using n-dimensional fuzzy sets, admissible orders and OWA operators.

We present the concept of admissible order for n-dimensional fuzzy sets.We give a construction method for those admissible orders using aggregation functions.We extent to the field of n-dimensional fuzzy sets the concept of OWA operators (which are always associated to a linear order).We design a decision making algorithm using n-dimensional fuzzy sets and n-tuple aggregation OWA operators.We justify our theoretical developments with an illustrative example applying the proposed algorithm. In this paper we propose an algorithm to solve group decision making problems using n-dimensional fuzzy sets, namely, sets in which the membership degree of each element to the set is given by an increasing tuple of n elements. The use of these sets has naturally led us to define admissible orders for n-dimensional fuzzy sets, to present a construction method for those orders and to study OWA operators for aggregating the tuples used to represent the membership degrees of the elements. In these conditions, we present an algorithm and apply it to a case study, in which we show that the exploitation phase which appears in many decision making methods can be omitted by just considering linear orders between tuples.