Ivanosca da Silva - Directorate of Material and Heritage, Federal University of Rio Grande do Norte, Natal, RN, Brazil.
Berta Bedregal - Production Engineering Course State University of Rio de Janeiro.
Benjamin Bedregal - Department of Informatics and Applied Mathematics, Federal University of Rio Grande do Norte, Natal, RN, Brazil.
Regivan Santiago - Department of Informatics and Applied Mathematics, Federal University of Rio Grande do Norte, Natal, RN, Brazil.

In this paper we extend the notion of interval representation for interval-valued Atanassov’s intuitionistic representations, in short Lx-representations, and use this notion to obtain the best possible one, of the Weighted Average (WA) and Ordered Weighted Average (OWA) operators. A main characteristic of this extension is that when applied to diagonal elements, i.e. fuzzy degrees, they provide the same results as the WA and OWA operators, respectively. Moreover, they preserve the main algebraic properties of the WA and OWA operators. A new total order for interval-valued Atanassov’s intuitionistic fuzzy degrees is also introduced in this paper which is used jointly with the best Lx-representation of the WA and OWA, in a method for multi-attribute group decision making where the assesses of the experts, in order to take in consideration uncertainty and hesitation, are interval-valued Atanassov’s intuitionistic fuzzy degrees. A characteristic of this method is that it works with interval-valued Atanassov’s intuitionistic fuzzy values in every moments, and therefore considers the uncertainty on the membership and non-membership in all steps of the decision making. We apply this method in two illustrative examples and compare our result with other methods.

Interval-Valued Atanassov’s intuitionistic fuzzy sets, WA and OWA operators, Lx-representations, total orders, multi-attribute group decision making