Consistency for non Additive Measures: Analytical and Algebraic Methods Antonio Maturo 1 , Massimo Squillante 2 , and Aldo Ventre 3 1 University “G. d’Annunzio” of Chieti - Pescara, Department of Social Sciences, Faculty of Social Sciences, Campus Universitario, via dei Vestini 31, 66013 Chieti, Italy, amaturo@unich.it 2 University of Sannio, Faculty of Economical and Managerial Sciences, Department of Economical and social sciences, Faculty of Economic and business sciences, via Nazionale delle Puglie, Benevento, Italy, squillan@unisannio.it 3 2 th University of Napoli, Department of Culture of the Project, Faculty of Architecture, Abazia di San Lorenzo ad Septimum, I-81301 Aversa, Italy, aldoventre@yahoo.it Abstract We consider the problem of choosing an alternative in a set A = {A 1 ,A 2 , ..., A m } of alternatives, given a set D = {d 1 ,d 2 , ..., d h } of decision makers and a set Ω = {O 1 ,O 2 , ..., O n } of objectives. We assume that any decision maker d k assigns to any pair (alternative A i , objective O j ) a number a ijk that measures to what extent A i satisfies O j . We assume that Ω is a subset of a universal set U and, for every alternative A i and decision maker d k , the function m ik that associates a ijk to O j is a fuzzy measure. We propose to aggregate the scores a ijk by means of a t-conorm ⊕ λ of a family Φ λ of t-conorms such that every m ik is a ⊕ λ -decomposable measure. We consider also some algebraic and geometric representations of the Archimedean fuzzy unions and their additive generators in terms of the theory of hypergroups. By considering the O j as events, we propose also to assign the scores a ijk in such a way that for some λ the assessment is consistent and to aggregate such evaluations with the correspondent t-conorm ⊕ λ . Finally we generalize the previous procedure by considering fuzzy measures of type 2, having as a range a set of fuzzy numbers with the interval [0, 1] as support. 2000 MSC: 03E72, 08A72, 20N20, 91B06, 91B14. Key words: Fuzzy Measures, Multicriteria and Multiperson Decision Making, Fuzzy Models, Hypergroups.