Characterization of Complete Fuzzy Preorders Defined by Archimedean t-Norms

Classical complete preorders can be characterized in several ways. However, when we work with complete fuzzy preorders this equivalences do not hold in general. In previous works we have proven some connections among them when using the minimum and the Łukasiewicz t-norms. In this contribution we generalize the study and we work with two important families (nilpotent and strict t-norms) when defining the fuzzy counterparts of the characterizations of a crisp complete preorder.

[1]  Marc Roubens,et al.  Fuzzy Preference Modelling and Multicriteria Decision Support , 1994, Theory and Decision Library.

[2]  Philippe Vincke,et al.  Semiorders - Properties, Representations, Applications , 1997, Theory and decision library: series B.

[3]  Carlos Rodríguez-Palmero,et al.  Some algebraic characterizations of preference structures , 2004 .

[4]  Bernard De Baets,et al.  Fuzzy preference structures without incomparability , 1995, Fuzzy Sets Syst..

[5]  Bernard De Baets,et al.  Transitivity Bounds in Additive Fuzzy Preference Structures , 2007, IEEE Transactions on Fuzzy Systems.

[6]  Bernard De Baets,et al.  On the Transitivity of Fuzzy Indifference Relations , 2003, IFSA.

[7]  Francesc Esteva,et al.  Review of Triangular norms by E. P. Klement, R. Mesiar and E. Pap. Kluwer Academic Publishers , 2003 .

[8]  Susana Montes,et al.  Connection Among Some Characterizations of Complete Fuzzy Preorders , 2009, 2009 Ninth International Conference on Intelligent Systems Design and Applications.

[9]  Bernard De Baets,et al.  General results on the decomposition of transitive fuzzy relations , 2010, Fuzzy Optim. Decis. Mak..

[10]  Bernard De Baets,et al.  On Some Characterizations of Complete Fuzzy Preorders , 2005, EUSFLAT Conf..

[11]  Bernard De Baets,et al.  Characterizable fuzzy preference structures , 1998, Ann. Oper. Res..

[12]  M. Dasgupta,et al.  Factoring fuzzy transitivity , 2001, Fuzzy Sets Syst..

[13]  Bernard De Baets,et al.  Fuzzy Sets and Systems — IFSA 2003 , 2003, Lecture Notes in Computer Science.

[14]  Bernard De Baets,et al.  Generator triplets of additive fuzzy preference structures. , 2001 .