Some Results About Fuzzy Consequence Operators and Fuzzy Preorders Using Conjunctors

The purpose of this paper is to study fuzzy operators induced by fuzzy relations and fuzzy relations induced by fuzzy operators. Many results are obtained about the relationship between \(*\)-preorders and fuzzy consequences operators for a fixed t-norm \(*\). We analyse these properties by considering a semi-copula (generalization of t-norm concept) instead of a t-norm. Moreover, we show that the conditions imposed cannot be relaxed. We have been able to prove some important results about the relationships between fuzzy relations and fuzzy operators in this more general context.

[1]  Jorge Elorza,et al.  Connecting fuzzy preorders, fuzzy consequence operators and fuzzy closure and co-closure systems , 2003, Fuzzy Sets Syst..

[2]  Jan Pavelka,et al.  On Fuzzy Logic III. Semantical completeness of some many-valued propositional calculi , 1979, Math. Log. Q..

[3]  Fabrizio Durante,et al.  Supermigrative semi-copulas and triangular norms , 2009, Inf. Sci..

[4]  J. ELORZA,et al.  On the Relation Between Fuzzy Preorders and Fuzzy Consequence Operators , 1999, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[5]  Fabio Spizzichino,et al.  Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes , 2005 .

[6]  Bernard De Baets,et al.  On the compositional characterization of complete fuzzy pre-orders , 2008, Fuzzy Sets Syst..

[7]  Morgan Ward,et al.  The Closure Operators of a Lattice , 1942 .

[8]  Pere Garcia-Calvés,et al.  On implicative closure operators in approximate reasoning , 1999, EUSFLAT-ESTYLF Joint Conf..

[9]  Lluís Godo Lacasa,et al.  Fuzzy approximation relations, modal structures and possibilistic logic , 1998 .

[10]  Juan Luis Castro,et al.  Inducing implication relations , 1994, Int. J. Approx. Reason..

[11]  Jorge Elorza,et al.  Permutable fuzzy consequence and interior operators and their connection with fuzzy relations , 2015, Inf. Sci..

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

[13]  Jorge Elorza,et al.  On the relation between fuzzy closing morphological operators, fuzzy consequence operators induced by fuzzy preorders and fuzzy closure and co-closure systems , 2013, Fuzzy Sets Syst..