On Interrelations Between Fuzzy Congruence Axioms

Abstract

In this paper we establish interrelations between fuzzy direct revelation axiom (FDRA), fuzzy transitive-closure coherence axiom (FTCCA), fuzzy consistent-closure coherence axiom (FCCCA) and fuzzy intermediate congruence axiom (FICA). We also establish their relationships with weak fuzzy congruence axiom (WFCA), strong fuzzy congruence axiom (SFCA) and weak axiom of fuzzy revealed preference (WAFRP). Condition for equivalence of fuzzy Arrow axiom (FAA) and weak fuzzy congruence axiom (WFCA) on arbitrary domain is also given.

Compatible extensions and consistent closures: a fuzzy approach

“…Remark 6.1 The consistent closure R ∆ has been introduced in [6], Definition 2.2 and further studied in [7], [8].…”