We explain Giles’s characterization of Lukasiewicz logic via a dialogue game combined with bets on results of experiments that may show dispersion. The game is generalized to other fuzzy logics and linked to recent results in proof theory. We argue that these results allow one to place t-norm based fuzzy logics in a common framework with supervaluation as a theory of vagueness.

For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an H-type t-norm,  we present a method to construct a metric on a  fuzzy metric space. The induced metric space shares many important properties with the given fuzzy metric space.  Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some probl...

We study the norm induced by the supremum metric on the space of fuzzy numbers. And then we propose a method for constructing a norm on the quotient space of fuzzy numbers. This norm is very natural and works well with the induced metric on the quotient space.

The paper presents IF-inference systems of Takagi-Sugeno type. It is based on intuitionistic fuzzy sets (IF-sets), introduced by K.T. Atanassov, fuzzy t-norm and t-conorm, intuitionistic fuzzy t-norm and t-conorm. Thus, an IFinference system is developed for ozone time series prediction. Finally, we compare the results of the IF-inference systems across various operators.

In this paper, we apply the concept of t-norm T to fuzzy structure of B-algebras. The notion of a fuzzy B-subalgebra of B-algebras with respect to t-norm is introduced and several related properties are investigated. The direct product and T -product of T -fuzzy subalgebra of B-algebra is investigated.

The aim of this paper is further to develop the filter theory on residuated lattices. The concept of interval valued intuitionistic (T, S)-fuzzy filters on residuated lattices is introduced by linking the intuitionistic fuzzy set, t-norm, s-norm and filter theory of residuated lattices; The properties and equivalent characterizations of Interval valued intuitionistic (T, S)-fuzzy filters are in...

The Cai δ-equality of fuzzy sets corresponds to the Lukasiewicz t-norm. In this paper we study the notion of (∗, δ)-equality, a concept which generalizes the δ-equality to the case of the fuzzy set theory based on an arbitrary continuous t-norm ∗. We investigate the robustness of some fuzzy implication operators in terms of (∗, δ)-equality.

In this paper, we redefine the notion of fuzzy 2-normed linear space using t-norm and fuzzy anti-2-normed linear space using t-conorm and introduced the definition of intuitionistic fuzzy 2-norm on a linear space. Mathematics Subject Classification: 46S40, 03E72

The combination of Fuzzy Logics and Description Logics (DLs) has been investigated for at least two decades because such fuzzy DLs can be used to formalize imprecise concepts. In particular, tableau algorithms for crisp Description Logics have been extended to reason also with their fuzzy counterparts. Recently, it has been shown that, in the presence of general concept inclusion axioms (GCIs),...