Recommended by Akbar Rhemtulla We introduce the notion of fuzzy ideals in nearrings with respect to a t-norm T and investigate some of their properties. Using T-fuzzy ideals, characterizations of Artinian and Noetherian nearrings are established. Some properties of T-fuzzy ideals of the quotient nearrings are also considered.

Keywords: Fuzzy variable Independence Operation t-norm Convergence Law of large numbers a b s t r a c t T-independence of fuzzy variables is a more general concept than the classical independence. The objective of this study is to deal with some new properties of T-independent fuzzy variables. First of all, for any general t-norm, some criteria of T-independence are discussed for fuzzy variable...

This paper deals with Lipschitz triangular norms (t-norms). A partial answer to an open problem of Alsina, Frank and Schweizer is given with regard to strict t-norms with smooth additive generators. A new notion of local Lipschitz property for arbitrary t-norms is introduced. Some remarkable examples of non-Lipschitz continuous ones are provided.

In this paper we consider general t-norm in the definition of fuzzy normed linear space which is introduced by the authors in an earlier paper. It is proved that if t-norm is chosen other than ”min” then decomposition theorem of a fuzzy norm into a family of crisp norms may not hold. We study some basic results on finite dimensional fuzzy normed linear spaces in general t-norm setting. 2010 AMS...

In many-valued logics with the unit interval as the set of truth values, from the standard negation and the product (or, more generally, from any strict Frank t-norm) all measurable logical functions can be derived, provided that also operations with countable arity are allowed. The question remained open whether there are other t-norms with this property or whether all strict t-norms possess t...

The strongest and the weakest t-norms that coincide with the given t-norm on a subregion of the unit interval are discussed. The question whether such a t-norm can be obtained as a limit of the sequence of continuous t-norms that coincide with the original t-norm on the given subregion is investigated.

This paper describes a method for fusing a collection of classifiers where the fusion can compensate for some positive correlation among the classifiers. Specifically, it does not require the assumption of evidential independence of the classifiers to be fused (such as Dempster Shafer’s fusion rule). The proposed method is associative, which allows fusing three or more classifiers irrespective ...

Recently, the distributivity of fuzzy implications over t-norms, t-conorms and uninorms was studied in many articles. In this paper we characterize functions which satisfy one of the four generalized distributivity equations of classical implication in the case when t-conorms are continuous and Archimedean. Using the obtained characterizations we describe some solutions which are fuzzy implicat...

With a left-continuous t-norm ̄, we may associate the set of its vertical cuts, namely, the set F of functions fa : [0, 1] → [0, 1], x 7→ x ̄ a. Endowed with the pointwise order, with the functional composition, with the constant 0 function and with the identity function, F is an algebra which is isomorphic to ([0, 1];≤, ̄, 0, 1). We characterize the functional algebras arising in this way from ...

The paper presents the comparison of fuzzy conclusions derived from the use of t-norms with the fuzzy conclusions derived from the use of H-norm. The idea was to examine the application of H-logical norm to fuzzy reasoning, which is not monotonious while it is known that t-norms used in fuzzy reasoning have the characteristic of monotonicity. The comparison of fuzzy conclusions was performed by...