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...

This paper introduces and justifies a similaritybased concept of strict fuzzy orderings and provides constructions how fuzzy orderings can be transformed into strict fuzzy orderings and vice versa. We demonstrate that there is a meaningful correspondence between fuzzy orderings and strict fuzzy orderings. Unlike the classical case, however, we do not obtain a general one-to-one correspondence. ...

Let A be a complex m × n matrix. We find simple and good lower bounds for its spectral norm ‖A‖ = max{ ‖Ax‖ | x ∈ C, ‖x‖ = 1 } by choosing x smartly. Here ‖ · ‖ applied to a vector denotes the Euclidean norm.

The rotation construction for t-norms is introduced in (J. Appl. Non-Classical Logics 10 (2000) 83–92). In the present paper we characterize the widest class of operators with which the rotation construction results in left-continuous t-norms with involutive associated negations. c © 2002 Elsevier Science B.V. All rights reserved.

This paper continues and finishes other works toward proposing a method to measure the μ-T-conditionality character of any fuzzy relation for any continuous t-norm T.