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 ...

Let iX, 03, m) be a finite measure space. We shall denote by L*im) (1 èp< °°) the Banach space of all real-valued (B-measurable functions/ defined on X such that |/[ p is m-integrable, and by L°°(w) the Banach space of all real-valued, (B-measurable, w-essentially bounded functions defined on X; as usual, the norm in Lpim) is given by 11/11,.= {fx\fix)\pdm}1'*, and the norm in Lxim) by \\g\\x =...

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.

We show that the sup-t-norm and inf-residuum types of fuzzy relational equations, considered in the literature as two different types, are in fact two particular instances of a single, more general type of equations. We demonstrate that several pairs of corresponding results on the sup-t-norm and inf-residuum types of equations are simple consequences of single results regarding the more genera...

We generalize min-neighborhood groups to arbitrary T -neighborhood groups, where T is a continuous triangular norm. In particular, we point out that our results accommodate the previous theory on min-neighborhood groups due to T. M. G. Ahsanullah. We show that every T -neighborhood group is T -uniformizable, therefore, T -completely regular. We also present several results of T -neighborhood gr...

We present a procedure for constructing multi-valued tnorms and t-conorms. Our construction uses a pair of single-valued t-norms and the pair of dual t-conorms to construct interval-valued t-norms u and t-conorms t. In this manner we can combine desirable characteristics of different t-norms and t-conorms; furthermore if we use the t-norm ∧ and t-conorm ∨, then (X,u,t) is a superlattice, i.e. t...

In this study, we present a continuous-valued logical approach to generalize the sigmoid function. Our starting point is kappa function, which known as unary operator in logic. First extend function (a,b) interval, and then interpret generalized limit of extended when b tend negative positive infinity, respectively. Since induced by an additive generator strict t-norm or t-conorm, dependent. Ba...