In this paper we study t-norms on the lattice of closed subintervals of the unit interval. Unlike for t-norms on a product lattice for which there exists a straightforward characterization of t-norms which are join-morphisms, respectively meet-morphisms, the situation is more complicated for t-norms in interval-valued fuzzy set theory. In previous papers several characterizations were given of ...

Let H be an infinite--dimensional Hilbert space and K(H) be the set of all compact operators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate of higher derivation and higher Jordan derivation on K(H) associated with the following cauchy-Jencen type functional equation 2f(frac{T+S}{2}+R)=f(T)+f(S)+2f(R) for all T,S,Rin K(H).

Let H be an innite dimensional Hilbert space and K(H) be the set of all compactoperators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate ofhigher derivation and higher Jordan derivation on K(H) associated with the following Cauchy-Jensentype functional equation 2f((T + S)/2+ R) = f(T ) + f(S) + 2f(R) for all T, S, R are in K(...

We study here how to reduce a t-norm by subtracting a value (computed by a function). We obtain a general form of an operator that we call the reduced t-norm. We study this operator and some interesting generalization properties. We also investigate some interesting particular cases. We complete the study by analyzing the dual operator, which corresponds to augmenting a t-conorms.

We studied here the behavior of the t-norms at the point (1/2,1/2). We indicate why this point can be considered as significant in the specification of t-norms. Then, we suggest that the image of this point can be used to classify the t-norms. We consider some usual examples. We also study the case of parameterized tnorms. Finally using the results of this study, we propose a uniform method of ...

The structure of cancellative t-norms is studied. It is shown that a cancellative tnorm is generated if and only if it has no anomalous pair, and then it is Archimedean. Moreover, if it is also continuous in point (1,1) it is isomorphic to the product tnorm. Several examples of non-generated cancellative t-norms are also given.

So far, computational complextity of the general formula for the extended t-norm does not allow to construct fuzzy logic systems of type-2 other than interval type. In this paper, we derive new formulae for extended t-norms for arguments with Gaussian and piecewise-Gaussian membership functions basing on our original theorems.

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