Let K(X,Y) be the space of compact operators. For a proximinal subspace Z⊂Y, this paper deals with question, when does every Y-valued operator admit Z-valued best approximation? any reflexive Banach X and for L1-predual Y, if Z⊂Y is strongly finite codimension, we show that K(X,Z) under an additional condition on position K(X,Z). When Y c0-direct sum dimensional spaces achieve strong transitivi...

In this paper we study extensions of the arithmetic operators +, −, ·, ÷ to the lattice L of closed subintervals of the unit interval. Starting from a minimal set of axioms that these operators must fulfill, we investigate which properties they satisfy. We also investigate some classes of t-norms on L which can be generated using these operators; these classes provide natural extensions of the ...

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 ...

In this paper the Archimedean property of t-norms on the lattice L is investigated, where L is the underlying lattice of interval-valued fuzzy set theory (Sambuc, 1975) and intuitionistic fuzzy set theory (Atanassov, 1983). We discuss also two additional variations on this property: the weak and strong Archimedean property.

In this paper we introduce the notion of additive and multiplicative generators on the lattice L , which is the underlying lattice of interval-valued fuzzy set theory (which is equivalent to intuitionistic fuzzy set theory in the sense of Atanassov). We study the properties of these operators, some of which are similar to well-known results on ([0, 1],≤).

The n-dimensional fuzzy sets have been introduced as a generalization of interval-valued fuzzy sets, Atanassov’s intuitionistic and interval-valued intuitionistic fuzzy sets. In this paper we investigate t-norms on 3-dimensional sets which are joinmorphisms. Under some additional conditions we show that they can be represented using a representation which generalizes a similar representation fo...

We study the theory of best approximation in tensor product and the direct sum of some lattice normed spacesX_{i}. We introduce quasi tensor product space anddiscuss about the relation between tensor product space and thisnew space which we denote it by X boxtimesY. We investigate best approximation in direct sum of lattice normed spaces by elements which are not necessarily downwardor upward a...