Abstract The phase space of a relativistic system can be identified with the future tube complexified Minkowski space. As well as complex structure and symplectic structure, tube, seen an eight-dimensional real manifold, is endowed natural positive-definite Riemannian metric that accommodates underlying geometry indefinite metric, together its symmetry group. A unitary representation 15-paramet...

The generalized fuzzy valued $theta$-Choquet integrals will beestablished for the given $mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-doub...

Recent research has focused on feed-forward networks with complex weights and activation values such as GK92, Hir92b, Hir92a, Hir93]. This paper extends this formalism to feed-forward networks with weight and activation values taken from a Cliiord algebra (see also PB92, PB94b]). A Cliiord algebra is a multi-dimensional generalization of the complex numbers and the Quaternions. Essentially a Cl...

Let (X, ) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Assume that X satisfies; if a non-decreasing sequence xn → x in X , then xn x, for all n. Let F be a set valued mapping from X into X with nonempty closed bounded values satisfying; (i) there exists κ ∈ (0, 1) with D(F (x), F (y)) ≤ κd(x, y), for all x y, (ii) if d(x, y) < ε < 1 for some y ∈...

Based on previous results that study the completion of fuzzy metric spaces, we show that every intuitionistic fuzzy quasi-metric space, using the notion of fuzzy metric space in the sense of Kramosil and Michalek to obtain a generalization to the quasi-metric setting, has a bicompletion which is unique up to isometry.