We define a new topology, weaker than the gap topology, on the space of selfadjoint operators affiliated to a semifinite von Neumann algebra and define the real-valued spectral flow for a continuous path of selfadjoint Breuer-Fredholm operators in terms of a generalization of the winding number. We compare our definition with Phillips’ analytical definition. Furthermore we prove the homotopy in...

Our starting point is the Mosco-convergence result due to Hess ((He'89]) for integrable multivalued supermartingales whose values may be unbounded, but are majorized by a w-ball-compact-valued function. It is shown that the convergence takes place also in the slice topology. In the case when both the underlying space X and its dual X have the Radon-Nikodym property a weaker compactness assumpti...

We study the p-fine topology on complete metric spaces equipped with a doubling measure supporting a p-Poincaré inequality, 1 < p < ∞. We establish a weak Cartan property, which yields characterizations of the p-thinness and the p-fine continuity, and allows us to show that the p-fine topology is the coarsest topology making all psuperharmonic functions continuous. Our p-harmonic and superharmo...

Linguistic terms are often used to represent the truth degree or credibility degree to manage the uncertainty or imprecision as one of popular ways of knowledge representation in the perception-based decision making problem. This present work represents the credibility of uncertain knowledge using linguistic values. The linguistic-valued credibility is then modeled based on a lattice ordered lo...

Considering a frame L, we introduce the notions of stratified L-semi-topological neighborhood group, stratified L-quasi-topological neighborhood group, and stratified L-quasi-bi-topological neighborhood group. In so doing, we look at the notion of stratified L-right (left) semi-topological neighborhood group, provide some basic facts, and present a construction of a stratified L-right semi-topo...

This paper presents an investigation of many valued lattices from the point of view of enriched category theory. For a bounded partially ordered set P , the conditions for P to become a lattice can be postulated as existence of certain adjunctions. Reformulating these adjunctions, by aid of enriched category theory, in many valued setting, two kinds of many valued lattices, weak -lattices and -...

The aim of this paper is to introduce some classes of aggregation functionals when the evaluation scale is a complete lattice. We focus on the notion of quantile of a lattice-valued function which have several properties of its real-valued counterpart and we study a class of aggregation functionals that generalizes Sugeno integrals to the setting of complete lattices. Then we introduce in the r...

Lacking an explicit formula for the numbers T0(n) of all order relations (equivalently: T0 topologies) on n elements, those numbers have been explored only up to n = 13 (unlabeled posets) and n = 15 (labeled posets), respectively. In a new approach, we used an orderly algorithm to (i) generate each unlabeled poset on up to 14 elements and (ii) collect enough information about the posets on 13 e...

In order to establish a norm in a society of agents, metanorms have previously been proposed as a means of ensuring not that norms are complied with, but that they are enforced. Yet while experimental results have shown that metanorms are effective in fully-connected environments such as that used by Axelrod, there has been limited consideration of such metanorm models with different but more r...

*Correspondence: [email protected] 1Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an, 710121, China Full list of author information is available at the end of the article Abstract This study aims to explore modular inequalities of interval-valued fuzzy soft sets characterized by Jun’s soft J-inclusions. Using soft product operations...