The aim of this paper is to define an $L^p$ space intuitionistic fuzzy observables. We work in $({\mathcal F}, {\bf m})$ with product, where $\mathcal F$ a family events and ${\bf m}$ state. prove that the corresponding pseudometric $\rho_{IF}$ space.

In this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. Weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

K?nzi and Yilzid introduced the concept of convexity structures in sense Takahashi quasi-pseudometric spaces [7]. In this article, we continue study theory, introducing W-convexity for real-valued pair functions defined on an asymmetrically normed real vector space. Moreover, show that all minimal pairs space equipped with a convex structure which is W-convex whenever W translation-invariant.

in this paper we define ( , ) k  q -fuzzy h -sub hemirings, ( , ) k  q -fuzzy h -ideals, ( , ) k  q - fuzzy     h -bi-ideals and ( , ) k  q -fuzzy h -quasi-ideals. we characterize h -hemiregular and h -intrahemiregular hemirings by the properties of their     ( , ) k  q -fuzzy h -ideals, ( , ) k  q -fuzzy h -bi-ideals and     ( , ) k  q -fuzzy h -quasi-...

generalizing the concepts of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and   -fuzzy bi (generalized bi-) ideals in ternary semigroups, the notions of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and -fuzzy bi (generalized bi-) in ternary semigroups are introduced and several related properties are investigated. some new results are obtained.

In this paper, we introduce the concept of N -fuzzy quasi-ideals in ordered semigroups and investigate the basic theorem of quasi-ideals of ordered semigroups in terms of N -fuzzy quasi-ideals. We characterize left (resp. right) regular and completely regular ordered semigroups in terms of N -fuzzy quasi-ideals. We de ne semiprime N fuzzy quasi-ideals and characterize completely regular ordered...

This work represents a natural extension of our work on optimal probabilistic supervisory control of probabilistic discrete event systems (PDESs). In that work, a pseudometric on the initial states of two probabilistic automata that represent probabilistic systems is used to measure the distance between two systems. The pseudometric is given a fixed point characterization. This paper gives a lo...

Probabilistic bisimilarity is a fundamental notion of equivalence on labelled Markov chains. It has a natural generalisation to a probabilistic bisimilarity pseudometric, whose definition involves the Kantorovich metric on probability distributions. The probabilistic bisimilarity pseudometric has discounted and undiscounted variants, according to whether one discounts the future in observing di...

The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is considered. In fact, this concept is a generalized concept of the quasi-coincidence of a fuzzy point in a fuzzy set. By using this new concept, the authors define the notion of interval valued (∈,∈ ∨q)fuzzy h-ideals of hemirings and study their related properties. In addition, the authors also extend t...