The paper provides a study of pseudo MV-algebras with $n$-roots. We outline their main properties and establish that the class of MV-algebras with $n$-roots forms a variety. Then, we introduce the concept of a strict $n$-root to classify the class of pseudo MV-algebras with $n$-root and demonstrate an equivalence between this variety and the class of $n$-divisible unital $\ell$-groups. Finally, we find a relationship between strongly atomless pseudo MV-algebra and strict pseudo MV-algebras. \\ \textbf{Keywords}: Pseudo MV-algebra; Square root; n-root; n-strict MV-algebra; Boolean algebra; Strongly atomless
The right to education is a universally recognized right and school is a fundamental place in modern society. Everyone must have the opportunity to attend and receive quality education. For this reason, it is important that school facilities are accessible to all, eliminating architectural barriers that hinder or limit students with disabilities. Quantitative tools such as multicriteria models and artificial intelligence can represent a driving force to support the school system in the evaluation processes that are crucial for improving school accessibility but more generally the services provided to students and families in general. This work aims to offer a systematic analysis of the literature that analyzes the areas of application of tools such as MCDM (Multi Criteria Decision Making) and AI (Artificial Intelligence) in school contexts with particular attention to the accessibility of schools.
The Collatz algorithm gives the operations to apply to both even and odd numbers so that starting with any natural number and applying these operations repeatedly, the number one is eventually reached. The Collatz conjecture claims that this is true no matter what starting number is used. It happens that the natural numbers can be organised into a hierarchical structure of infinite geometric sequences and the Collatz algorithm is the means of ascending through this hierarchy.
This paper studies the robustness of fuzzy regression discontinuity designs under imperfect compliance with clinical assignment rules. When treatment assignment based on a biomarker threshold is probabilistic, the cutoff indicator can be interpreted as an instrumental variable identifying a Local Average Treatment Effect. A Monte Carlo simulation calibrated to a cardiovascular risk setting is used to evaluate the local two stage least squares fuzzy regression discontinuity estimator under controlled violations of its identifying assumptions. We consider departures from continuity of potential outcomes at the cutoff, reductions in first stage strength, and violations of monotonicity. The results show that, under approximate continuity and sufficiently strong first stages, the estimator recovers the target local effect with limited bias and near nominal coverage. Weak first stages mainly reduce precision, whereas violations of continuity lead to severe bias even when the instrument is strong. Monotonicity violations increase variability and reduce coverage. Overall, the findings highlight that fuzzy regression discontinuity designs provide reliable local causal inference only under carefully assessed assumptions.
The aim of this paper is to study the generalization of intuitionistic fuzzy normed spaces to intuitionistic fuzzy $n$-normed spaces. In this framework, we discuss intuitionistic fuzzy $n$-continuity and intuitionistic fuzzy $n$-boundedness. Furthermore, we introduce the intuitionistic fuzzy $\psi$-$n$-normed space, which generalizes the intuitionistic fuzzy $n$-normed space. Several results and properties in this new set-up are also presented and analyzed.
