We describe a certified arbitrary-precision framework for evaluating a family of generalized multiple zeta functions. The family includes strict and weak-star chain sums, ordinary and colored multiple zeta values, affine-base and polynomial-base variants, and composite levels containing several affine or polynomial letters with complex coefficients. The numerical strategy combines finite-prefix recurrences with two complementary analytic-tail mechanisms: recursive Euler-Maclaurin expansion of one-variable tails and direct absolute tail majorants. The Euler-Maclaurin branch is fast when the relevant suffix expansions are regular, while the direct-tail branch gives robust certificates for multi-letter, weak-star, complex-coefficient, and branch-sensitive inputs. A computation is called certified only when its reported radius is obtained from a proved analytic bound for the omitted infinite tail. Strict-disk colored sums and boundary-color cases with summable absolute majorants are therefore within the certified scope; conditionally convergent colored cases whose convergence relies only on non-one unit-modulus oscillation are kept separate and reported as explicitly non-certified diagnostic outputs unless an independent analytic remainder bound is available.

In many real-world domains, knowledge is inherently vague or imprecise - features that classical ontology languages, based on crisp Description Logics (DLs), are unable to capture. This shortcoming poses particular challenges for applications in the Semantic Web and Explainable Artificial Intelligence (XAI), where robust reasoning over graded information is essential. Fuzzy ontologies address this limitation by enriching DLs with fuzzy logic, enabling the expression of partial truth and supporting more nuanced modelling of real-world knowledge. We present fuzzy-dl-owl2, a complete re-engineering in Python of the fuzzyDL reasoner and the Fuzzy OWL 2 framework. The former is an expressive fuzzy DL reasoner, while the latter allows for defining fuzzy ontologies within OWL 2. Our contribution addresses several shortcomings of the original software, including semantic inconsistencies, rigid architectural design, and limited solver integration. The re-implementation features a modular class hierarchy tailored for extensibility, supports a broader range of Mixed-Integer Linear Programming (MILP) solvers (including open-source alternatives), and corrects IRI ambiguities arising from overlapping ontological elements. Furthermore, a dedicated Python library (pyowl2) has also been developed to handle OWL 2 annotations in a standards-compliant manner, improving interoperability with existing Semantic Web tooling and resolving IRI ambiguities. The resulting framework offers a portable, extensible, and theoretically grounded platform for reasoning with fuzzy ontologies, suitable for both research and deployment in vague-aware systems. Performance tests have also been conducted that show improved execution times w.r.t. the original Java implementation. The source code and full documentation are publicly available to facilitate community adoption and further development.

The essence of the density topology lies in the family of Lebesgue measurable sets where each point of a set is a density point of that set. The motivation of this work is to investigate the family of measurable sets for which, at every point within a set belonging to this family, the upper density of that set is positive. We obtain a strong generalized topology, and its essential properties are demonstrated in comparison with those of the classical density topology.