http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7436 JAEM 2026, Vol 16, No 10 koleksiyonunu içerir. 2026-10-10T04:00:35Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7445 Typical families and T-compactness in proximity spaces Almohammed, Raghad; AL-Ftlawy, Dunia M.K.; Habeeb, Nadiha Abed; Al-Swidi, Luay In this work we introduce a family of subsets of a proximity space, called the typical family, defined as the complement of a cluster family, and we study its main properties and its relation to the cluster concept. We show explicitly that the typical family is, up to the language of proximity spaces, the ideal that is dual to the associated cluster in the classical sense of Choquet’s grill ideal duality, and we compare it in detail with ideals, filters, grills, and bornologies, establishing a necessary and sufficient condition under which it is a bornology. Building on this family we define a generalized compactness notion, called T-compactness, relate it to the classical notion of compactness with respect to an ideal, and establish preservation results for finite unions, closed subsets, and via a pushforward construction introduced here images under proximity isomorphisms. We illustrate the framework with a fully worked finite numeric example. We close with a discussion of the broader implications of these results for the relationship between cluster theory and generalized compactness. 2026-10-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7444 Wiener and Harary indices of the generalized zero-divisor graph Khairnar, Anil; Lande, Anita; Bhavar, Geetali; Phatangare, Nanasaheb Let R be a commutative ring, and let Z∗(R) denote the set of all non-zero zero-divisors in R. The generalized zero-divisor graph of R, denoted by Γ′(R), is a simple (undirected) graph with the vertex set Z∗(R), and two distinct vertices x and y are adjacent in Γ′(R) if and only if xny = 0 or ynx = 0, for some positive integer n. The Wiener and Harary indices are topological indices widely used in chemistry to analyze the structures of molecules. In this paper, we determine the Wiener and Harary indices of Γ′(Zn) for n = pq, p2q, p2q2, where p, q are distinct primes. 2026-10-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7443 General fuzzy automata under semantically similar environment: an application to enhanced search engine performance Kaur, Ranjeet; Tripathi, Alka Automata theory provides a systematic framework for modelling computational processes; however, many real-world systems require greater adaptability and flexibility. This paper presents a general fuzzy automata model (GF ASE) designed to address these challenges, particularly in environments where the set of states is not predetermined. The proposed model is capable of dynamically integrating semantically similar states based on contextual relevance, enhancing its robustness in handling real-world data variability. Algorithms are introduced to measure the similarity between states. This advancement extends the capabilities of existing General Fuzzy Automata (GFA) frameworks, allowing them to function effectively in uncertain or evolving environments. A practical application of this model is demonstrated in the domain of search engine performance, where the proposed approach improves the handling of queries by mapping them to semantically related states, thereby enhancing the relevance and accuracy of results. 2026-10-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7442 A flexible Unit Chen quantile regression model for bounded response data: estimation, model diagnostics, and applications Salih, Ahmed Mahdi; Al-Majidi, Arkan Jebur Bounded response variables are common in disciplines such as dependability, finance, environmental sciences, and biostatistics, where traditional regression models based on the conditional mean may fail to capture varied covariate effects throughout the response distribution. To solve this issue, this work proposes a flexible quantile regression model based on the Unit Chen distribution for evaluating continuous data on the unit intervals. The proposed methodology defines the conditional quantile via a logit link function, allowing explanatory factors to impact diverse parts of the answer distribution while maintaining limited support. Maximum likelihood estimation is created for the inference of parameters, and the appropriate estimation approach is executed by means of numerical optimization techniques. A number of model diagnostic techniques are included to check the adequacy and robustness of the model, to detect influential data and to examine the sensitivity of the fitted model, including generalized Cook’s distance, likelihood displacement and local influence analysis. The finite-sample performance of the suggested estimators is examined via a comprehensive Monte Carlo simulation analysis employing bias, mean squared error and root mean squared error as assessment measures for varying sample sizes and quantile levels. The practical applicability of the proposed model is illustrated using a real boundedresponse dataset and is compared with several competing unit quantile regression models using information criteria and diagnostic measures. The empirical findings demonstrate that the proposed Unit Chen quantile regression model provides accurate parameter estimation, effective diagnostic performance, and competitive model fitting, making it a valuable alternative for modeling bounded response data exhibiting heterogeneous distributional characteristics. 2026-10-01T00:00:00Z