https://hdl.handle.net/11436/907 Fri, 25 Sep 2026 02:12:26 GMT 2026-09-25T02:12:26Z https://hdl.handle.net/11436/10969 A novel BPA derivation method using linguistic fuzzy sets in dempster-shafer theory Başkan, Elif; Şahin, Rıdvan In this study, we present a new method for developing Basic Probability Assignment (BPA) using Linguistic Fuzzy Sets (LFS). Dempster-Shafer Theory (DST) is used to efficiently combine different data sources. The use of LFS provides a robust structure for managing uncertainty in decision making by representing knowledge in linguistic terms. However, effectively integrating multiple uncertain sources requires a strong probabilistic approach. To overcome this challenge, we propose a method to derive BPA values directly from linguistic terms, ensuring compatibility with the DST fusion rule. We then use the Dempster-Shafer combination rule to combine information from various sources, thereby improving the reliability of the decision-making process. Wed, 01 Jan 2025 00:00:00 GMT https://hdl.handle.net/11436/10969 2025-01-01T00:00:00Z https://hdl.handle.net/11436/10968 Intuitionistic multiplicative MABAC method and its application on multi criteria decision making Köseoğlu, Ali Intuitionistic multiplicative sets, an extension of multiplicative preference relations, incorporate both asymmetrical and non-uniform membership and non-membership degrees, making them particularly useful for handling uncertainty in decision-making problems. These sets have been widely studied in the literature and applied across various domains, including engineering, economics, and artificial intelligence. In this study, we extend the Multi-Attributive Border Approximation Area Comparison (MABAC) method, a well-established multi-criteria decision-making (MCDM) approach, by integrating intuitionistic multiplicative set elements into its framework. This extension enhances the MABAC method’s ability to process decision-making problems involving uncertain, asymmetrical, and non-uniform data, making it a more robust and flexible approach in complex decision environments. To demonstrate the effectiveness of the proposed intuitionistic multiplicative MABAC (IM-MABAC) method, a numerical example is presented, illustrating its applicability in a real-world decision-making scenario. Furthermore, a comparative analysis with other well-known MCDM methods, such as intuitionistic multiplicative TOPSIS (IM-TOPSIS) and intuitionistic multiplicative TODIM (IM-TODIM), is conducted to validate its reliability and consistency. The results indicate that the intuitionistic multiplicative MABAC method provides a structured and systematic decision-making framework, offering an alternative approach for handling imprecise and uncertain information in multi-criteria problems. Wed, 01 Jan 2025 00:00:00 GMT https://hdl.handle.net/11436/10968 2025-01-01T00:00:00Z https://hdl.handle.net/11436/10911 Inversion transformations with respect to conics in hybrid number planes Öztürk, İskender; Çakır, Hasan; Özdemir, Mustafa This paper presents a comprehensive study of geometric inversion with respect to central conics in hybrid number planes, which unify complex, hyperbolic, and dual numbers within a single algebraic structure. By employing the hybrid scalar product and the associated pseudo-Euclidean metric, the hybridian planes were classified as elliptic, hyperbolic, or parabolic. Explicit inversion formulas were derived for points, lines, and conics in each plane type. It was shown that lines passing through the inversion center remain invariant, while others transform into conics. Homothetic conics preserve their type under inversion, whereas non-homothetic conics yield cubic or quartic curves depending on their relation to the inversion center. These results extend classical inversion geometry into a unified hybrid setting, providing a new framework for geometric transformations in generalized number systems. Wed, 01 Jan 2025 00:00:00 GMT https://hdl.handle.net/11436/10911 2025-01-01T00:00:00Z https://hdl.handle.net/11436/10843 Moment-based approximation for a renewal reward process with generalized gamma-distributed interference of chance Yazır, Tülay; Kamışlık, Aslı Bektaş; Khaniyev, Tahir; Hanalıoğlu, Zülfiye This study investigates the renewal reward process under the assumption that the random variables describing the discrete interference of chance follow a generalized gamma distribution. A moment-based approximation method is employed to derive novel results for the renewal function, enabling an approximation of the ergodic distribution of the process. Furthermore, the limiting distribution of the ergodic distribution is also derived. The theoretical findings are illustrated through a specific example in which the demand random variable eta 1 {\eta }_{1} is represented by a third-order Erlang distribution with parameter theta = 1 \theta =1 . Wed, 01 Jan 2025 00:00:00 GMT https://hdl.handle.net/11436/10843 2025-01-01T00:00:00Z