ئەز   Saman Sh. Othman

This paper presents a novel decision-making approach based on the complex (n,m)th power root fuzzy set, which provides a powerful framework for managing two-dimensional uncertainty in evaluation problems. Existing models often struggle to offer the flexibility and robustness needed to handle diverse and uncertain real-world scenarios. To address this gap, we introduce two innovative aggregation operators–the (n,m)th power root fuzzy Dombi-weighted average operator and the weighted geometric operator–developed using flexible Dombi operations. These operators incorporate adjustable parameters, allowing for more precise control of uncertainty representation, and are formulated through rigorous mathematical principles, including sum, product, scalar multiplication, and power. Their theoretical properties are thoroughly analyzed to confirm logical consistency and reliability. A practical application involving university selection illustrates the effectiveness of the proposed method, where one alternative consistently emerges as the top choice across various parameter settings. Compared to existing methods, the new operators show significantly improved ranking stability, consistency, and robustness. Furthermore, sensitivity analysis and visual evaluation reveal how parameter changes influence decision outcomes, adding interpretive depth to the model. This study not only contributes new mathematical tools to the field of fuzzy decision-making but also offers a flexible and reliable solution for complex multi-attribute decision problems.

The concept of the reversible ring property concerning nilpotent elements was introduced by A.M. Abdul-Jabbar and C. A. Ahmed, who introduced the concept of commutativity of nilpotent elements at zero, termed as a CNZ ring, as an extension of reversible rings. In this paper, we extend the CNZ property through the influence of a central ring endomorphism alpha , introducing a new type of ring called a right alpha -skew central CNZ ring. This concept not only expands upon CNZ rings but also serves as a generalization of right alpha -skew central reversible rings. We explore various properties of these rings and delve into extensions of right alpha -skew central CNZ rings, along with examining several established results, which emerge as corollaries of our findings.

The object of this paper is to present the notion of right CNZ rings with involutions, or, in short, right *-CNZ rings which are a generalization of right *-reversible rings and an extended of CNZ property . A ring R with involution * is called right *-CNZ if for any nilpotent elements x, y є R, xy = 0 implies yx * = 0. Every right *-CNZ ring with unity involution is CNZ but the converse need not be true in general, even for the commutative rings. In this note, we discussed some properties right *-CNZ ring. After that we explored right *-CNZ property on the extensions and localizations of the ring R.