Decision-making in complex and uncertain environments often involves handling multidimensional, conflicting, and partially contradictory information. While existing fuzzy frameworks— such as bipolar, n,m-rung orthopair, and complex fuzzy sets—address specific aspects of uncertainty, none fully capture bipolarity, complex-valued membership, and flexible n,m-rung representation simultaneously. To address this gap, this study introduces the bipolar complex n,m-rung orthopair fuzzy set (BCn,m-ROFS), a unified framework capable of representing positive and negative evaluations alongside complex-valued uncertainties with adjustable n and m parameters. Within this framework, two novel aggregation operators—BCn,m-ROF weighted averaging (BCn,m-ROFWA) and weighted geometric (BCn,m-ROFWG)—are developed to integrate multidimensional attribute information efficiently, while maintaining discriminative power and computational feasibility. The proposed approach is applied to multi-attribute decision-making problems, illustrating its capability to rank alternatives consistently and interpretably under varying conditions. Comparative analyses with traditional fuzzy models demonstrate that BCn,m-ROFS-based operators offer superior stability, ranking discrimination, and adaptability in uncertain decision environments. Sensitivity studies further confirm the robustness of the approach, highlighting practical considerations for extreme parameter settings. Overall, the BCn,m-ROFS framework provides a flexible, theoretically grounded, and computationally practical methodology for decision support, enabling more informed and balanced choices in scenarios characterized by complex, bipolar, and uncertain information.

In this paper, we study different properties of δ∗-semiopen set. We define the concept of δ∗-semi generalized closed sets and present some characteristics. In addition, as applications to δ∗-semi generalized closed set, we introduce δ∗-semi T1/2 space and obtain some of their basic properties. Moreover, we defined the notions of δ∗-semi symmetric space, δ∗-semi difference sets and δ∗-semi kernel of sets, and investigate some of their fundamental properties. At the latest, some new types of spaces are introduced and the relationships of these spaces are studied

The purpose of this paper is to define and study a new class of set called T*-B-closed sets, and investigating the characteristics of T*-B-closed set. Furthermore, the new type of continuous function is introduce and find some of its basic properties.