Solution of supply chain management problems using rough t spherical fuzzy set lower and upper approximation spaces.

The importance of supply chain management lies in its direct influence on efficiency, customer satisfaction, and competitiveness. These issues are addressed, enabling organizations to minimize expenses, enhance reliability, respond to market dynamics, and sustain growth. Therefore, it is not an easy task to assess the most appropriate supply chain management system based on multiple attributes. The theory of multi-attribute decision-making (MADM) is a valuable mechanism that simplifies the analysis of complex information involving multiple sets of alternatives and attributes. The rough t-spherical fuzzy set (Rt-SFS) framework is a fairly standard approach to aggregating fuzzy information, and the theory of Dombi operations will broaden its scope. Through the generalized version of t-norm (TNM) and t-conorm (TCNM) operations, we define the Dombi t-norm (DTNM) and Dombi t-conorm (DTCNM), which provide a versatile framework for aggregating incomplete and fuzzy information. In earlier eras, many decision-making problems were not evaluated accurately due to deficiencies in the MADM models developed at the time. But after the introduction of the Rt-SFS framework, the data aggregation process is more precise and accurate than before. The theory of Rt-SFS is the most general of all existing extension fuzzy set frameworks due to the presence of lower and upper approximation spaces. To apply MADM and Rt-SFS models, this paper introduces a new model, utilizing a novel conception of rough t-spherical fuzzy Dombi weighted averaging (Rt-SFDWA) and rough t-spherical fuzzy Dombi weighted geometric (Rt-SFDWG) operators. We have given an MADM algorithm based on the proposed theory. To examine the accuracy of management in relation to the suggested theory of supply chain management, we address a numerical problem based on real-world situations. The sensitivity analysis is conducted to test the validity of the proposed theory. To demonstrate the authenticity of the developed theory, we made comparisons with other methods available in the literature. At last, we concluded.