A novel dominance based pythagorean fuzzy rough set model

The dominance-based rough sets extend conventional rough sets by substituting the equivalence relation with a dominance relation. Nonetheless, the current dominance relations remain overly limited in practical utility, as they consistently require a precise decrease or increase for every attribute to be considered. Indeed, for numerous practical scenarios, it is sufficient to utilize the ascending or descending arrangement of fractional characteristics instead of considering all attributes or focusing only on the overall assessment of objects. This research established two novel dominance relations derived from the observed phenomenon. Subsequently, we formulated a comprehensive rough set models based on these relations, enabling us to define overall assessments and specific criteria for individual attributes. First, we established a broader form of dominance relations and created a rough set model rooted in this generalized dominance concept. We achieved this by employing the Pythagorean fuzzy additive operator to combine the individualized attribute values of every object in Pythagorean fuzzy environments, resulting in an overall evaluation. Next, we introduced a different form of dominance relationship indicated as the "generalized -dominance relation," along with the corresponding "generalized -dominance rough set model." This is accomplished by integrating a parameter , which is within the range of (0, 1), into the general dominance relationship. The inclusion of this parameter allows us to manage the number of attributes that fulfill dominance relationships, leading to the derivation of decision rules encompassing both "at least" and "at most" conditions. The objective is to develop new dominance relations and rough set models in Pythagorean fuzzy settings, including a generalised -dominance relation for flexible attribute evaluation. As a result, the models generate effective decision rules under "at least" and "at most" conditions, with numerical examples validating their applicability. The proposed models support decision making in complicated and unpredictable situations by producing exact rules that are helpful in planning, risk analysis, and supply chain management. They can be used by managers to more clearly and transparently assess options, establish priorities, and justify group decisions.