article · Journal of Function Spaces
Vagueness and uncertainty often complicate complex decision-making processes. Square-root fuzzy sets, known as SR-Fuzzy sets, offer a distinct extension to conventional fuzzy sets for managing imprecise information, contrasting with both intuitionistic and Pythagorean fuzzy sets. The framework establishes fundamental mathematical operations, associated properties, and a dedicated score function designed to rank these sets accurately. To resolve multi-attribute decision-making problems, four weighted aggregation operators are formulated: the SR-Fuzzy weighted average, weighted geometric, weighted power average, and weighted power geometric operators. These tools aggregate uncertain data to support structured evaluations. The effectiveness of the approach is demonstrated through a practical selection scenario that identifies a top-ranked university by evaluating and comparing aggregate outcomes using the derived score values.
Organisations regularly face complex decisions involving conflicting criteria and incomplete information. By refining mathematical tools that capture uncertainty more flexibly than existing models, decision-makers can better evaluate competing options. This provides a more structured and objective foundation for high-stakes evaluations, such as institutional ranking or strategic resource allocation.
This research represents early-stage theoretical modelling with an applied demonstration in institutional ranking. It could eventually inform multi-criteria decision-support software for administrators, procurement teams, or policy analysts who evaluate complex, qualitative, and uncertain data. However, the abstract indicates the work remains at an academic proof-of-concept stage, tested on an illustrative university selection problem, and is not yet packaged into an operational commercial tool.
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An intuitionistic fuzzy set is one of the efficient generalizations of a fuzzy set for dealing with vagueness/uncertainties in information. Under this environment, in this manuscript, we familiarize a new type of extensions of fuzzy sets called square-root fuzzy sets (briefly, SR-Fuzzy sets) and contrast SR-Fuzzy sets with intuitionistic fuzzy sets and Pythagorean fuzzy sets. We discover the essential set of operations for the SR-Fuzzy sets along with their several properties. In addition, we define a score function for the ranking of SR-Fuzzy sets. To study multiattribute decision-making problems, we introduce four new weighted aggregated operators, namely, SR-Fuzzy weighted average (SR-FWA) operator, SR-Fuzzy weighted geometric (SR-FWG) operator, SR-Fuzzy weighted power average (SR-FWPA) operator, and SR-Fuzzy weighted power geometric (SR-FWPG) operator over SR-Fuzzy sets. We apply these operators to select the top-rank university and show how we can choose the best option by comparing the aggregate outputs through score values.
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DOI: 10.1155/2022/3653225
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