Faculty Performance Evaluation through Multi-Criteria Decision Analysis Using Interval-Valued Fermatean Neutrosophic Sets

The Neutrosophic Set ( N s e t ) represents the uncertainty in data with fuzzy attributes beyond true and false values independently. The problem arises when the summation of true ( T r ) , false ( F a ) , and indeterminacy I n values crosses the membership value of one, that is, T r + I n + F a < 1 . It becomes more crucial during decision-making processes like medical diagnoses or any data sets where T r + I n + F a < 1 . To achieve this goal, the F N s e t is recently introduced. This study employs the Interval-Valued Fermatean Neutrosophic Set ( I V F N s e t ) as its chosen framework to address instances of partial ignorance within the domains of truth, falsehood, or uncertainty. This selection stands out due to its unique approach to managing such complexities within multi-decision processes when compared to alternative methodologies. Furthermore, the proposed method reduces the propensity for information loss often encountered in other techniques. IVFNS excels at preserving intricate relationships between variables even when dealing with incomplete or vague information. In the present work, we introduce the I V F N s e t , which deals with partial ignorance in true, false, or uncertain regions independently for multi-decision processes. The I V F N s e t contains the interval-valued T r m e m b e r s h i p value, I n m e m b e r s h i p value, and F a m e m b e r s h i p for knowledge representation. The algebraic properties and set theory between the interval-valued F N s e t have also been presented with an illustrative example.