A new approach to three‐way decisions making based on fractional fuzzy decision‐theoretical rough set.

The main aim of the proposed work is to develop the new technique based on decision‐theoretical rough sets (DTRSs) and their applications in three‐way decision‐making problems. This study first develop a fractional fuzzy set (FFS) and their operations, the FFS is a more generalized and accurate tool for describing uncertainty in real‐life data information. A new form of decision technique for dealing with the issue of choice based on DTRSs is included in the three‐way decisions. The loss function of DTRSs is being used in the proposed decision method model. Initially, the idea of fractional fuzzy α‐covering (FF α‐covering), fractional fuzzy α–neighborhood (FF α–neighborhood) was introduced. Under the fractional fuzzy state, we integrated the loss function of DTRSs with covering‐based fractional fuzzy rough sets. Furthermore, we proposed and established performance characteristics for a new fractional fuzzy α‐covering decision‐theoretical rough sets model (FFCDTRSs). Then, according to the level of fractional fuzzy numbers (FFN's) positive and negative membership and related three‐way decision‐making, four methods to solve the expected loss expressed in the form of (FFNs) are described. We have developed a multicriteria decision algorithm (MCDM) based on FFCDTRS. Then an example is used to prove the feasibility of the four methods to solve the MCDM problem. Finally, the results of four distinct decision procedures with various loss functions are compared. The proposed three‐way decision‐making models are more accurate as compared with particular fuzzy sets. [ABSTRACT FROM AUTHOR]