Novel distance and entropy definitions for linear Diophantine fuzzy sets and an extension of TOPSIS (LDF-TOPSIS)

The literature of multiple attribute decision making (MADM) is fruitful since there are various and successful applications of different fuzzy set extensions such as intuitionistic, Pythagorean and q-Rung orthopair fuzzy sets (IFS, PFS and q-ROFS). Besides their powerful aspects, some definitional limitations are known. In order to eradicate these boundaries regarding the definitions of membership and non-membership degrees, linear Diophantine fuzzy set (LDFS) concept has been recently emerged. By considering two parameters, LDFS extends the representation area of the previous fuzzy set definitions and provides more extensive human judgement coverage field. In this study, the first distance and entropy measures in the literature have been developed for LDFSs. Their axiomatic definitions are given, and the proofs are shown. Also, thanks to our extensive literature review, we became aware that there is no MADM extension dedicatedly proposed for LDFS. So, the first MADM method extension for LDFS environment has also been developed in this study. A very well-known MADM approach, TOPSIS, has been extended into LDFS environment for the first time in the literature. The applicability is shown in a healthcare management decision problem and the validity is checked and approved by comparing the alternative rankings LDF-TOPSIS and the aggregation operators that were obtained from the literature produced.