Novel Linear Diophantine Fuzzy Information Measures Based Decision Making Approach Using Extended VIKOR Method

One of the purposes of fuzzy set theory is to overcome the uncertainties in the problems of multi-criteria decision-making (MCDM) via membership functions. But the fuzzy set theory has own limitations. To remove the limitations on membership functions of fuzzy sets, such as intuitionistic fuzzy, Pythagorean fuzzy, q-rung orthopair fuzzy sets, the linear Diophantine fuzzy (LDF) concept is defined with the reference parameters. The benefit of this approach is that it is more flexible and efficient at handling uncertain data than other fuzzy sets. In this study, firstly, new information measures (distance, similarity, entropy) have been proposed for linear Diophantine fuzzy sets and their properties are studied. Secondly, the LDF-VIKOR method is given in as full detail. In the proposed method, the weights of criteria are calculated using the entropy-based objective weighting method. Thirdly, the effect of entropy measures in the LDF-VIKOR method on the best and compromise solutions is examined. Finally, an application of LDF-VIKOR on a healthcare management decision problem is given to show applicability of proposed method.