New information measures for linear diophantine fuzzy sets and their applications with LDF-ARAS on data storage system selection problem

Abstract

In addition to membership and non-membership degrees, linear Diophantine fuzzy set (LDFS) incorporates two reference parameters in fuzzy set definition to represent human judgment more comprehensively. It also provides flexibility in updating the decision setting by changing the meaning of the reference parameters when required by the decision-maker. Information measures in fuzzy sets have many application areas in the literature. Especially, distance and entropy measures are utilized in multiple attribute decision-making (MADM) field. Distance measures are needed by distance-based methods like TOPSIS and EDAS because their alternative ranking procedure is based on measuring the distances between alternatives and some artificial ideal or average solutions. Entropy measure is a very important tool being used in objective attribute weighting procedures of MADM applications. Thus, new distance and entropy measure propositions for LDFS are the first contribution of the study. Also, Additive Ratio Assessment (ARAS) method is extended into LDFS (LDF-ARAS) for the first time in the literature as a second contribution. In this extension, we selected ARAS as one of the most cited tools because it is found flexible and easily adaptable by researchers who do not have any background in MADM. The proposed entropy measure is integrated with the objective attribute weighting procedure of the novel LDF-ARAS approach. The third contribution is the newly developed decision model proposed for a real-life data storage system (DSS) selection problem. Three DSS options were evaluated with respect to thirteen attributes by five skilled and well-educated experts and LDF-ARAS was performed to rank alternatives. The entropy-based LDF-ARAS approach was validated by comparing the results of six different applications. In the first three, different entropy formulas are used and in the last three, these entropy measures are integrated with LDF-TOPSIS. All six comparisons gave similar alternative rankings.