Simplified neutrosophic multiplicative sets and decision making methods

The aim of this study is to define the simplified neutrosophic multiplicative sets by generalizing intuitionistic multiplicative sets to neutrosophic sets and to apply these sets to multicriteria decision making problems. Fuzzy sets, intuitionistic fuzzy sets and neutrosophic sets are frequently used concepts in solving problem that contain uncertain and incomplete information. The range of the characteristic functions of these sets is defined in the interval of [0,1]. This interval is scaled uniformly and symmetrically while assigning the problem information to numerical values. However, the problems encountered in real life also include information that must be taken into account as non-symmetrical and non-uniformly. In order to apply this type of information to real life problems, multiplicative preference relations are defined to evaluate problem information in the interval of [1/9,9] which is an unsymmetrical and non-uniform interval. Then, these relations are generalized to intuitionistic multiplicative preference relations (IMPR) and the concept of intuitionistic multiplicative set (IMS) is defined. Although the IMS can be applied to real-life problems, since the hesitant information of these sets depends on membership and non-membership information, it restricts decision-makers (DMs) that provide the assessment information on these problems. To overcome this situation, in this work, the IMS is generalized to the simplified neutrosophic multiplicative set (SNMS). In order to do this, the SNMSs and some of their properties are given first. In addition, the concept of simplified neutrosophic multiplicative number (SNMN) is defined and basic algebraic operations are presented. Then, the distance measures and the aggregation operators are defined by using SNMN operations. In order to show the effect of the proposed SNMS approach on multi-criteria decision making problems (MCDM), the SNM-TODIM method is developed by applying SNMNs to the TODIM method. Furthermore, a method based on water filling theory is presented to determine the criterion weights in such problems. Finally, a numerical example is given to demonstrate the superiority of the defined set over the IMS, a comparison analysis is performed using IMS and all results are interpreted in detail.