Rough neutrosophic multisets

Multiple uncertainty conditions exist in real life with incomplete knowledge gathered by human observation. These conditions are about vagueness, imprecision, ambiguity, and inconsistency which need to be taken into consideration. It has not, however, been satisfactorily modeled by the classical and existing mathematical concept for uncertainty theory. To capture all the associated uncertainty factors, this research aims to develop a new concept of uncertainty with more representable defined boundary sets. A rough neutrosophic multisets theory which is a fusion between neutrosophic multisets and rough sets theory was introduced as a novel finding of this research. It is a more appropriate and representable theory for a real problem in resolving multiple uncertainty information with boundary regions involving lower and upper approximation. Another significant finding of the research is the basic rough neutrosophic multi sets operations, such as complement, union, intersection, contained, and equality, are defined with numerical examples. The "AND" and "OR" rough neutrosophic multisets operators are shown. The algebraic operations over rough neutrosophic multisets, including addition, subtraction, multiplication, and scalar multiplication, are also introduced. It also determined the level of relevant uncertainty factors in every situation. Other findings indicated that a roughness measure is defined as a principal for the development of rough neutrosophic multisets in equivalence relations. As a result, rough neutrosophic multisets are derived concerning relations properties for single and two universal sets, four types of vector similarity measures and three types of distance measures, two types of distance-based similarity measures, two types of entropies measures, and three types of aggregation operator. Finally, this research contributed a procedure of rough neutrosophic multisets operators as a novel approach to improving the representation of the evaluation process involving multiple-criteria decisions-making. The highlighted medical diagnosis problem is used for illustrative purposed to explain the applicability of the procedure. In addition, the rough neutrosophic multisets with multi-criteria decision-making is applicable to be used in solving problems of a similar nature.