MADM Using m-Generalized q-Neutrosophic Sets

Abstract

Although the single valued neutrosophic sets (SVNSs) are effective tool to express uncertain information and
are superior to the fuzzy sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets and q-rung orthopair fuzzy sets, there is not yet
reported an operation which can provide desirable generality and flexibility under single valued neutrosophic environment,
although many operations have been developed earlier to meet above such eventualities. So, the primary aim of this paper is
to propose the concept of m-generalized q-neutrosophic sets (mGqNSs) as a further generalization of fuzzy sets, intuitionistic
fuzzy sets, Pythagorean fuzzy sets and q-rung orthopair fuzzy sets, single valued neutrosophic sets, n-hyperspherical
neutrosophic sets and single valued spherical neutrosophic sets. Under the m-generalized q-neutrosophic environment, we
develop some new operational laws and study their properties. Using these operations, we define m-generalized
q-neutrosophic weighted aggregation operators. The distinguished features of these proposed weighted aggregation operators
are studied in detail. Furthermore, based on these proposed operators, a MADM (multi-attribute decision making) approach is
developed. Finally, an illustrative example is provided to show the feasibility and effectiveness of the proposed approach.