M-parameterized N-soft set-based aggregation operators for multi-attribute decision making

Fuzzy sets, soft sets and N-soft set are essential concepts for fuzzy modeling, decision making under uncertainty and computational intelligence. Nevertheless, all these models have some limitations imposed on the alternatives and attributes. These mathematical models were unable to handle the situations whenever decision makers need to assign non-binary evaluations to both attributes and alternatives. To overcome these problems, Riaz et al. (Symmetry 13(5):1-31, 2021) proposed the idea of M-parameterized N-soft set (MPNSS), through examining independent non-binary evaluations to both parameters and alternatives. MPNSSs are highly convenient in representation of ambiguous and uncertain data in decision analysis during ranking, rating and grading the objects. The proposed model has greater efficiency to handle the imprecision rather than existing mathematical models. Additionally, we develop multi-attribute decision-making (MADM) techniques on account of M-parameterized N-soft sets (MPNSSs), M-parameterized N-soft aggregation operators (MPNSAO) and M-parameterized N-soft weighted aggregation operators (MPNSWAO). For these objectives, we define fundamental operations on MPNSSs and their properties. Meanwhile, several related results are well proven and some algorithms for MADM are also developed. Moreover, the applications of MADM techniques corresponding to proposed algorithms are explained by illustrative material. To explain the presumption, authenticity and effectiveness of the suggested course of actions, we compared the techniques with few existing MADM methods.