Parametrized Trapezoidal Neutrosophic Set and its Application to Multi-Attribute Decision-Making

Abstract

In modern engineering, management, and information systems, decision-making is faced with a variety of conflicting traits, various heterogeneous information sources, and pervasive uncertainty. Typical multi-attribute decision-making (MADM) techniques are not suitable for modeling the indeterminacy, nonlinear preference behavior, and asymmetric risk attitude present in real-world decision-making scenarios. To overcome these limitations, this paper introduces a new concept of the Parametrized Trapezoidal Neutrosophic Set (PTNS) to fully extend Ye's traditional trapezoidal neutrosophic numbers concept by adding truth- and falsity-based influence regulation parameters (α, β) for nonlinear shapes. On this basis, rank and accuracy functions are designed in parametric form and derived from the proposed PTNS. This keeps the full compatibility with traditional neutrosophic ranking functions in the linear case (where (α, β) = (1, 1)). In addition, a decision-making framework for PTNS--SYAI is proposed by combining the parametric scoring measure with the Simplified Yielded Aggregation Index (SYAI), enabling efficient normalization, aggregation, and ranking of alternatives under uncertainty. A well-defined, easily understood software selection problem from the literature is presented to illustrate the proposed approach's ability and interpretability. Key properties of the proposed score, such as boundedness, monotonicity, smoothness in (α, β), and exact reduction to the classical model at (α, β) = (1, 1), are formally demonstrated. Under varying $(\alpha,\beta)$ setups, sensitivity analysis reveals that the system gracefully rebalances the ranks, solving the real closeness of ties with justifiable results, but preserving the rank order of alternatives when no significant closeness exists. The ranking results of the proposed method are compared with those of TOPSIS, VIKOR, and COPRAS in a cross-method comparison of the second-largest problem, demonstrating consistent rankings. The outcomes established that the PTNS--SYAI framework is a powerful, flexible, and low-cost decision-making tool for complex, multi-attribute, and uncertain decision problems.