A new distance measure for single-valued neutrosophic set and an improved method based on TOPSIS and TODIM to multi-attribute decision-making

In venture capital, fuzzy information can be effectively represented using single-valued neutrosophic sets, and TOPSIS and TODIM are commonly used methods in multiattribute decision making. Distance measurement plays a crucial role in these methods. This paper introduces a novel parameter distance measure for single-valued neutrosophic sets and an improved method based on TODIM and TOPSIS. First, the proposed distance measure addresses limitations of existing metrics and is rigorously proven to satisfy axiomatic distance definitions. Secondly, to consider the decision-maker’s risk attitude and simplify the calculation process, we propose a new method with the known parameter of risk attitude based on TODIM and TOPSIS. Finally, a case study of venture capital application is provided to showcase the effectiveness and practicality of the proposed distance measure and decision-making method in addressing multi-attribute decision-making problems within SVNS environments. Furthermore, sensitivity analysis of the distance measure parameters demonstrates consistent ranking results across various parameter values, thereby validating the robustness of the proposed approach. Comparative evaluations with other decision-making methods in identical scenarios underscore the rationality and superiority of our proposed methodology. The proposed distance measure and decision-making method offer significant contributions to the theory of single-valued neutrosophic sets and the resolution of venture capital problems.