A visual analytics approach for multi-attribute decision making based on intuitionistic fuzzy AHP and UMAP

Abstract

Multi-attribute decision making (MADM) has been extensively explored and applied in many real-world problems. However, comprehending the decision-making process and selecting a satisfactory choice from a large set of alternatives characterized by multiple conflicting attributes impose a significant cognitive burden on decision-makers. A visual analytics approach for MADM (MADM-VA) that integrates visual representations of alternatives with the decision-making analysis process is proposed to solve this problem. Firstly, to ensure the final decision meets the actual needs and expectations of decision-makers, an Intuitionistic Fuzzy Analytic Hierarchy Process based on Nonlinear Programming (IFAHP-NLP) is proposed. This approach directly determines the optimal crisp attribute weight vector according to the preferences of decision-makers and avoids information loss and distortion of attribute weights caused by defuzzification. Next, the Uniform Manifold Approximation and Projection (UMAP) is used to map the high-dimensional weighted normalized decision matrix to two-dimensional space, illustrating the distribution of alternatives. The concept of similarity to the ideal solution is introduced to enhance the interpretability of the generated space. Furthermore, the Voronoi diagram is innovatively adopted to assist decision-makers in gaining a better understanding of the decision-making process and help them visually identify the best choice, which is closest to the positive ideal solution and farthest from the negative ideal solution. Finally, experimental results from two case studies verify that MADM-VA is efficient and reliable.