<p><i>n</i>-intuitionistic polygonal fuzzy sets have significant advantages over traditional fuzzy sets in handling uncertain information. Due to the fact that information measure is an effective tool for handling uncertain information, this paper proposes distance measures, symmetric cross entropies and knowledge measures for <i>n</i>-intuitionistic polygonal fuzzy sets. First, this paper initially formulates distance measure models, which is based on theoretical underpinnings of t-conorms. Then, we explore a conversion mechanism between the distance measure and symmetric cross entropies, in conjunction with the conversion path from these measures to knowledge measures. These transformations can elicit a series of formula for delineating symmetric cross entropy and knowledge measure. Moreover, this study affords a compendium of precise mathematical formulations to support the interconvertibility relationships delineated, this conversion can enable the selection of appropriate measures for optimization according to different needs. Subsequently, we consider constructing a fuzzy graph by graph theory and information measures for the decision model. Graph theory can visually depict diverse attributes and their intrinsic interconnections, which possesses significant practical utility in facilitating a more precise assessment of alternatives. Ultimately, we provide a case study of purchasing a house, which demonstrates the effectiveness and practical application value of the proposed method through detailed comparative evaluation, rigorous sensitivity assessment and robustness analysis.</p>