Fuzzy geometric spaces and their application to Persian medicine as a multicriteria decision-making problem

Abstract

In this article, we introduce fuzzy geometric spaces as a generalization of broader concepts of fuzzy sets, such as q-rung orthopair, picture, spherical, and multi-fuzzy sets. The primary objective of this study is to develop a comprehensive framework capable of handling diverse variable types, thereby overcoming the limitations of existing methods that are typically restricted to specific categories (e.g., discrete, continuous, qualitative, or quantitative). We define distance and similarity measures for these spaces and present an algorithm for their application in multicriteria decision-making problems. A key advantage of this framework is its ability to accommodate diverse fuzzification methods within a single problem, a capability absent in conventional fuzzy methodologies. Finally, this framework is applied to to analyze Mizaj questionnaires in Persian medicine, yielding more accurate and reliable results.