Novel Forms of Fuzzy Math on Rational Homotopy Theory

Abstract

              This paper explores recent developments in applying fuzzy mathematics to rational homotopy theory. Fuzzy mathematical concepts allow for impreciseness and vagueness to be incorporated into mathematical models. This has enabled new techniques for analyzing topological spaces and homotopy groups. After reviewing foundational concepts in fuzzy mathematics and rational homotopy theory, this paper examines three novel approaches for integrating fuzzy methods into rational homotopy theory: fuzzy homotopy groups, fuzzy topological spaces, and fuzzy homological algebra. Challenges and opportunities for further research are also discussed.