On Fuzzy Fundamental Groups and Fuzzy Folding of Fuzzy Minkowski Space

Abstract

In this paper, we studied the relations between new types of fuzzy retractions, fuzzy foldings, and fuzzy deformation retractions, on fuzzy fundamental groups of the fuzzy Minkowski space M˜4. These geometrical transformations are used to give a combinatorial characterization of the fundamental groups of fuzzy submanifolds on M˜4. Then, the fuzzy fundamental groups of the fuzzy geodesics and the limit fuzzy foldings of M˜4 are presented and obtained. Finally, we proved a sequence of theorems concerning the isomorphism between the fuzzy fundamental group and the fuzzy identity group.