Abstract
This paper attempts to introduce and study new connection between fuzzy retractions, fuzzy foldings and fuzzy deformation retracts of open fuzzy spheres in fuzzy Lobachevsky space and fuzzy open ball in fuzzy Euclidean space. Types of fuzzy foldings and fuzzy deformation retracts of fuzzy open sphere are discussed. Types of minimal fuzzy retractions of fuzzy open sphere are presented. The fuzzy foldings of fuzzy open sphere is deduced, also the limit of this folding is obtained. The connection between fuzzy foldings and fuzzy central projection map is achieved; also the connection between fuzzy retractions and fuzzy exponential map is discussed. Some applications are presented.
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