FUZZY SET ON PERMUTATIONS OF Sn

This study extends the symmetric group 𝑺 𝒏 (a symmetric group of n objects) to a fuzzy set and investigate various fuzzy properties.A constructed membership function was design to assign membership values ranging from 𝟎 to 𝟏, facilitating the examination of fuzzy characteristics.The alpha level set, support, height, and core of the fuzzy symmetric group were being investigated, providing insights into the fuzzy structure.The extension of 𝑺 𝒏 to a fuzzy set allows the capture of uncertainties and ambiguities inherent in permutation-based problems.The findings of this research contribute to the development of fuzzy group theory and its applications in algebra, The constructed membership function offers a simple way for assigning membership values, allowing for exploration of fuzzy properties.This work serves as an insight on fuzzy set in permutation and also allows further research in fuzzy group theory and its potential applications in various fields.