Abstract
This paper discussed the relation between fuzzy sets and rough sets by theory of the isomorphism and homomorphism of fuzzy sets, and two main conclusions are reached. Firstly, for any group of fuzzy sets which are isomorphic for each other in X, an approximation space could be defined uniquely. Secondly, for any group of fuzzy equivalence relations which are isomorphic, similarly a group of fuzzy approximation spaces which are isomorphic could be defined. Moreover, the construction of fuzzy approximation space is given. Finally, we illustrate an concrete example to show the construction of the fuzzy approximation space, and discussed their related properties.
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Chengyi, Z., Haiyan, F. (2007). Isomorphic Fuzzy Sets and Fuzzy Approximation Space. In: Cao, BY. (eds) Fuzzy Information and Engineering. Advances in Soft Computing, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71441-5_33
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DOI: https://doi.org/10.1007/978-3-540-71441-5_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71440-8
Online ISBN: 978-3-540-71441-5
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