Abstract
The space, Fcc(R), of all fuzzy intervals in R cannot form a vector space. However, the space Fcc(R) maintains a vector structure by treating the addition of fuzzy intervals as a vector addition and treating the scalar multiplication of fuzzy intervals as a scalar multiplication of vectors. The only difficulty in taking care of Fcc(R) is missing the additive inverse element. This means that each fuzzy interval that is subtracted from itself cannot be a zero element in Fcc(R). Although Fcc(R) cannot form a vector space, we still can endow a norm on the space Fcc(R) by following its vector structure. Under this setting, many different types of open sets can be proposed by using the different types of open balls. The purpose of this paper is to study the topologies generated by these different types of open sets.
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