Equivalent Structures of Interval Sets and Fuzzy Interval Sets |
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| Authors: | Bao Qing Hu Heung Wong Ka‐fai Cedric Yiu |
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| Affiliation: | 1. School of Mathematics and Statistics, Wuhan University, Wuhan, People's Republic of China;2. Computational Science Hubei Key Laboratory, Wuhan University, Wuhan, People's Republic of China;3. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, People's Republic of China |
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| Abstract: | Ideas of interval sets come from the lower and upper approximations of rough sets to study a unified structure of rough sets and their generalizations. Starting from the interval sets and their operations, this paper summarizes and analyzes other sets that have similarities with the interval sets or fuzzy interval sets. Our conclusions are that interval sets are mathematically equivalent to shadowed sets and flou sets, respectively, and fuzzy interval sets are mathematically equivalent to interval‐valued fuzzy sets and intuitionistic fuzzy sets, respectively. |
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