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Equivalent Structures of Interval Sets and Fuzzy Interval Sets
Author(s) -
Hu Bao Qing,
Wong Heung,
Yiu Kafai Cedric
Publication year - 2018
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.21940
Subject(s) - interval (graph theory) , fuzzy set , mathematics , rough set , discrete mathematics , fuzzy logic , computer science , artificial intelligence , combinatorics
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.