What is it about?
Picture fuzzy set is a extended model from fuzzy set(PFS). It is similar to intuitionistic fuzzy set, but more delicate than intuitionistic. However, the existing basic operations on PFSs have obvious defects: For example, the intersection of a set with the universal set is not equal to this set, and the union of a set and the empty set is not equal to this set yet. This paper presents some new operations, which are more consistent with the basic characteristics of set operations.
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Why is it important?
we redefine partial order operation on picture fuzzy sets(PFSs), which has more consistency with objective reality, and then we establish a lattice on PFSs with respect to this operation in order to statement handily. Based on the new partial order operation, we redefine some basic operations on PFSs, and make them follow basic operation rules as fuzzy sets and intuitionistic fuzzy sets(IFSs). It is important to unify operations on PFSs with those on fuzzy sets and IFSs, and provide a foundation for further research on PFSs.
Perspectives
Writing this paper is to unify operations on picture fuzzy sets with those on fuzzy sets and intuitionistic fuzzy sets. It is helpful for those who do some further researches on picture fuzzy sets.
创邦 张
Qinghai Normal University
Read the Original
This page is a summary of: Redefinitions of Basic Operations on Picture Fuzzy Sets, March 2022, ACM (Association for Computing Machinery),
DOI: 10.1145/3532213.3532227.
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