Cut sets of outer P-fuzzy sets and extended rough sets models
- HAO Xiu-mei, LIU Ji-qin
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(10):
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The P-fuzzy sets are a pair of inner and outer P-fuzzy sets. Inner and outer P-fuzzy sets are two different kinds of dynamic fuzzy sets. The cut sets method is frequently used in fuzzy sets discussed. The concepts of λ-cut sets, strong λ-cut sets, interval cut sets and cut sets granularity are proposed, and the cut sets and interval cut sets granularity theorems of outer P-fuzzy sets are discussed. Then, the interval cut sets decomposition theorems of outer P-fuzzy sets are given. By using the concept of the outer P-fuzzy rough membership function, four rough sets extended models are proposed such as (αF,βF) rough sets, (1F,0F) rough sets, (αF,βF)probability rough sets and (αF,βF) variable precision rough sets. The (αF,βF)rough sets theorems of the outer P-fuzzy sets are discussed. In the end, the quantitative characteristics and relationship theorem are given.