
Cut sets of outer Pfuzzy sets and extended rough sets models
 HAO Xiumei, LIU Jiqin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(10):
16.
doi:10.6040/j.issn.16719352.0.2020.196

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The Pfuzzy sets are a pair of inner and outer Pfuzzy sets. Inner and outer Pfuzzy sets are two different kinds of dynamic fuzzy sets. The cut sets method is frequently used in fuzzy sets discussed. The concepts of λcut sets, strong λcut sets, interval cut sets and cut sets granularity are proposed, and the cut sets and interval cut sets granularity theorems of outer Pfuzzy sets are discussed. Then, the interval cut sets decomposition theorems of outer Pfuzzy sets are given. By using the concept of the outer Pfuzzy rough membership function, four rough sets extended models are proposed such as (α_{F},β_{F}) rough sets, (1_{F},0_{F}) rough sets, (α_{F},β_{F})probability rough sets and (α_{F},β_{F}) variable precision rough sets. The (α_{F},β_{F})rough sets theorems of the outer Pfuzzy sets are discussed. In the end, the quantitative characteristics and relationship theorem are given.