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Abstract

P-sets (packet sets) is improved by introducing function into it, and the concept and structure of function P-sets (function packet sets) is proposed, which is a set pair composed of the function internal P-set \( S^{{\bar{F}}} \)(function internal packet set \( S^{{\bar{F}}} \)) and the function outer P-set S F (function outer packet set S F). Function P-sets has dynamic characteristics and law characteristics. Under certain conditions, function P-sets can return to the “origin” of function ground sets S. In the paper, it is proved that function P-sets is extension of P-sets, conversely, P-sets is special case of function P-sets. Applications of function P-sets in discovery of unknown information laws hidden information systems, are provided. Function P-sets is a new theory and a new method to research dynamic information laws for information systems.

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References

  1. Shi K (2008) P-sets. J Shandong Univ Nat Sci 43(11):77–84 (in Chinese)

    MATH  Google Scholar 

  2. Shi K (2009) P-sets and its applications. Int J Adv Syst Sci Appl 9(2):209–219

    Google Scholar 

  3. Shi K (2010) P-sets and their application characteristics. Comput Sci 37(8):1–8 (in Chinese)

    Google Scholar 

  4. Shi K, Li X (2010) Camouflaged information identification and its applications. Int J Adv Syst Sci Appl 10(2):157–167

    Google Scholar 

  5. Shi K, Zhang L (2009) Internal P-sets and data outer-recovery. J Shandong Univ Nat Sci 44(4):8–14 (in Chinese)

    MathSciNet  MATH  Google Scholar 

  6. Lin H, Li Y (2010) P-sets and its P-separation theorems. Int J Adv Syst Sci Appl 10(2):209–215

    Google Scholar 

  7. Zhang L, Cui Y, Shi K (2010) Outer P-sets and data inner-recovery. Syst Eng Electron Tech 32(6):1233–1238 (in Chinese)

    MathSciNet  Google Scholar 

  8. Zhou Y, Zhang G, Shi K (2010) P-sets and double information laws generation. Math Pract Theory 40(13):71–80 (in Chinese)

    Google Scholar 

  9. Wang Y, Geng H, Shi K (2010) The mining of dynamic information based on P-sets and its applications. Int J Adv Syst Sci Appl 10(2):234–240

    Google Scholar 

  10. Zhang G, Li E (2010) Information gene and identification of its information Knock-out/Knock-in. Int J Adv Syst Sci Appl 10(2):308–315

    Google Scholar 

  11. Zhou Y, Zhang G, Zhang L (2010) Internal and outer data circle and dynamic data-recovery. J Shandong Univ Nat Sci 45(8):21–26 (in Chinese)

    MathSciNet  Google Scholar 

  12. Li Y, Zhang L, Shi K (2010) Generation and recovery of compressed data and redundant data. Quant Log Soft Comput 2(1):661–671

    Article  Google Scholar 

  13. Huang S, Wang W, Geng D (2010) P-sets and its internal P-memory characteristics. Int J Adv Syst Sci Appl 10(2):216–222

    Google Scholar 

  14. Ming Xiu, Kaiquan Shi, Li Zhang (2010) P-sets and \( \bar{F}\) -data selection-discovery. Quant Log Soft Comput 2(1):791–799

  15. Yu X (2010) Identification and selection of P-sets. J Shandong Univ Nat Sci 45(1):94–98 (in Chinese)

    MathSciNet  Google Scholar 

  16. Jihua Tang, Baohui Chen, Kaiquan Shi (2009) P-sets and \( \left( {\bar{F},F} \right) \) -data generation-identification. J Shandong Univ Nat Sci 44(11):83–92 (in Chinese)

    Google Scholar 

  17. Yuying Li, Weiqi Xie, Kaiquan Shi (2010) Identification and recovery of \( \bar{F} \) -incomplete data. J Shandong Univ Nat Sci 45(9):57–64 (in Chinese)

    Google Scholar 

  18. Shi K, Yao B (2008) Function S-rough sets and law identification. Sci Chin E Inf Sci 38(4):553–564 (in Chinese)

    Google Scholar 

  19. Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 32(11):341–356

    Article  MathSciNet  Google Scholar 

Download references

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Correspondence to Kaiquan Shi.

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Shi, K. Function P-sets. Int. J. Mach. Learn. & Cyber. 2, 281–288 (2011). https://doi.org/10.1007/s13042-011-0032-1

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  • DOI: https://doi.org/10.1007/s13042-011-0032-1

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