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A unified view of consistent functions

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Abstract

In order to compare the structures and properties of two generalized information systems, a class of special mappings, called consistent functions in some literature, have been extensively studied over the past years. Most recently, consistent functions have been unified and extended into the framework of neighborhood systems which have general binary relations, dominance relations, and coverings as instances. In this paper, we further extend and investigate the notion of consistent functions for fuzzy neighborhood systems. After introducing the definition of extended consistent functions and showing their relationships with related functions, we present some basic properties of the new consistent functions with respect to set-theoretic operations and fuzzy neighborhoods, respectively. As an application, we consider the attribute reduction based on consistent functions. In doing so, we contribute to a unified view of consistent functions and attempt to develop a general theory for investigating the invariant properties of fuzzy neighborhood systems under consistent functions.

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References

  • Ganivada A, Ray SS, Pal SK (2013) Fuzzy rough sets, and a granular neural network for unsupervised feature selection. Neur Netw 48:91–108

    Article  MATH  Google Scholar 

  • Ge H, Li L, Xu Y, Yang C (2015) Bidirectional heuristic attribute reduction based on conflict region. Soft Comput 19(7):1973–1986

    Article  MATH  Google Scholar 

  • Gong ZT, Xiao ZY (2010) Communicating between information systems based on including degrees. Int J Gen Syst 39(2):189–206

    Article  MathSciNet  MATH  Google Scholar 

  • Grzymala-Busse J (1986) Algebraic properties of knowledge representation systems. In: Proceedings of the ACM SIGART international symposium on methodologies for intelligent systems, ACM, pp 432–440

  • Grzymala-Busse J, Sedelow W Jr (1988) On rough sets and information system homomorphism. Bull Pol Acad Sci Tech Sci 36(3):233–239

    MATH  Google Scholar 

  • Intan R, Mukaidono M (2002) Degree of similarity in fuzzy partition. In: Pal NR, Sugeno M (eds) Advances in soft computing-AFSS 2002, Lecture Notes in Computer Science, vol 2275. Springer, Berlin, pp 20–26

    Chapter  Google Scholar 

  • Li DY, Ma Y (2000) Invariant characters of information systems under some homomorphisms. Inf Sci 129:211–220

    Article  MathSciNet  MATH  Google Scholar 

  • Lin TY (1989b) Chinese wall security policy-an aggressive model. In: Proceedings of the fifth annual computer security applications conference, pp 282–289

  • Lin TY (1989b) Neighborhood systems and approximation in relational databases and knowledge bases. In: Proceedings of the fourth international symposium on methodologies of intelligent systems, pp 75–86

  • Lin TY (1997) Granular computing: From rough sets and neighborhood systems to information granulation and computing in words. In: European congress on intelligent techniques and soft computing, pp 1602–1606

  • Lin TY (2009) The “final” model of granular computing. In: IEEE international conference on fuzzy systems, IEEE, pp 1523–1528

  • López V, del Río S, Benítez JM, Herrera F (2014) Cost-sensitive linguistic fuzzy rule based classification systems under the mapreduce framework for imbalanced big data. Fuzzy Sets Syst 258:5–38

    Article  MathSciNet  Google Scholar 

  • Pedrycz W, Chen SM (eds) (2015) Information granularity, big data, and computational intelligence, studies in big data, vol 8. Springer, Berlin

    Google Scholar 

  • Pedrycz W, Vukovich G (2000) Granular worlds: representation and communication problems. Int J Intell Syst 15(11):1015–1026

    Article  MATH  Google Scholar 

  • Pedrycz W, Al-Hmouz R, Morfeq A, Balamash A (2015) Distributed proximity-based granular clustering: towards a development of global structural relationships in data. Soft Comput 19(10):2751–2767

    Article  Google Scholar 

  • Qian Y, Wang Q, Cheng H, Liang J, Dang C (2014) Fuzzy-rough feature selection accelerator. Fuzzy Sets Syst 258:61–78

    Article  MathSciNet  MATH  Google Scholar 

  • Ruspini EH (1969) A new approach to clustering. Inf Contr 15(1):22–32

    Article  MATH  Google Scholar 

  • Sierpiński W, Krieger CC (1956) General topology. University of Toronto, Toronto

    Google Scholar 

  • Tsang ECC, Wang C, Chen D, Wu C, Hu Q (2013) Communication between information systems using fuzzy rough sets. IEEE Trans Fuzzy Syst 21(3):527–540

    Article  Google Scholar 

  • Wang C, Wu C, Chen D, Du W (2008a) Some properties of relation information systems under homomorphisms. Appl Math Lett 21:940–945

    Article  MathSciNet  MATH  Google Scholar 

  • Wang C, Wu C, Chen D, Hu Q, Wu C (2008b) Communicating between information systems. Inf Sci 178:3228–3239

    Article  MathSciNet  MATH  Google Scholar 

  • Wang C, Chen D, Zhu L (2009) Homomorphisms between fuzzy information systems. Appl Math Lett 22:1045–1050

    Article  MathSciNet  MATH  Google Scholar 

  • Wang C, Chen D, Hu Q (2010) Some invariant properties of ordered information systems under homomorphism. Sci China Inf Sci 53(9):1816–1825

    Article  MathSciNet  Google Scholar 

  • Wang C, Chen D, Wu C, Hu Q (2011) Data compression with homomorphism in covering information systems. Int J Approx Reason 52(4):519–525

    Article  MathSciNet  MATH  Google Scholar 

  • Wang C, Chen D, Sun B, Hu Q (2012) Communication between information systems with covering based rough sets. Inf Sci 216:17–33

    Article  MathSciNet  MATH  Google Scholar 

  • Wang C, Chen D, Hu Q (2014) Fuzzy information systems and their homomorphisms. Fuzzy Sets Syst 249:128–138

    Article  MathSciNet  MATH  Google Scholar 

  • Yang X, Li X, Lin TY (2009) First grc model-neighborhood systems the most general rough set models. In: IEEE international conference on granular computing, GrC’09, pp 691–695

  • Yao YY (2004) A partition model of granular computing. Lecture Notes in Computer Science, vol 3100. Springer, Berlin, pp 232–253

    Google Scholar 

  • Ye D, Chen Z (2015) A new approach to minimum attribute reduction based on discrete artificial bee colony. Soft Comput 19(7):1893–1903

    Article  Google Scholar 

  • Zadeh LA (1997) Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst 90(2):111–127

    Article  MathSciNet  MATH  Google Scholar 

  • Zhai Y, Qu K (2009) On characteristics of information system homomorphisms. Theory Comput Syst 44(3):414–431

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang X, Dai J, Yu Y (2015) On the union and intersection operations of rough sets based on various approximation spaces. Inf Sci 292:214–229

    Article  MathSciNet  MATH  Google Scholar 

  • Zheng L, Diao R, Shen Q (2015) Self-adjusting harmony search-based feature selection. Soft Comput 19(6):1567–1579

    Article  Google Scholar 

  • Zhu P, Wen Q (2010) Some improved results on communication between information systems. Inf Sci 180(18):3521–3531

    Article  MathSciNet  MATH  Google Scholar 

  • Zhu P, Wen Q (2011a) Homomorphisms between fuzzy information systems revisited. Appl Math Lett 24:1548–1553

    Article  MathSciNet  MATH  Google Scholar 

  • Zhu P, Wen Q (2011b) A note on communicating between information systems based on including degrees. Int J Gen Syst 40(8):837–840

    Article  MathSciNet  MATH  Google Scholar 

  • Zhu P, Xie H, Wen Q (2014) A unified definition of consistent functions. Fund Inf 135:331–340

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Ping Zhu

  2. College of Science, Beijing Forestry University, Beijing, 100083, China

    Huiyang Xie

  3. State Key Laboratory of Networking and Switching, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Qiaoyan Wen

Authors
  1. Ping Zhu
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  2. Huiyang Xie
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  3. Qiaoyan Wen
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Corresponding author

Correspondence to Ping Zhu.

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Funding

This work was funded by the National Natural Science Foundation of China (Grant Numbers 61370053, 61370193, and 61572081).

Conflict of interest

Author Ping Zhu declares that she has no conflict of interest. Author Huiyang Xie declares that she has no conflict of interest. Author Qiaoyan Wen declares that she has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Communicated by A. Di Nola.

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Zhu, P., Xie, H. & Wen, Q. A unified view of consistent functions. Soft Comput 21, 2189–2199 (2017). https://doi.org/10.1007/s00500-016-2133-y

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