Skip to main content
SpringerLink
Log in

The consistent functions and reductions of fuzzy neighborhood systems

  • Fuzzy systems and their mathematics
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Neighborhood systems have been investigated extensively because of their applicability in granular computing. The consistent functions have been used to compare the structures of neighborhood systems. This paper is devoted to a further study of consistent functions and reductions of fuzzy neighborhood systems. Based on some equivalence relations on the universe, we propose a general method for constructing consistent functions. Some equivalent conditions for a function to be consistent are examined. In addition, the discernibility function of fuzzy neighborhood information systems is constructed which is used to compute all reductions of fuzzy neighborhood information systems. Accordingly, we make an analysis of fuzzy neighborhood systems based on three-way classification by using reductions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Data Availability

Data sharing not applicable to this article as no data sets were generated or analyzed during the current study.

References

  • Alshammari M, Al-Smadi MH, Arqub OA, Hashim I, Alias AM (2020) Residual series representation algorithm for solving fuzzy Duffing oscillator equations. Symmetry 12(4):572

    Article  Google Scholar 

  • Arqub AO, Singh J, Alhodaly M (2021) Adaptation of kernel functions-based approach with Atangana–Baleanu–Caputo distributed order derivative for solutions of fuzzy fractional Volterra and Fredholm integrodifferential equations. Math Methods Appl Sci 46(7):7807–7834

  • Arqub OA (2017) Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations. Neural Comput Appl 28:1591–1610

    Article  Google Scholar 

  • Arqub OA , Singh J, Maayah B, Alhodaly M (2023) Reproducing kernel approach for numerical solutions of fuzzy fractional initial value problems under the Mittag–Leffler kernel differential operator. Math Methods Appl 46(7):7965–7986

  • Day MM (1944) Convergence, closure, and neighborhoods. Duke Math J 11:181–199

    Article  MathSciNet  MATH  Google Scholar 

  • Deer L, Cornelis C, Godo L (2017) Fuzzy neighborhood operators based on fuzzy coverings. Fuzzy Sets Syst 312(C):17–35

    Article  MathSciNet  MATH  Google Scholar 

  • Diker M (2015) A category approach to relation preserving functions in rough set theory. Int J Approx Reason 56:71–86

    Article  MathSciNet  MATH  Google Scholar 

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

  • Grzymala-Busse JW, Sedelow WA (1988) On rough sets, and information system homomorphism. Bull Pol Acad Sci Tech Sci 36(3–4):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

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Liau CJ, Lin EB, Syau YR (2020) On consistent functions for neighborhood systems. Int J Approx Reason 121:39–58

    Article  MathSciNet  MATH  Google Scholar 

  • Lin TY (1989a) 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 (1989b) Chinese wall security policy-an aggressive model. In: Fifth annual computer security applications conference, ACSAC, pp 282–289

  • Lin TY (1997a) Granular computing: from rough sets and neighborhood systems to information granulation and computing with words. In: Proceedings of the 5th European Congress on intelligent techniques and soft computing, EUFIT97, pp 1602–1606

  • Lin TY (1997b) Neighborhood systems-a qualitative theory for fuzzy and rough sets. In: Wang P (ed) Advances in machine intelligence and soft computing. Duke University, North Carolina, pp 132–155

  • Lin TY, Syau YR (2011) Granular mathematics-foundation and current state. In: Proceedings of the 2011 IEEE international conference on granular computing, pp 4-12

  • Lin TY, Liu Y, Huang W (2013) Unifying rough set theories via large scaled granular computing. Fundam Inform 127(1–4):413–428

    Article  MathSciNet  MATH  Google Scholar 

  • Liu GL, Zhu K (2014) The relationship among three types of rough approximation pairs. Knowl Based Syst 60:28–34

    Article  Google Scholar 

  • Lowen R (1982) Fuzzy neighborhood spaces. Fuzzy Sets Syst 7(2):165–189

    Article  MathSciNet  MATH  Google Scholar 

  • Pawlak Z (1981) Information systems theoretical foundations. Inf Syst 6(3):205–218

    Article  MATH  Google Scholar 

  • Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):341–356

    Article  MATH  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 

  • Qin KY, Yang JL, Zheng P (2008) Generalized rough sets based on reflexive and transitive relations. Inf Sci 178(21):4138–4141

    Article  MathSciNet  MATH  Google Scholar 

  • Skowron A, Rauszer C (1992) The discernibility matrices and functions in information systems. In: Slowinski R (ed) Intelligent decision support, handbook of applications and advances of the rough sets theory. Kluwer, Dordrecht, pp 331–362

    Chapter  Google Scholar 

  • Syau YR, Lin EB (2014) Neighborhood systems and covering approximation spaces. Knowl Based Syst 66:61–67

    Article  Google Scholar 

  • Syau YR, Lin EB, Liau CJ (2018) Neighborhood systems: rough set approximations and definability. Fundam Inform 159(4):429–450

  • Wang C, Wu C, Chen D, Hu Q, Wu C (2008) Communicating between information systems. Inf Sci 178(16):3228–3239

    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, Huang Y, Fan X, Shao M (2019) Homomorphism between ordered decision systems. Soft Comput 23(2):365–374

    Article  MATH  Google Scholar 

  • Xie N, Li Z, Wu W, Zhang G (2019) Fuzzy information granular structures: a further investigation. Int J Approx Reason 114:127–150

    Article  MathSciNet  MATH  Google Scholar 

  • Yang B, Hu B (2018) Communication between fuzzy information systems using fuzzy covering based rough sets. Int J Approx Reason 103:414–436

    Article  MathSciNet  MATH  Google Scholar 

  • Yang X, Zhang M, Dou H, Yang J (2011) Neighborhood systems based rough sets in incomplete information system. Knowl Based Syst 24(6):858–867

    Article  Google Scholar 

  • Yang XB, Liang SC, Yu HL, Gao S, Qian YH (2019) Pseudo-label neighborhood rough set: measures and attribute reductions. Int J Approx Reason 105:112–129

    Article  MathSciNet  MATH  Google Scholar 

  • Yao YY (1998a) Relational interpretations of neighborhood operators and rough set approximation operators. Inf Sci 111(1–4):239–259

  • Yao YY (1998b) Constructive and algebraic method of theory of rough sets. Inf Sci 109:21–47

  • Yao YY, Yao B (2012) Covering based rough set approximations. Inf Sci 200:91–107

    Article  MathSciNet  MATH  Google Scholar 

  • Yu Z, Wang D (2020) Accuracy of approximation operators during covering evolutions. Int J Approx Reason 117:1–14

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  • Zadeh LA (1975) The concept of a linguistic variable and its applications in approximate reasoning. Inf Sci 8:199–251

    Article  MATH  Google Scholar 

  • Zhang XH, Wang JQ (2020) Fuzzy \(\beta \)-covering approximation spaces. Int J Approx Reason 126:27–47

    Article  MathSciNet  MATH  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, Xie H, Wen Q (2014) A unified definition of consistent functions. Fundam Inform 135(3):331–340

    Article  MathSciNet  MATH  Google Scholar 

  • Zhu P, Xie H, Wen Q (2017) A unified view of consistent functions. Soft Comput 21(9):2189–2199

    Article  MATH  Google Scholar 

  • Ziarko W (1993) Variable precision rough set model. J Comput Syst Sci 46:39–59

    Article  MathSciNet  MATH  Google Scholar 

Download references

Funding

This work has been partially supported by the National Natural Science Foundation of China (Grant Nos. 61976130 and 12271319).

Author information

Authors and Affiliations

  1. School of Mathematics, Southwest Jiaotong University, Xi’an Road, Chengdu, 611756, Sichuan Province, People’s Republic of China

    Keyun Qin

  2. School of Computing and Artificial Intelligence, Southwest Jiaotong University, Xi’an Road, Chengdu, 611756, Sichuan Province, People’s Republic of China

    Qian Hu

  3. Westone Information Industry INC., Chengdu, 610031, Sichuan Province, People’s Republic of China

    Binbin Xue

Authors
  1. Keyun Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qian Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Binbin Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

KQ involved in conceptualization, methodology, investigation, writing—original draft, and funding acquisition. QH involved in data curation and writing—review and editing. BX involved in writing—review and editing.

Corresponding author

Correspondence to Qian Hu.

Ethics declarations

Conflict of interest

The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qin, K., Hu, Q. & Xue, B. The consistent functions and reductions of fuzzy neighborhood systems. Soft Comput 27, 9281–9291 (2023). https://doi.org/10.1007/s00500-023-08294-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-023-08294-7

Keywords

Search

Navigation