Skip to main content
Log in

Abstract

This paper extends the concept of generalized equivalence relation on type-2 fuzzy set and presents a comprehensive study of type-2 fuzzy G-equivalence relation. Notions like partition of a type-2 fuzzy G-equivalence relation, type-2 fuzzy balance mappings in the type-2 fuzzy set theory are introduced and related theorems are discussed.

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

Access this article

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

References

  1. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8:199–249

    Article  MathSciNet  Google Scholar 

  2. Mizumoto M, Tanaka K (1976) Some properties of fuzzy sets of type-2. Inf Control 31:312–340

    Article  MathSciNet  Google Scholar 

  3. Mizumoto M, Tanaka K (1981) Fuzzy sets of type 2 under algebraic product and algebraic sum. Fuzzy Sets Syst 31:277–290

    Article  MathSciNet  Google Scholar 

  4. Mendel JM, John RIB (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10(2):117–127

    Article  Google Scholar 

  5. Walker C, Walker E (2003) Algebraic Structures of fuzzy sets of type-2. In: Proceedings of International Conference on Fuzzy Information Processing March, 1-4:97–100

  6. Dubois D, Prade H (1978) Operations on fuzzy numbers. Int J Syst Sci 9(6):613–626

    Article  MathSciNet  Google Scholar 

  7. Dubois D, Prade H (1979) Operations in a fuzzy-valued Logic. Inf Control 43:224–240

    Article  MathSciNet  Google Scholar 

  8. Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Acdemic Press Inc., New York

    MATH  Google Scholar 

  9. Karnik NN, Mendel JM (1999) Applications of type-2 fuzzy logic systems to forecasting of time-series. Inf Sci 120:89–111

    Article  Google Scholar 

  10. Karnik NN, Mendel JM (2001) Operations on type-2 fuzzy sets. Fuzzy Sets Syst 79:327–348

    Article  MathSciNet  Google Scholar 

  11. Wu D, Tan W (2006) A simplified type-2 fuzzy logic controller for real-time control. ISA Trans 45(4):503–516

    Article  Google Scholar 

  12. Hu BQ, Wang CY (2014) On type-2 fuzzy relations and interval-valued type-2 fuzzy sets. Fuzzy Sets Syst 236:1–32

    Article  MathSciNet  Google Scholar 

  13. Mendel JM (2007) Computing with words and its relationship with fuzzistics. Inf Sci 177:988–1006

    Article  MathSciNet  Google Scholar 

  14. Gilan SS, Sebt MH, Shahhosseini V (2012) Computing with words for hierarchical competency based selection of personal in construction companies. Appl Soft Comput 12:860–871

    Article  Google Scholar 

  15. Aliev R, Pedrycz W, Guirimov B, Aliev R, Iihan U, Babagil M, Mammadli S (2011) Type-2 fuzzy nueral networks with fuzzy clustering and differential evolution optimization. Inf Sci 181:1591–1608

    Article  Google Scholar 

  16. Ozkan I, Turksen IB (2012) MiniMax e-star cluster validity index for type-2 fuzziness. Inf Sci 184:64–74

    Article  Google Scholar 

  17. Choi B, Rhee F (2009) Interval type-2 fuzzy membership function generation methods for pattern recognition. Inf Sci 179:2102–2122

    Article  Google Scholar 

  18. Dereli T, Baykasoglu A, Altun K, Durmusoglu A, Turksen B (2011) Industrial applications of type-2 fuzzy sets and systems: a concise review. Comput Ind 62:125–137

    Article  Google Scholar 

  19. Leal-Ramirez C, Castillo O, Melin P, Rodriguez-Diaza A (2011) Simulation of the bird age-structured population growth based on an interval type-2 fuzzy cellular structure. Inf Sci 181:519–535

    Article  MathSciNet  Google Scholar 

  20. Chakravarty S, Dash PK (2012) A PSO based integrated functional link net and interval type-2 fuzzy logic system for predicting stock market indices. Appl Soft Comput 12:931–941

    Article  Google Scholar 

  21. Tung SW, Quek C, Guan C (2013) eT2FIS: an evolving type-2 neural fuzzy inference system. Inf Sci 220:124–148

    Article  Google Scholar 

  22. Kundu P, Kar S, Maiti M (2015) Multi-item solid transportation problem with type-2 fuzzy parameters. Appl Soft Comput 31:61–80

    Article  Google Scholar 

  23. Murthy NVES, Lokavarapu S (2014) Lattice (Algebraic) properties of (Inverse) images of type-2 fuzzy subsets. Int J Sci Res 3(12):1741–1746

    Google Scholar 

Download references

Acknowledgements

The work and research of the first author of this paper is financially supported by National Institute of Technology Silchar, Assam, India.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dhiman Dutta.

Ethics declarations

Statement of the Work in Broad Context

The theory of fuzzy relations is a generalization of crisp relations on a set. Fuzzy relations have been widely studied as a way to measure the degree of similarity between the objects of a given universe of discourse. Type-2 fuzzy relations further generalize the concept of type-1 fuzzy relations.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dutta, D., Sen, M. & Deshpande, A. Generalized Type-2 Fuzzy Equivalence Relation. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 92, 129–136 (2022). https://doi.org/10.1007/s40010-020-00707-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40010-020-00707-8

Keywords

Navigation