Skip to main content
SpringerLink
Log in

Some arithmetic operations on the generalized sigmoidal fuzzy numbers and its application

  • Original Paper
  • Published:
Granular Computing Aims and scope Submit manuscript

Abstract

The objective of this work is to present an alternative method, under the fuzzy environment, for computing the various arithmetic operations of a system using the sigmoidal number. In the literature, authors have used the linear membership function using \(\alpha \)-cut approach for finding the membership function of the system, but in the present study, a nonlinear membership function has been taken in the study. The major advantage of the proposed operations is that they do not need the computation of \(\alpha \)-cuts of the number and hence becomes successful to solve the real-life problems. The approach has been illustrated with some elementary examples and compared their results with some of the existing approaches.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Akther T, Ahmad SU (2009) A computational method for fuzzy arithmetic operations. Daffodil Int Univ J Sci Technol 4(1):18–22

    Google Scholar 

  • Banerjee S, Roy TK (2012) Arithmetic operations on generalized trapzoidal fuzzy number and its applications. Turk J Fuzzy Syst 3(1):16–44

    Google Scholar 

  • Bansal A (2011) Trapezoidal fuzzy numbers (a, b, c, d): arithmetic behavior. Int J Phys Math Sci 2:39–44

    Google Scholar 

  • Chutia R, Mahanta S, Datta D (2011) Arithmetic of triangular fuzzy variable from credibility theory. Int J Energy Inf Commun 2(3):9–20

    Google Scholar 

  • Deschrijver G (2007) Arithmetic operators in interval-valued fuzzy set theory. Inf Sci 177:2906–2924

    Article  MathSciNet  MATH  Google Scholar 

  • Dhiman P (2016) Reliability analysis of an industrial systems using an improved arithmetic operations, Master’s thesis. School of Mathematics, Thapar University Patiala, India

  • Gao S, Zhang Z, Cao C (2006) Multiplication operation on fuzzy numbers. J Softw 4(4):331–338

    Google Scholar 

  • Garg H (2014) A novel approach for analyzing the behavior of industrial systems using weakest t-norm and intuitionistic fuzzy set theory. ISA Trans 53:1199–1208

    Article  Google Scholar 

  • Garg H (2016) A novel approach for analyzing the reliability of series-parallel system using credibility theory and different types of intuitionistic fuzzy numbers. J Braz Soc Mech Sci Eng 38(3):1021–1035

    Article  Google Scholar 

  • Garg H (2015) An approach for analyzing the reliability of industrial system using fuzzy kolmogorov’s differential equations. Arab J Sci Eng 40(3):975–987

    Article  Google Scholar 

  • Garg H, Ansha A (2016) Arithmetic operations on generalized parabolic fuzzy numbers and its application. Proc Natl Acad Sci India Sect A Phys Sci. doi:10.1007/s40010-016-0278-9

    Google Scholar 

  • Garg H, Rani M (2013) An approach for reliability analysis of industrial systems using PSO and IFS technique. ISA Trans 52(6):701–710

    Article  Google Scholar 

  • Garg H, Sharma SP (2013) Multi-objective reliability-redundancy allocation problem using particle swarm optimization. Comput Ind Eng 64(1):247–255

    Article  Google Scholar 

  • Garg H, Agarwal N, Choubey A (2015) Entropy based multi-criteria decision making method under fuzzy environment and unknown attribute weights. Glob J Technol Optim 6(3):13–20

    Google Scholar 

  • Kaufmann A, Gupta MM (1991) Introduction to fuzzy arithmetic. Van Nostrand, New York

    MATH  Google Scholar 

  • Kechagias P, Papadopoulos BK (2007) Computational method to evaluate fuzzy arithmetic operations. Appl Math Comput 185:169–177

    MathSciNet  MATH  Google Scholar 

  • Kovalerchuk B, Kreinovich V (2016) Concepts of solutions of uncertain equations with intervals, probabilities and fuzzy sets for applied tasks. Granul Comput. doi:10.1007/s41066-016-0031-4

    Google Scholar 

  • Kreinovich V (2016) Solving equations (and systems of equations) under uncertainty: how different practical problems lead to different mathematical and computational formulations. Granul Comput 1(3):171–179

    Article  Google Scholar 

  • Kumar P, Aggarwal KK (1993) Petri net modeling and reliability evaluation of distributed processing systems. Reliab Eng Syst Saf 41(2):167–176

    Article  Google Scholar 

  • Liao TW (2017) A procedure for the generation of interval type-2 membership functions from data. Appl Soft Comput 52:925–936

    Article  Google Scholar 

  • Liu H, Gegov A, Cocea M (2016) Rule-based systems: a granular computing perspective. Granul Comput 1(4):259–274

    Article  Google Scholar 

  • Mahanta S, Chutia R, Baruah HK (2010) Fuzzy arithmetic witwith using the method of \(\alpha \)- cuts. Int J Latest Trends Comput 1(2):73–80

    Google Scholar 

  • Piegat A (2005) A new definion of the fuzzy set. Int J Appl Math Comput Sci 15(1):125–140

    MathSciNet  MATH  Google Scholar 

  • Stefanini L, Guerra ML (2006) On fuzzy arithmetic operations: some properties and distributive approximations. Int J Appl Math 19:171–199

    MathSciNet  MATH  Google Scholar 

  • Sanchez MA, Castro JR, Castillo O, Mendoza O, Rodriguez-Diaz A, Melin P (2016) Fuzzy higher type information granules from an uncertainty measurement. Granul Comput. doi:10.1007/s41066-016-0030-5

    Google Scholar 

  • Taleshian A, Rezvani S (2011) Multiplication operation on trapezoidal fuzzy numbers. J Phys Sci 11:17–26

    MathSciNet  MATH  Google Scholar 

  • Vahidi J, Rezvani S (2013) Arithmetic operations on trapezoidal fuzzy numbers. J Nonlinear Anal Appl 2013:Article ID jnaa-00111

    Google Scholar 

  • Wang G, Li Y, Li X (2017) Approximation performance of the nonlinear hybrd fuzzy system based on variable universe. Granul Comput 2:73–84

    Article  Google Scholar 

  • Xue F, Tang W, Zhao R (2008) The expected value of a function of a fuzzy variable with a continuous membership function. Comput Math Appl 55:1215–1224

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Zhou X (2017) Membership grade mining of mutually inverse fuzzy implication propositions. Granul Comput 2(1):55–62

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work has been supported by Thapar University under SEED Money Grant wide letter no. TU/DORSP/57/1910.

Author information

Authors and Affiliations

  1. School of Mathematics, Thapar University Patiala, Punjab, 147004, India

    Harish Garg

Authors
  1. Harish Garg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Harish Garg.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Garg, H. Some arithmetic operations on the generalized sigmoidal fuzzy numbers and its application. Granul. Comput. 3, 9–25 (2018). https://doi.org/10.1007/s41066-017-0052-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41066-017-0052-7

Keywords

Search

Navigation