Advances in Fuzzy Sets and Systems

The Advances in Fuzzy Sets and Systems publishes original research papers in the field of fuzzy sets and systems, covering topics such as artificial intelligence, robotics, decision-making, and data analysis. It also welcomes papers on variants of fuzzy sets and algorithms for computational work.

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NONSTANDARD FUZZY MATHEMATICS

Authors

  • John N. Mordeson
  • Sunil Mathew

Keywords:

fuzzy mathematics, nonstandard analysis, natural extension, transfer principle, nonstandard unit interval, standard part.

DOI:

https://doi.org/10.17654/0973421X22002

Abstract

In this paper, we extend the concept of fuzzy mathematics to nonstandard mathematics. This is accomplished by extending the notion of a fuzzy subset of a set as a function of the set into [0, 1] by replacing [0, 1] with the nonstandard unit interval $]^{-} 0,1^{+}[$. Our main focus is to develop the ideas of fuzzy complements, fuzzy t-norm, and fuzzy t-conorms for nonstandard fuzzy subsets.

Received: September 29, 2021
Revised: October 7, 2021
Accepted: October 31, 2021

References

I. Goldberg, Lecture notes on nonstandard analysis, UCLA Summer School in Logic, 2014.

T. Imamura, Note on the definition of neutrosophic logic, arXiv:1811.02961v1 [math.LO] 7 Nov. 2018.

G. J. Klir and Bo Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall PTR, Upper Saddle River, New Jersey, 1995.

P. A. Loeb and M. Wolff, Nonstandard Analysis for the Working Mathematician, Kluwer, 2000.

J. N. Mordeson, S. Mathew and M. Binu, Applications of Mathematics of Uncertainty: Grand Challenges, Human Tracking, Coronavirus, Biodiversity, and Extinction, Studies in Systems, Decision and Control, Springer, in press.

D. A. B. Rayo, Introduction to non-standard analysis, http://math.uchicago.edu REUPapers 2015.

A. Robinson, Nonstandard Analysis, North-Holland Publishing Co., 1966.

E. Stauton (R. Ryan Supervisor), Infinitesimals, nonstandard analysis and applications to finance, NUI Galway OE Gaillimh, National University of Ireland, Galway, 2013.

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Published

2021-11-17

Issue

Vol. 27 No. 1 (2022)

Section

Articles

License

Copyright (c) 2022 Pushpa Publishing House, Prayagraj, India

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How to Cite

NONSTANDARD FUZZY MATHEMATICS. (2021). Advances in Fuzzy Sets and Systems, 27(1), 35-52. https://doi.org/10.17654/0973421X22002

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