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  Our main focus is to develop the ideas of fuzzy complements, fuzzy t-norm, and fuzzy t-conorms for nonstandard fuzzy subsets.

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

Received: September 29, 2021; Revised: October 7, 2021; Accepted: October 31, 2021; Published: November 17, 2021

How to cite this article: John N. Mordeson and Sunil Mathew, Nonstandard Fuzzy Mathematics, Advances in Fuzzy Sets and Systems 27(1) (2022), 35-52. DOI: 10.17654/0973421X22035

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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