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 Volume 8, Issue 12 (December 2021), Pages: 9-13


 Original Research Paper

 Title: Some properties of integration of real-valued function over a fuzzy interval

 Author(s): M. A. Shakhatreh *, A. M. Al-Shorman


 Department of Mathematics, Yarmouk University, Irbid, Jordan

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One of the most fundamental concepts in fuzzy set theory is the extension principle. It gives a generic way of dealing with fuzzy quantities by extending non-fuzzy mathematical concepts. There are a few examples, including the concept of fuzzy distance between fuzzy sets. The extension approach is then methodically applied to real algebra, with considerable development of fuzzy number operations. These operations are computationally appealing and generalized interval analysis. Although the set of real fuzzy numbers with extended addition or multiplication is no longer a group, it retains many structural qualities. The extension concept is demonstrated to be particularly beneficial for defining set-theoretic operations for higher fuzzy sets. We need some definitions related to our properties before we can create the properties of integration of a crisp real-valued function over a fuzzy interval. It is our goal in this article to develop and demonstrate certain characteristics of a real-valued function over a fuzzy interval in order to broaden the scope of the notion of integration of a real-valued function over a fuzzy interval. Some of these characteristics are linked to the operations of extended addition and extended subtraction, while others are not. 

 © 2021 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (

 Keywords: Fuzzy set, Extension principle, Fuzzy interval, Extended addition, Extended subtraction

 Article History: Received 10 June 2021, Received in revised form 25 August 2021, Accepted 10 September 2021


No Acknowledgment.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.


 Shakhatreh MA and Al-Shorman AM (2021). Some properties of integration of real-valued function over a fuzzy interval. International Journal of Advanced and Applied Sciences, 8(12): 9-13

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