New Results in the Calculus of Fuzzy-Valued Functions Using Mid-Point Representations

Stefanini, Luciano; Sorini, Laerte; Shahidi, M.

doi:10.1007/978-3-030-50143-3_3

Cited by 1 publication

(1 citation statement)

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“…The method accurately approximates both linear and nonlinear fuzzy Volterra integral equations of the second type, as shown by numerical results and graphs. The authors of Stefanini et al (2020) gave new calculus results for fuzzy-valued functions on a single real variable. They employ the midpoint-radius representation of intervals in the real half-plane extensively and demonstrate its utility in fuzzy calculus.…”

Section: Introductionmentioning

confidence: 99%

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

Shakhatreh¹,

Al-Shorman²

2021

Int. j. adv. appl. sci.

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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.

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Section: Introductionmentioning

confidence: 99%