New Arithmetic Operations on Developed Parabolic Fuzzy Numbers and Its Application
الموضوعات : مجله بین المللی ریاضیات صنعتی
F. Abbasi
1
(Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran.)
الکلمات المفتاحية: Developed parabolic fuzzy numbers, Transmission average, Extension principle, Fuzzy system reliability, Fuzzy arithmetic operations,
ملخص المقالة :
In this paper, we have studied the basic arithmetic operations for developed parabolic fuzzy numbers by using the concept of the transmission average, which was already implied in [F. Abbasi et al., A new attitude coupled with fuzzy thinking to fuzzy rings and fields, Journal of Intelligent and Fuzzy Systems, 2015] in its rudimentary form and was finally presented in its fully-fledged form in [F. Abbasi et al., A new and efficient method for elementary fuzzy arithmetic operations on pseudo-geometric fuzzy numbers, Journal of Fuzzy Set Valued Analysis, 2016]. The major advantage of these operations is that they findings are closer to reality than extension principle-based fuzzy arithmetic operations (in the domain of the membership function) or interval arithmetic (in the domain of $\alpha$-cuts). A technical example is given to illustrate applying the method. The proposed method can model and analyze the fuzzy system reliability in a more flexible and intelligent manner in comparison with the other methods.
