New ‎A‎rithmetic Operations on Developed Parabolic Fuzzy Numbers and Its Application‎

Document Type : Research Paper


Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran.


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.‎