New ‎A‎rithmetic Operations on Developed Parabolic Fuzzy Numbers and Its Application‎

محورهای موضوعی : مجله بین المللی ریاضیات صنعتی

F. Abbasi ¹ (Department of Mathematics, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran.)

تاریخ دریافت : 1395/12/13 تاریخ پذیرش : 1396/03/04 تاریخ انتشار : 1398/05/10

کلید واژه: Developed parabolic fuzzy numbers, Transmission average‎‎, Extension principle, Fuzzy system reliability, Fuzzy arithmetic operations,

چکیده مقاله :

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.‎