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Power series of fuzzy numbers with real or fuzzy coefficients

Kadak Uğur (Bozok University, Faculty of Art and Sciences, Department of Mathematics, Yozgat, Turkey + Gazi University, Faculty of Art and Sciences, Department of Mathematics, Ankara, Turkey)
Başar Feyzi (Fatih University, Faculty of Art and Sciences, Department of Mathematics, Istanbul, Turkey)

Following Talo and Başar [Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations, Comput. Math. Appl. 58 (2009) 717-733], we essentially deal with the power series of fuzzy numbers. We give two examples on the geometric series of fuzzy numbers and by using the four different cases of un of nth power of a fuzzy number u, we interest in the convergence of a power series of fuzzy numbers. Finally, we introduce the concept of a power series of fuzzy numbers with fuzzy coefficients.

Keywords: fuzzy numbers, level set, level convergence, series of fuzzy sets, power series of fuzzy numbers