Elementary fuzzy calculus |
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| Institution: | 1. Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul 34349, Turkey;2. Department of Engineering Science, Kermanshah University of Technology, Kermanshah, Iran;3. Department of Mathematics, Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul 34349, Turkey;1. Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan;2. Facultad de Economía y Empresa and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, 37007 Salamanca, Spain;3. Department of Electrical Engineering, College of Engineering, Taif University, 11099, Taif 21944, Saudi Arabia |
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| Abstract: | In 2] Dubois and Prade introduced the notion of fuzzy numbers and defined the basic operations of addition, subtraction, multiplication, and division. A slightly modified definition of fuzzy numbers was presented in 4], and in that paper a metric was defined for this family of fuzzy sets. Another less restrictive definition of fuzzy numbers can be found in 1].In the present paper we consider fuzzy numbers from a somewhat different perspective. Basically, we shall view fuzzy numbers in a topological vector space setting. Using the customary vector space operations together with the metric given in 4] we will define differentiation and integration of fuzzy-valued functions in ways that parallel closely the corresponding definitions for real differentiation and integration. |
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