Differentiability of type-2 fuzzy number-valued functions |
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| Institution: | 1. Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile;2. Departamento de Análisis Matemático, Universidad de Santiago de Compostela, Santiago de Compostela, 15782, Spain;3. Departamento de Estadística e I.O., Universidad de Sevilla, Spain;1. Universidad Industrial de Santander, Escuela de Matemáticas, A.A.678, Bucaramanga, Colombia;2. Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile |
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| Abstract: | In this paper, we define a differentiability of the type-2 fuzzy number-valued functions. The definition is based on type-2 Hukuhara difference which is defined in the paper as well. The related theorem of the differentiability of the type-2 fuzzy number-valued functions is derived. In addition, a parametric closed form of the perfect triangular quasi type-2 fuzzy numbers is introduced, and finally, the applicability and an approach to solving type-2 fuzzy differential equations are illustrated using some examples and cases. |
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| Keywords: | Type-2 fuzzy sets Type-2 Hukuhara difference Type-2 fuzzy differential equations Quasi type-2 fuzzy numbers Perfect type-2 fuzzy numbers |
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