2022•AxiomsOpen access

The Relationships among Three Kinds of Divisions of Type-1 Fuzzy Numbers

Yadan Jiang, Dong Qiu

Abstract

The division operation for type-1 fuzzy numbers in its original form is not invertible for the multiplication operation. This is an essential drawback in some applications. To eliminate this drawback several approaches are proposed: the generalized Hukuhara division, generalized division and granular division. In this paper, the expression of granular division is introduced, and the relationships among generalized Hukuhara division, generalized division and granular division are clarified.

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Key concepts: Division (mathematics), Multiplication (music), Mathematics, Invertible matrix, Type (biology), Division ring, Algebra over a field, Pure mathematics