Operations on Fuzzy Numbers with Two Fuzziness Sources

The extension principle for n-ary operations is suitable for operations on different fuzzy numbers, while the unreasonable results will be concluded when it is used for operations on several fuzzy numbers with same fuzziness source. A concept called fuzziness source is proposed. Then, the unit fuzzy number is defined to simplify the operation. The operation rules are respectively constructed for fuzzy numbers with same fuzziness source and two fuzziness sources by means of the unit fuzzy number. The linear system of equations of the fuzzy numbers with two fuzziness sources is defined and the solving method is also presented.