期刊
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
卷 86, 期 8, 页码 1433-1452出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207160701874789
关键词
fuzzy matrix; degree of regularity; extension principle; fuzzy arithmetic operators; natural cubic splines; fuzzy inverse; epsilon-inverse; interval matrix
The aim of this paper is to extend the concept of inverse of a matrix with fuzzy numbers as its elements, which may be used to model uncertain and imprecise aspects of real-world problems. We pursue two main ideas based on employing real scenarios and arithmetic operators. In each case, exact and inexact strategies are provided. In the first idea, we give some necessary and sufficient conditions for invertibility of fuzzy matrices based on regularity of their scenarios. And then Zadeh's extension principle and interpolation on Rohn's approach for inverting interval matrices are followed to compute fuzzy inverse. In the second idea, Dubois and Prade's arithmetic operators will be employed for the same purpose. But with respect to the inherent difficulties which are derived from the positivity restriction on spreads of fuzzy numbers, the concept of epsilon-inverse of a fuzzy matrix and its relaxation are generalized and some useful theorems will be revealed. Finally fuzzifying the defuzzified version of the original problem for introducing fuzzy inverse, which can be followed by each idea, will be presented.
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