Soft Computing and Its Applications, Volume One

64 Soft Computing and Its Applications

REMARK 2.1

Note that - where 0 and 1 are singletons whose fuzzy representa-

tions are (0, 0, 0) and (1, 1, 1). It follows that the solution of the fuzzy linear equa-

tion = is not as we would expect, = - .

For example, + = (2, 4, 6) + (1, 2, 3) = (3, 6, 9) = .

But (1, 2, 3) = (3, 6, 9) – (2, 4, 6) = (-3, 2, 6) .

The same annoyance appears when solving the fuzzy equation = whose

solution is not given by = .

For example, = (2, 8, 18) = .

But = = = (0.33, 2, 9) .

Thus, it is not possible to solve the inverse problems exactly using the standard

fuzzy arithmetic operators.

Example ...