Method of Solution to Fuzzy Inverse Problem

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  • Fuzzy 逆問題の解法
  • Fuzzy ギャク モンダイ ノ カイホウ

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The problem, “Given a fuzzy relation R⊂X×Y and a fuzzy subset B⊂Y, find all A⊂X such that A°R=B, where°denotes maxmin composition” is called an “inverse problem of fuzzy relation”. It was investigated by E. Sanchez in 1976.<br>This paper proposes a new algorithm to solve the inverse problem of fuzzy relational equations and, further, that of fuzzy correspondence. The latter problem is described as follows; given a fuzzy correspondence R:[0 1]m→S⊂ P([0 1]n) and a fuzzy subset b⊂[0 1]n, find all a∈[0 1]m such that a∈R-1(b), where P(·) denotes the family of all the fuzzy subsets of [0 1]n. It is shown that the algorithm to solve this problem is reduced to one which is similar to the algorithm to solve the inverse problem of fuzzy relational equations by introducing strong α-cuts. The method of solution shown in this paper is very simple and, therefore, it is expected to be useful for some practical applications such as fault diagnosis with human sensory measures.

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