Kybernetika 50 no. 2, 216-233, 2014

Calculations of graded ill-known sets

Masahiro InuiguchiDOI: 10.14736/kyb-2014-2-0216


To represent a set whose members are known partially, the graded ill-known set is proposed. In this paper, we investigate calculations of function values of graded ill-known sets. Because a graded ill-known set is characterized by a possibility distribution in the power set, the calculations of function values of graded ill-known sets are based on the extension principle but generally complex. To reduce the complexity, lower and upper approximations of a given graded ill-known set are used at the expense of precision. We give a necessary and sufficient condition that lower and upper approximations of function values of graded ill-known sets are obtained as function values of lower and upper approximations of graded ill-known sets.


ill-known set, lower approximation, upper approximation


03E72, 26E25, 68T37


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