Geodesic
Calculations of graded ill-known sets
Kybernetika, Tome 50 (2014) no. 2, pp. 216-233
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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.
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.
DOI : 10.14736/kyb-2014-2-0216
Classification : 03E72, 26E25, 68T37
Keywords: ill-known set; lower approximation; upper approximation 
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Inuiguchi, Masahiro. Calculations of graded ill-known sets. Kybernetika, Tome 50 (2014) no. 2, pp. 216-233. doi: 10.14736/kyb-2014-2-0216

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