Development of Empirical Fragility Curves in Earthquake Engineering considering Nonspecific Damage Information

Table 13

The calculated monotone measures in possibility theory.

Subset	Monotone measures in possibility theory
{1}	cert({1}) = 1 – sup [π({2}), π({3})] = 1 – sup [0.7, 0.4] = 0.3
	pos({1}) = π({1}) = 1
{1, 2}	cert({1, 2}) = 1 − π({3}) = 1 − 0.4 = 0.6
	pos({1, 2}) = sup [π({1}), π({2})] = sup [1, 0.7] = 1
{1, 2, 3}	cert ({1, 2, 3}) = 1
	pos({1, 2, 3}) = sup [π({1}), π({2}), π({3})] = sup [1, 0.7, 0.4] = 1