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

Table 11

The calculated monotone measures in a special case of evidence theory which is the same with possibility theory.

Subset	Monotone measures in evidence theory
{1}	bel({1}) = m({1}) = 0.3
	pl({1}) = m({1}) + m({1, 2}) + m({1, 3}) + m({1, 2, 3}) = 0.3 + 0.3 + 0 + 0.4 = 1
	ign({1}) = pl({1}) − bel({1}) = 1 − 0.3 = 0.7
{1, 2}	bel({1, 2}) = m({1}) + m({2}) + m({1, 2}) = 0.3 + 0 + 0.3 = 0.6
	pl({1, 2}) = m({1})+ m({2}) + m({1, 2}) + m({2, 3})+ m({1, 3}) + m({1, 2, 3})= 0.3 + 0 + 0.3 + 0 + 0 + 0.4 = 1
	ign({1, 2}) = pl({1, 2}) − bel({1, 2}) = 1 − 0.6 = 0.4
{1, 2, 3}	bel({1, 2, 3}) = all = 1
	pl({1, 2, 3}) = all = 1
	ign({1, 2, 3}) = pl({1, 2, 3}) − bel({1, 2, 3}) = 1 − 1 = 0