Earthquake Engineering Research - HKU Libraries - The University ...

373
have a membership degree between 0 and 1).
A fuzzy set A of a universe X is characterized by a membership function ju 4 (x) which affects to
each element x of Xa real number of the interval [0, I],ju 4 : X -> [0,1] It is usually represented as:
A = & A (x)/x\x€X} (1)
Where ju±(x) is the membership degree of* to A: the closest is this value to unity, the highest is the
membership of x to A. The symbol "/" is used as a separator between the element x and its membership
degree
JJ. A (x) .If A is a. crisp set, this function can take only one of the two values 0 or 1 whether x
belongs to A or not. The construction of the membership function of a parameter requires statistical
data or the opinion of an expert who gives an estimation of the interval where the parameter can vary
as well as its most likely value.
The survey in both "building users" and "building owners" is carried out to know their demands. In the
survey, informants are requested to answer to "hazard to human life", "loss of property value" and
"required function of structure" according to various probabilities of earthquake occurrence. Its results
are shown with the form of membership functions of fuzzy theory for damage level expressed by
language. The derivation of the membership functions uses the number of the relevant option selected
divided by the total number (ratio of each option selected). The evaluation points are evaluated as this
membership value. The fuzzy set H is used to expressed severity degree of hazard to human life,
whose membership function is defined as:
(2)
Based on the same method, the fuzzy set, L and F, about "loss of property value" and "required
function of structure" can also be obtained.
"Hazard to human life", "loss of property value" and "required function of structure" due to structural
damage should not be independently and individually evaluated, but should be properly correlated.
Hence, the damage levels corresponding to items studied about clients' demands are expressed by
means of fuzzy reasoning method.
In view of engineering, economic and social evaluation for earthquake resistant safety of structures,
stressed degrees of three aspects about clients' demands are different. In this paper, the Cfc weight" of
each aspect is used to measure its stressed degree. The sum of "weight" values is equal to 1.
The studies about all information collected are carried out for using fuzzy reasoning method. These
results are input into the three fuzzy relationships, the membership functions of the structural damage,