Seismic hazard analysis in last few decades has been become very important issue. Recently, new technologies and available data have been improved that helped many scientists to understand where and why earthquakes happen, physics of earthquakes, etc. They have begun to understand the role of uncertainty in Seismic hazard analysis. However, there is still significant problem how to handle existing uncertainty. The same lack of information causes difficulties to quantify uncertainty accurately.

Many attenuation relations for strong ground motion have been developed as an important component of seismic hazard studies. The attenuation relation gives us information about dependency on parameters such as magnitude, depth of the event and distance from the site to the source.

Usually attenuation curves are obtained in statistical way: regression analysis. Statistical and probabilistic analysis shows overlapped results for the site coefficients. This overlapping takes place not only at the border between two neighboring classes, but also among more than three classes. Although the analysis starts from classifying sites using the geological terms, these site coefficients are not classified at all. In the present study, this problem is solved using Fuzzy set theory. Fuzzy set theory starts from the membership function. Thus, in this study, fuzzy membership functions designed for each site class depend on the available information related with site classification for attenuation relation that is popularly used in Seismic hazard assessment. The obtained membership functions allow us to avoid the ambiguities at the border between neighboring classes. After some fuzzy arithmetic and operations are used to obtained site class index which is used for attenuation relation instead of mean value of station coefficients obtained by regression analysis by classical way.

This study is aimed to show the effect of Fuzzy set theory as an advanced methodology to reduce uncertainty in seismic hazard assessment. Some applications of the Fuzzy set theory are performed for several cases in Japan and southern California by conventional way. In this study standard deviations that show variations between each site class obtained by Fuzzy set theory and classical way are compared. Results on this analysis show that even when we have very insufficient data for hazard assessment site classification based on Fuzzy set theory shows values of standard deviations less than obtained by classical way which is direct proof of less uncertainty