Seismic hazard assessment like many other issues in seismology is a complicated problem, which is due to variety of parameters affecting the occurrence of earthquake. Uncertainty, which is a result of vagueness and incompleteness of the data, should be considered in a rationale way. Herein, fuzzy set theory is used to take into account the uncertainty existed in the seismic hazard analysis. The Fuzzy Set Theory (FST) is an attractive methodology when vague and subjective judgments of a unique phenomenon enter probabilistic or mathematical models. Fuzzy sets are sets whose elements have degrees of membership. In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition; an element either belongs or does not belong to the set. By contrast, fuzzy set theory permits the gradual assessment of the membership of elements in a set; this is described with the aid of a membership function valued in the real unit interval [0, 1]. Fuzzy sets generalize classical sets, since the indicator functions of classical sets are special cases of the membership functions of fuzzy sets, if the latter only take values 0 or 1. In fuzzy set theory, classical bivalent sets are usually called crisp sets.
Tehran is a densely populated metropolitan in which more than 10 million people live. Many destructive earthquakes happened in Iran in the last centuries. It comes from historical references that at least 6 times, Tehran has been destroyed by catastrophic earthquakes. The oldest one happened in the 4th century BC.
In this study, seismic hazard assessment of Tehran region, capital city of Iran, is conducted using a combination of probabilistic approach and fuzzy sets theory. The earthquake catalog used in the current study contains occurrence times and hypocentre locations of Iranian earthquakes and is derived from the seismic catalog published by Mirzaei et al (2002) for earthquakes during 1975 to 2000. The International Seismological Centre catalog (www.isc.ac.uk) was used to update the catalog data up until the year 2007.
In order to calculate seismic hazard for different return periods in probabilistic procedure for the Tehran region, an area encompassed by the 49.5°–54°E longitudes and 34°–37°N latitudes has been divided by 0.1° intervals generating 1350 grid points. Seismicity parameters are evaluated using the method in which magnitude uncertainty and incompleteness of earthquake data are considered.
A total of 20 area potential seismic sources are introduced, and several seismicity rates and b-values, maximum expected magnitudes are assigned to each of seismotectonic province and potential seismic sources.
To carry out seismic hazard analysis in the framework of fuzzy sets theory, all of the variables converted into triangular fuzzy sets with -cut method. Eventually, the fuzzy response is defuzzified using the surface center method. Two maps are developed to indicate the earthquake hazard of the region in the form of iso-acceleration contours. They display a fuzzy-probabilistic estimate of peak ground acceleration (PGA) over bedrock for the return periods of 475 and 50 years. PGA values for this region are estimated to be 0.35g-0.38g and 0.12g-0.15g for 475- and 50-years return periods, respectively. Outcomes of this study would contribute for the quick and better estimation of the seismic design of structures.