A Methodology for Assessing the Effect of Countermeasures Against a Nuclear Accident Using Fuzzy Set Theory

A methodology for assessing the effectiveness of countermeasures against a nuclear accident has been designed by means of the concept of fuzzy set theory. In most of the existing countermeasure models in actions under radiological emergencies, the large variety of possible features is simplified by a number of rough assumptions. During this simplification procedure, a lot of information is lost which results in much uncertainty concerning the output of the countermeasure model. Furthermore, different assumptions should be used for different sites to consider the site specific conditions. In this study, the diversity of each variable related to protective action has been modelled by the linguistic variable. The effectiveness of sheltering and evacuation has been estimated using the proposed method. The potential advantage of the proposed method is in reducing the loss of information by incorporating the opinions of experts and by introducing the linguistic variables which represent the site specific conditions. INTRODUCTION The necessity of emergency response planning has increased since the accident of TMI-2 in the USA. One of the essential parts of emergency planning is how to decide countermeasures including sheltering, evacuation, interdiction, and decontamination. Decision makers should have access to rational decision model that can be used to support the selection of appropriate off-site protective action in the event of nuclear reactor accident(1,2). The effects of these protective actions may be dependent on the site-specific conditions such as shielding factors, population density, and road conditions. The variables representing these conditions have a wide distribution of values to the complexity of real situation. Representative values of these variables are used in most existing countermeasure models for simplicity and tractability. The simplification procedure inevitably results in the loss of information and the occurrence of uncertainty(3). There are several facts which may cause the uncertainty in a countermeasure model. Real situation is very often not crisp and deterministic due to uncertainty or vagueness. The future state of a system might not be known completely due to the lack of information. The human behavior is dependent on the situation. There is a lot of uncertainty due to the assumed values of parameters such as the fraction of population with different shielding factor, driving speed, etc. Therefore, different values in the existing countermeasure model should be assumed for different site. The shielding factors may be different with respect to site as well as direction from the source even in the same site. But, the site specific factors which are dependent on the effect of wind direction used to bee not reflected in the most existing models. Decision making process is a complex web of problems involving engineering, economic, environmental, social and management aspects. It therefore deals with entities and relations which are often not precisely known and indeed are difficult to quantify(4). The concept of fuzzy set provides the mathematical formulations which can characterize the uncertain parameters involved in the existing countermeasure models. By the application of linguistic variables and fuzzy algorithms, it is possible to provide an approximate and effective tool to describe system which is too complex or ill-defined to use precise mathematical analysis(5). A countermeasure model is very complex system mainly due to the diversity of real environment. In this study, a method to reduce the parameter uncertainty in a countermeasure model is proposed, using the concept of fuzzy set and system. The broad spectrum of the parameter values expressing the characteristics of shielding and evacuation is represented by linguistic variables. A linguistic variable is defined as one whose values are sentences in natural or artificial languages as large, good, and poor. The relationship between the parameters representing the site condition and the effects of these parameters on radiation exposure is represented by fuzzy conditional statements which has the form "IF A THEN B", where A and B have fuzzy meaning(6,7). Fuzzy reasoning with the obtained fuzzy relations and the given site-specific input variable gives the fuzzy set to the parameter which will be estimated. The main objective of this study is to demonstrate a potential use of fuzzy set theory in countermeasure modeling. The proposed method can be used to describe other uncertain parameters in a countermeasure model by incorporating the reliable membership function and fuzzy conditional statements based on the opinions of experts.