Haresh C. Shah

Vertex method for computing functions of fuzzy variables

Abstract This paper is to introduce a new approach — the vertex method — for computing functions of fuzzy variables. The method is based on the α-cut concept and interval analysis. The vertex method can avoid abnormality due to the discretization technique on the variables domain and the widening of the resulting function value set due to multi-occurrence of variables in the functional expression by conventional interval analysis methods. The algorithm is very easy to implement and can be applied to many practical problems. Some examples are given to illustrate the applications.

Fuzzy computations in risk and decision analysis

Abstract This paper describes an algorithm for performing extended algebraic operations such as those encountered in risk and decision analysis under fuzzy conditions. The method makes use of the lambda-cut representations of fuzzy sets and interval analysis. It is an approximate computational technique but is highly efficient compared with the exact method of nonlinear programming, with an accuracy which is much better than the conventional discretization approach. The effectiveness and utility of the procedure are illustrated with examples of fuzzy risk and decision analysis taken from available literature.

Engineering role in failure cost evaluation for buildings

Cost benefit analysis is a common tool for decision making on safety. The appropriate degree of safety in structural design can be discussed based on a simple formula for optimum reliability including parameters such as coefficient of variation of lifetime maximum load, cost-up constant and normalized failure cost. In many cases, the degree of safety is determined as specified in codes or regulations. However, when additional information is available, such as owners demands, engineers are responsible for providing quantitative values for various parameters, in particular for failure cost. This paper examines sources of failure costs and relations between the engineers role in structural safety and discusses failure costs.

A rational approach to pricing of catastrophe insurance

A methodology for rational pricing of catastrophe insurance is described. The methodology has two components: a solvency- and stability-based pricing framework, and an engine to quantify the loss variability that drives solvency and stability. Generalization to account for contagious effects of catastrophes and multiple occurrence of peril is presented in detail.

Fuzzy information processing in seismic hazard analysis and decision making

Abstract This paper describes a methodology to incorporate vague information, based upon heuristic knowledge and expertise, into the conventional probabilistic approach for the seismic hazard analysis. The interval analysis method is introduced to process interval information with interpretation from Dempster and Shafers evidence theory. The Vertex Method is discussed to handle fuzzy information which is a generalization of interval information. These methods, along with the current approach of seismic hazard analysis, are used to assess the seismic hazard for the San Francisco Bay Area in California and to provide information for deciding strengthening policy of existing buildings.

Utilization of geophysical information in Bayesian seismic hazard model

Abstract This paper first describes the inferential structure of the Bayesian model and uses it to show why the empirical method using only short historical earthquake data cannot obtain a reliable hazard estimation. For improving the hazard prediction, newly developed information from the geophysical and geological studies should be incorporated with the historical data within the Bayesian framework. The paper, then, concentrates on the methodologies of how to use the energy flux concept, seismic moment and geological observation in the seismic hazard analysis. A refined Bayesian model, where some of the geophysical and geological input can be used flexibly and consistently, is suggested. Finally, numerical examples are presented for illustrating the application of the improved method.

The strategy effectiveness chart: A tool for evaluating earthquake disaster mitigation strategies

Abstract Professionals in the field of emergency response and risk management are frequently unable to assess the cost-effectiveness of alternative earthquake mitigation strategies. This is partly because such strategies vary widely by type, target group and method of implementation, and also because a simple and readily usable evaluation tool does not currently exist. In addition to shedding light on cost-effectiveness, a good evaluation tool would address a variety of other issues such as: who benefits and who pays; and how much safety does a given investment provide? This paper describes a decision support tool, the Strategy Effectiveness Chart (SEC), which is currently being formulated to assist in answering these questions. The construction of an SEC and the results of applying it to the residential sector of Los Angeles, California, are discussed to show the utility of this approach.

Earthquake recurrence relationships from fuzzy earthquake magnitudes

This paper presents a methodology for determining earthquake recurrence relationships using fuzzy information on earthquake magnitude. The conventional least-squares method is extended to deal with fuzzy earthquake magnitude by using the vertex method. The differences between using crisp values and vague information of earthquake magnitude in earthquake recurrence relationships are discussed and examined through two examples. The fuzzy recurrence relationship developed in this paper is intended for use in seismic hazard analysis or seismic zonation.

Reliability assessment of existing buildings subjected to probabilistic earthquake loadings

Abstract In order to mitigate the losses induced by major earthquake, it is important to strengthen vulnerable existing structures. To identify this vulnerability, a probabilistic method is needed in which uncertainties from different sources are incorporated. based on seismic hazard evaluation for a site, a single peak power spectrum is used to represent the intensity and frequency content of the ground motion. Assuming a non-stationary Gaussian model for earthquake time history. Monte-Carlo simulation technique is used to generate a set of time histories. Since the input peaks occur at random time and at different random frequencies, the response of the structural system is also random. A statistical analysis of a suitable response parameter (such as ductility demand or moment demand) is conducted and the Gumble Extreme Value distribution is fitted. The ultimate ductility capacity is assumed to have a probability distribution. The reliability of the structure is evaluated by convolving the demand and capacity distributions. A numerical example is presented for illustration. It is shown that with further modification in the proposed method, one could obtain a reasonable estimation of structural safety based upon which a rational decision for strengthening policy can be made.

Understanding time variation of risk: Crucial implications for megacities worldwide

Abstract Information about temporal variations in risk, attributable to changes in the human component of natural disasters, is rarely included in disaster assessments carried out by hazard management professionals. Whereas the risk of extreme natural events will probably remain unchanged during the lifetimes of todays population, the probability of large urban disasters appears to be increasing rapidly. Recent earthquakes in Northridge (1994) and Kobe (1995) are indicators of these trends. This paper introduces an integrated approach to urban risk assessment that focuses on the changing risk and vulnerabilities of large cities to earthquakes. These cities can be thought of as complex socio-technical systems, comprising interdependent subsystems that may be modelled econometrically. The construction of one such model is discussed, as well as the procedure for simulating changes in case-study urban areas over different time periods, with and without the occurrence of major earthquakes. Implications of the model for hazard management are identified.