Uncertainty due to randomness of hydraulic and hydrologic variables is modeled when probability distributions of the parameters may be estimated. Uncertainties due to imprecision in the management problem may be addressed by use of the fuzzy sets theory. In addition, some parameters in most of the water resources and environmental systems need to be addressed as grey parameters, due to inadequate data for an accurate estimation but with known extreme bounds of the parameter values. Such grey uncertainty in the model parameters can be addressed by representing them as interval grey numbers, a closed and bounded interval with known lower and upper bounds but unknown distribution information. Considerable research works are available on uncertainty modeling addressing stochastic nature of different input parameters, and uncertainty due to imprecision in various components of a water management problem. Most parameters involved in the optimization model are, however, also uncertain and such uncertainty has so far not been considered in different optimization models for water resources and environmental systems. This book aims to bridge this gap.

Dr. S. Karmakar has obtained Ph. D. degree in Water Resources and Environmental Engineering from Indian Institute of Science, Bangalore, India. He is presently an Assistant Professor at Centre for Environmental Science and Engineering (CESE), Indian Institute of Technology Bombay, India.