A fuzzy risk approach for performance evaluation of an irrigation reservoir system

In this paper, a model for fuzzy risk of low yield of a crop is developed to study the implications of a reservoir operating policy model. When an optimal operating policy is derived based on a known objective, the policy itself does not, in general, indicate a measure of the system performance unless a criterion to this effect is embedded in the objective function. While a systems analyst is interested in the nature of the objective function used in arriving at a policy, the irrigation decision maker would look for the implications of using the policy through answers to the questions such as, how often the system will fail and how quickly it will recover from a failure. It is, therefore, important that the implications of reservoir operation with a given policy be studied keeping in view the interests of the decision makers. Some earlier studies on reservoir operation models for irrigation have considered reliability, resiliency and productivity index, as the performance indicators of the operating policy. In this paper, fuzzy risk of low yield of a crop is considered as another performance indicator to address uncertainties due to both randomness and fuzziness. Uncertainty due to randomness arises primarily because of the random variations of hydrologic variables such as reservoir inflows and rainfall in the command area. Uncertainty due to imprecision or fuzziness arises because of uncertain crop yield response to various factors (such as farm practices and climatic variables) other than to the applied water. Two important concepts are introduced in this paper with respect to irrigation reservoir system. The first one is related to viewing the low yield of a crop, as a fuzzy event. The second concept is related to the definition of fuzzy risk of low yield of a crop. The fuzzy risk of low yield is derived using the concept of probability of a fuzzy event. Application of the methodology is demonstrated with a case study in India.