Fuzzy Number Linear Programming Technique for Design of Rectangular Canals

Abstract

Despite many deterministic approaches for the optimal design of a canal already proposed, a methodology capable of considering the risk value when there is uncertainty in flow estimation is still lacking. In real engineering problems, we confront linear programming models in which all included uncertain parameters are fuzzy numbers. In the task of canal design, this assumption is because it involves uncertain parameters (load and resistance) estimated by short historical data and limited knowledge about the environment, respectively. This limitation hinders the usage of probabilistic linear programming approaches because the probability of satisfying a constraint should be known with certainty. This paper provides a new method for solving fuzzy number linear programming problems using the concept of fuzzy risk and Yager’s fuzzy ranking function. The result is used for proposing a novel optimization formula that can aid in rectangular canal design. The application of our insightful new methodology is presented in a stormwater canal design example. The findings presented in this paper will appeal to decision-makers and practicing engineers.