Planning Water Resources Systems under Uncertainty Using an Interval-Fuzzy De Novo Programming Method

Abstract

This study presents an interval-fuzzy De Novo programming (IFDNP) method for planning water-resourcesmanagement systems under uncertainty. IFDNP is derived by incorporating the concepts of interval parameters and fuzzy sets within a De Novo programming framework. IFDNP has the advantages in constructing optimal system design through introducing the flexibility into the available resources in the model's constraints. Moreover, IFDNP allows the decision makers to achieve a metaoptimal system performance and improve the performance of compromise solutions, and it is effective for dealing with the system design problems involving multiple objectives and multiple uncertainties. The IFDNP is then applied to a case study of designing an inexact optimal system with budget limit for water resources management and planning. Various scenarios that are associated with different levels of economic implication consequences and water allocation patterns under uncertainty are analyzed. Results can help decision makers to evaluate alternatives of system designs and to determine which of these designs can most efficiently achieve the desired economic objective constrained by limited resources.

Interval-fuzzy municipal-scale energy model for identification of optimal strategies for energy management – A case study of Tianjin, China

“…where m D ,m G and m C denote membership functions of fuzzy decision D, fuzzy goal G, and fuzzy constraint C, respectively [35,36]. Assume that we have n goals (G 1 , G 2 , …, G n ) and m constraints (C 1 , C 2 , …, C m ).…”

“…An interactive two-step algorithm is developed to solve the above problem through analyzing the detailed interrelationships between the parameters and the variables and between the objective function and the constraints [36,41]. The submodel for l þ corresponding to f À can be formulated in the first step when the system objective is to be minimized; the other submodel for l À can then be formulated based on the solution of the first submodel.…”

“…Fuzzy programming (FP) can deal with vagueness and ambiguity based on fuzzy set theory, where uncertainties are handled in a direct way without a large number of realizations [36]. Given a fuzzy goal (G) and a fuzzy constraint (C) in a space of decision alternatives (X), a fuzzy decision set (D) can then be formed in the intersection of G and C. In a symbolic form, we have D∩C, and correspondingly:…”

“…Model (5) can be converted into an ordinary linear programming one by introducing a new variable of l ¼ m D ðX ± Þ, which corresponds to the membership function of the fuzzy decision [36]. Specifically, the flexibility in the constraints and fuzziness in the objective (which are represented by fuzzy sets and denoted as "fuzzy constraints" and "fuzzy goal", respectively) can be expressed as membership grades (l) corresponding to degrees of overall satisfaction for the constraints and objective.…”

Evaluation of water resources conserved by forests in the Hani rice terraces system of Honghe County, Yunnan, China: an application of the fuzzy comprehensive evaluation model

“…At present, researches on water resources in the world mainly concentrated on water quality analysis (Zhang et al 2014), water resource management (Umapathi et al 2013;Miao et al 2014), water resources use (Maier et al 2010), and the influence impacted by climate change with wide-ranging consequences for human societies and ecosystems (Abutaleb 2000;Arnell 2004;Barnett et al 2004;Higashi 2006), while, there is few study about water resources value outside of China. Water resources value refers to the money paid for water resource owners (nation or collective) by the users in order to obtain the right of using the water.…”