This is evident in the element of chance and randomness inserted into design by painters like Arp and Pollock, but, beyond that, it is evident in the larger urge, shared by poets and writers, to make a career of violations, risks, wagers.
Therefore, the results can provide tradeoffs among water productivity, confidence level and constraint-violation risk level.
The tradeoff among system cost, violation risk, and the related policy implications are also analyzed.
The (overline{k}) increase may reduce the privacy violation risk, but however, it degrades the information usefulness.
A case study is presented to demonstrate the practicality and efficiency of the model, and different constraint violation risk levels and related results are also obtained.
The FTSOQP improves upon the existing fuzzy linear programming methods through more effectively both minimizing the variation of satisfaction degrees among the objective and constraints, and tackling the trade-off between the system cost and the constraint-violation risk.
Sensitivity analyses under different constraint violation risk levels are also given, which can give the authority insights as to the tradeoffs required between the different decision makers as well as identify the equilibrium between environmental protection and economic development.
Li et al. ([2009b]) developed a constraint-softened interval-fuzzy linear programming (CS-IFLP) method for violation analysis of waste management systems, which can deal with uncertainties presented in terms of fuzzy sets and intervals, allow fuzzy relaxation levels for system constraints, and help to analyze tradeoffs among economic objectives, satisfaction degrees, and constraint-violation risk.
The RILP approach can provide a series of interval solutions under varied protection levels and help analyze the interactions among protection level, violation risk, and system cost under various projected system conditions as well as tolerance levels that decision-makers will pay and risk.
More recently, Li et al. ([2010]) introduced interval-fuzzy possibilistic programming (IFPP) to solving solid waste management problems under uncertainties expressed as interval values and fuzzy sets, which can help analyze tradeoffs among system cost, possibility degrees, and constraint-violation risk.
