An interactive approach for integrated multilevel systems in a fuzzy environment

This study proposes a total solution of an interactive approach for integrated multilevel systems or multilevel programming problems (MLPPs) in a fuzzy environment. Simulating the actual decision-making process of the hierarchical structure of an organization, MLPP is a practical and useful approach to decentralized planning problems. Because of the complexity of the problems, there are no traditional techniques efficient enough to obtain the numerical solution of a reasonable size problem. Hence, Shih et al. [1] propose a fuzzy approach for MLPPs, to simplify the complex structure, which is proven to be feasible and efficient. The imprecise MLPPs will be involved when the coefficients of MLPPs cannot be estimated exactly. Because of such a complicated situation in the real world, we will take advantage of an interactive technique to improve the flexibility and robustness of its decision through progressive articulation of decision information from decision makers (DMs). Roughly speaking, there are two interactive procedures for imprecise MLPPs: inside loop and outside loop. The former is for the preference of the DMs, represented by fuzzy membership functions; the latter for the imprecision of coefficients, described by possibility distributions or cut-off values. Special considerations will be given to the compensatory operator, positive and negative ideal solutions, risk attitude, and ε-constraints. In the final section, linear-programming type and network-flow type of imprecise MLPPs will be solved separately as an integrated multilevel system.