Interactive Intuitionistic Fuzzy Methods For Hierarchical Optimization Problems And Their Applications In Cloud Computing Pricing Problems

Hierarchical optimization problems,which are nonconvex optimization problems with multilayer structure,are very difficult to solve and have been widely applied in industry,agriculture,transportation,finance,government policy,supply chain man-agement,cloud computing pricing.Cloud computing is a powerful tool in the era of big data.The cloud computing pricing problem is a key issue for the development of cloud computing market.Therefore,the studies on the algorithms for hierarchical op-timization problems and cloud computing pricing are of great theoretical significance and practical value.In this dissertstion,we study the following four types of hierarchi-cal optimization problems and their applications in cloud computing pricing problems:pessimistic bilevel programming problem,multilevel programming problem,bilevel pro-gramming problems with multiple followers and multilevel multi-objective programming problem.The main research content includes the following five parts:In the first part,we propose an algorithm for solving pessimistic bilevel program-ming problem.Pessimistic bilevel programming problem is a special bilevel program-ming problem and is more difficult to solve than optimistic bilevel programming problem even to obtain a local solution.We study the theoretical relationship between pes-simistic bilevel programming problem and generalized Nash equilibrium problem in this dissertstion.By virtue of value function,we translate pessimistic bilevel programming problem into generalized Nash equilibrium problem.Then the theoretical research and the algorithm for solving the global solution of pessimistic bilevel programming prob-lem by the equilibrium solution of generalized Nash equilibrium problem are presented.Finally,numerical experiments illustrate the feasibility of the algorithm.In the second part,we propose interactive intuitionistic fuzzy methods for solv-ing multilevel programming problems.Multilevel programming problems are NP-hard problems and it is more difficult to solve the problems with more layers which are more complexity.The existing methods are not only inefficient to obtain the solution for multilevel programming problems,but also few consider the desires of the decision makers.In this dissertstion,we propose three interactive intuitionistic fuzzy methods for solving multilevel programming problems by virtue of the intuitionistic fuzzy set.We first present a score function to objectively depict the satisfactory degrees of decision makers and reduce the subjectivity of the interactive fuzzy methods.Then we develop three interactive intuitionistic fuzzy methods to obtain different satisfactory solutions for the requirements of decision makers.Finally,a case study for cloud computing pricing problems and several numerical examples are given to verify the applicability and the effectiveness of the proposed models and methods.In the third part,we propose a method for the satisfactory solutions of bilevel pro-gramming problems with multiple followers(BLPMF).Firstly,the membership func-tion,non-membership function and a sore function are defined to depict the satisfactory degrees of decision makers.Then a new ratio of the satisfactory balances between de-cision makers is given to ensure the priority of the leader and the balance relationships between the leader and the followers.Furthermore,we propose an interactive intuition-istic fuzzy method for the satisfactory solutions of BLPMF.Finally,a case study for cloud computing pricing problems and the resource allocation problems are given to verify the feasibility and the effectiveness of the proposed method.In the fourth part,we propose a method for the satisfactory solutions of multilevel multi-objective programming(MLMOP)problems.(MLMOP)problems,which have a hierarchical relationship between decision makers with multiple conflict objective func-tions,are very difficult to solve.In this dissertstion,we propose interactive intuitionistic fuzzy methods for solving(MLMOP).Firstly,a sore function is defined to depict the satisfactory degrees of decision makers.Then considering the different requirements of decision makers,we develop five optimization models and five interactive intuitionistic fuzzy methods for(MLMOP)by virtue of the intuitionistic fuzzy set and the technique for order preference by similarity to an ideal solution.Finally,numerical experiments illustrate the feasibility of the proposed methods.In the fifth part,we propose a tri-level decision-making model to characterize cloud computing pricing problem by considering the hierarchical relationship among Infras-tructure as a Service,Software as a Service and the users.The existing pricing schemes few consider this hierarchical relationship and the interests of the users.At present,most users use their internal resources instead of cloud services for lower the value of user experience.In the tri-level decision-making model,users take part in the cloud computing pricing problems.Furthermore,we develop an interactive intuitionistic fuzzy method to solve the tri-level decision-making model for the satisfactory solution for users and cloud providers.Finally,three kinds of numerical experiments are implemented to evaluate the efficiency and feasibility of the proposed model and method.