On Fuzzy Optimization Theory Based On G-derivative And Its Application

Information plays a vital role in decision.In order to make the decision be useful,the information needs accurate and reliable.In the real world,fuzzy information is a common phenomenon.The concept of a fuzzy mathematics relates to the issue of fuzziness of information.L.A.Zadeh proposed the concept of fuzzy set for describing fuzzy phenomenon.In 2011,he proposed a concept of Z-number on the basis of fuzzy set.In describing the fuzziness of the problem,Z-number is more accurate than the description of the fuzzy set.In this thesis,on the basis of definition of Z-number and fuzzy optimization theory,the fuzzy optimizations based on g-derivative are discussed.Firstly,we introduce the related definition of Z-number.We also present the process of computing the generalized Hukuhara difference of discrete Z-numbers and the generalized difference of continuous Z-numbers respectively.Some examples are given to illustrate the effectiveness of the proposed computing methods.Secondly,we define a new partial order to ranking the Z-numbers with generalized centroid.The optimality conditions for optimization problems based on Z-number are proposed.We also study the existing conditions of optimal solution and the validity of the discussion is illustrated by an example.Finally,we convert Z-numbers to classical fuzzy numbers to simplify calculation.A new dominance relationship of two fuzzy numbers based on the lower limit of the possibility degree is proposed.Then according to this dominance relationship,we present a multi-objective evolutionary algorithm to solve the optimization problems.Finally,a simple example is used to demonstrate the validity of the suggested algorithm.