Interval And Fuzzy Multi-Objective Programming And Their Applications In Decision Making

Human knowledge is the integration of facts and rules to some extent.Both facts and rules can be represented and characterized by fuzzy relation,and then fuzzy relation equation becomes a method to represent the knowledge.The fuzzy relation equation has been widely utilized in information processing,data mining,decision making,system control,image processing,expert system and so on.Moreover,the fuzzy relation equation is one of the important research topics in fuzzy set theory.In order to make better use of the fuzzy relation equation in practice,it is very significant to systematically research how to solve the fuzzy relation equation.In recent years,with the wide application of data information exchange and utilization in industrial and agricultural productions,it is imperative to manage many productions in the industrial chain using data information in order to save the cost.However,the incompleteness of data and the uncertainty and fuzziness of available data result in some challenges for decision makers.Considering the uncertainty of data information and the behaviors of decision maker,the decision-making with expressing the knowledge by fuzzy relation equation has advantages which classical the classical decision-making method cannot provide.This dissertation mainly discusses the sup-t product composition fuzzy relation equation,fuzzy linear programming,interval linear programming and their applications in decision making.The results obtained are shown as follows:1.LU-factorization was used to solve the sup-t product fuzzy relation equation by Molai recently.Considering that forward and backward substitution play an important role in this method,this section first modifies the forward and backward substitution and solves the sup-t product fuzzy relation equation with LU-factorization.Then,the computational complexity of improved forward and backward substitution is analyzed in detail.Finally,we find that LU-factorization acts as splitting an irredundant covering of sup-product fuzzy relation equation into two parts.It therefore cannot change the fact that finding the solutions of sup-t product fuzzy relation equation with LU-factorization is an NP hard problem.On the contrary,the computational expense will linearly increase with the number of minimal solutions of L(?)x=b.2.A counter-example is provided to demonstrate some flaws in a recent paper titled “A new equivalent transformation for interval inequality constraints of interval linear programming”.We point the logic error in the proof of Theorem 5.2 and discuss some remedial works.A numerical example is used to solve the multiple-objective linear programming problems subject to an inf-? composition fuzzy relation equations constraint.Since the feasible region of an inf-? composition fuzzy relation equations constraint is generally non-convex,the multiple-objective linear programming problems is first converted into a traditional linear programming model applying the two-phase approach.And then a compromise model with an average operator method is proposed for decision makers in order to generate more efficient solutions for this problem.3.Based on the convenience of obtaining marine resources,a marine product processing plant in Zhoushan plans to make full use of the resources and optimize its processing industry chain to achieve sales,in order to maximize the profit of sales.In view of this,we obtain the relevant data and construct a mathematical model based on P2 P network transport protocol according to the actual situation,and analyze the practical utility of the industrial chain by combining the optimization problem with fuzzy relation equation.