Research On EA Solutions And Solvability Of Interval Linear Systems On Maximal Algebra

The definition and characteristics of various solution sets of interval systems are important research topics in the field of interval analysis and interval optimization.In recent decades,the research results of weak solutions,strong solutions,tolerance solutions,control solutions and AE solutions of interval linear systems on classical algebra and maximal algebra are more abundant,but the EA solutions of interval linear systems on these two algebras There are few studies on the characteristics and solvability.Since the theory of maximal algebra has important applications in many aspects,it is of great theoretical and practical significance to perfect the solution and solvability of interval linear systems on maximal algebra.This thesis mainly studies the problems of EA solutions and its solvability of the maximal algebraic interval linear systems,the main work is as follows:The first chapter is an introduction.We first introduce the research background and the significance of EA solutions and its solvability of the maximal algebraic interval linear systems.Then,we give some basic notations about the thesis.Finally,we sum up the status of EA solutions and its solvability of the maximal algebraic interval linear systems.The second chapter discusses the EA solutions and its solvability of the interval linear one-sided inequality systems on the maximal algebra max-plus type.First of all,We propose the concept of EA solutions for interval linear one-sided inequality systems,characterize the EA solution set by using inequalities,give Sufficient and necessary conditions for the existence of EA solutions and two related corollaries.Next,we give the concept of EA solvability and explore the relationship between EA solutions and its solvability.Finally,we give some examples to illustrate our main results.The third chapter discusses the EA solutions and its solvability of the interval linear two-sided inequality systems on the maximal algebra max-plus type.Firstly,we propose the concept of the EA solutions of the interval linear two-sided inequality systems,discuss the expression set of the EA solutions and characterize the EA solutions set.Then we give the concept of EA solvability of interval linear two-sided inequality systems,study the necessary and sufficient conditions of EA solvability。Finally,discuss the different relations between EA solutions and EA solvability in the interval linear two-sided inequality systems and two-sided equality systems on max-plus algebra,we give the relevant counter-examples and verify the conclusions by examples.The fourth chapter discusses the EA solutions and its solvability of the interval linear inequality systems on the maximal algebra max-min type.Firstly,we respectively give the concept of the EA solutions of the interval linear one-sided inequality systems and the two-sided inequality systems on max-min algebra,and explore the characteristics of the EA solutions based on the second chapter and the third chapter,and give the necessary and sufficient conditions for EA solutions of one-sided and two-sided inequality systems respectively.Then we propose the concept of EA solvability for interval linear one-sided and two-sided inequality systems on maxmin algebra,and study the relationship between EA solvability and EA solutions.Finally,we use some examples to illustrate further.The fifth chapter makes a brief summary of this thesis and presents some prospects for the future work.