Optimal Solution And Value Of Interval Linear Programming

Interval number theory has very strong application background in decision analysis,transportation etc, that is also an important means to solve the problem of uncertainty effectively.Because of the complexity of the objective things, and uncertainty and fuzziness and the limitationof the human mind, people often can’t clear information given the properties, can only give it ainterval range, with more interval theory matured, it solves the uncertainty also more and more bemore people use. The interval theory is applied to linear programming, the uncertainty of the linearprogramming problems effectively is solved, make linear programming in science, engineering,economic, industrial, military and other areas of a more prominent role. So the intervalprogramming model and the optimal solution of the optimal value has the extremely vitalsignificance.The thesis in the former research based on the planning of the interval, the systemcomprehensive summarizes the interval linear programming theory, through summing up the weaksolution, weak feasible solution, strong solution, strong feasible solution and related concepts andtheorem and then put forward the optimal solution of the interval planning and the optimal value,and makes a further discussion, among of the optimal solution of the optimal value and are studiedand that the relevant conclusions, and kinds of the typical situation for example, and through Matlabverification, from scientific point of view shows the accuracy, the concrete content as follows:Paper first chapter introduces the interval planning in the real world and the important role thatinterval has extensive research planning of the actual meaning, and the interval of the dynamicplanning research; The second chapter basically summed up the interval operation rule, and thevector, matrix of interval form of extension and nature summaries; Chapter 3 according to thespecial properties of the interval number and the system introduced interval linear programming theweak solution, strong solution, weak feasible solution, strong feasible solution, and from the Angleof calculation complexity that their difficulty and related theorem, based on interval linearprogramming of the optimal solution, analyzed the previous puts forward the optimal solution of theinterval of the deficiencies, and then puts forward personal point of view, and put forward therelative theorem and to prove it, it shows the correctness. At last the optimal inspection weaksynthesizes; The fourth chapter basically for interval linear programming problem of two types ofthe optimal value interval bounds induces summary, considering the optimal value bounds todetermine the optimal value of interval is not necessarily contains the optimal value, from theperspective of satisfaction of the optimal value interval appear clearance of reason, introducing the B-stable the related concept, and puts forward the optimal value interval no gap between thesufficient condition is given strict proof, at last, the paper introduces the interval quadraticprogramming, and puts forward a new definition, and the optimal solution methods, gives theoremand proves it.