Some Applications Of Interval Numbers In Classical Mathematics

Due to the imprecision of the various measuring and computing and because ofthe incomplete information causing the lack of data, they result in an uncertaindata—an interval number. Based on the knowledge of binary interval number, thispaper effectively overcomes the value of uncertainty, which is caused by the datafuzziness. And it carries on the thorough research of the dual band theory, further putsforward some new algorithms and properties of interval number. According to theclassical mathematics methods of interval number, this paper obtains the answers inthe group and binary quadratic of the interval number, and gets the maximum orminimum interval distance, and studies interval matrix, and the adjacency matrixeigenvalues algorithm and the definitions and properties of fuzzy interval graph andso on.This paper includes the following aspects:1. It mainly introduces the development background and the research status ofinterval number, and states the main contents in this paper: the related definitions ofinterval number, basic theory, and the interval number’s application and analysis. Itstudies some properties of interval number with the methods of classical mathematics,and studies the transformation from the uncertainty interval number to the realnumber using the interval number distance. So it’s more convenient to study someproperties of classical mathematics, and it effectively overcomes the interval numberof uncertainty.2. This paper studies the operations of the interval number and its basic properties.The interval distance stipulates the interval arithmetic, and for all multiplications ofthe positive interval number[a,b], here, a≠0, which can make it an Abelian group.And we get that it is an equivalence relation, if we set the interval numbers whichhave same interval distance to a classification.3. It defines the secondary range equation and the unit, and states the method toobtain the results of dual range equation. Also it gives the method that how to operatesecondary range number to get the maximum or minimum interval distance.4. It defines interval matrix, and gives the proof of its arithmetic rule followsclassic algorithms in mathematics, and gives the definition of interval linear equationsis given.5. It gives the definition of the interval graph, and gives the definitions of theincidence matrix and adjacency matrix of the interval graph. Moreover, this paper studies the eigenvalues and the related properties of the interval equations.6. According to the interval graph, it defines the interval fuzzy graph and thestrong arcs of the fuzzy graph, and successfully solves the connecting strength ofthe interval fuzzy graph and obtains the properties of the strong arcs.7. Summary this paper and do some follow-up work.