The Natrue Of Similarity Measure And A New Formula

The fuzzy mathematics is a bridge between the precise classical mathematics and the objective world which has filled fuzziness.Fuzzy mathematics' foundation is the fuzzy set theory.In 1965,the concept of fuzzy set was brought forward by American automatic cybernetics expert L.A.Zadeh for the first time in his groundbreaking paper- "the Fuzzy set".And the similarity measure and the measure of fuzziness are in the very important two concepts in fuzzy sets.The similarity measure is a important quantitative index which describes two fuzzy sets similar or a drawing close to degree,it proposed first time by our country scholar Professor Wang Peizhuang, and the lattice close-degree formula is given.Luo Chengzhong has given kinds of similarity measure formulas.The measure of fuzziness is a quantitative index which describes a fuzzy set's fuzzy degree,it was introduced first time by Termini and Deluca,and its quota description axiom is given.This article mainly discusses the general nature of similarity measure and the measure of fuzziness,study the relations between similarity measure and the measure of fuzziness,and last obtained a new similarity measure formula.The prime task is as follows:1.The relations between similarity measure and the measure of fuzzinessWe study the axiomization definition of similarity measure and the measure of fuzziness profoundly,and discussed their basic property,such as the symmetry,contains,full contains,nonconsitency of measure of fuzziness and so on.We found that there are some relations between similarity measure and the measure of fuzziness from theirs definitions,and the similarity measure can be constructed by the known measure of fuzziness,and the method is not only.This article gives the new relations between similarity measure and the measure of fuzziness,which are the theorem of expressing the similarity measure based on the measure of fuzziness and the theorem of expressing the measure of fuzziness based on the similarity measure,and proved theyare established.The deduction of the two kinds of relations were given.These results can be used in the pattern recognition,and the policy decision science.2.Constructing new similarity measure formulaThe similarity measure formula has many kinds,for instance Hamming similarity measure, Eculid similarity measure,lattice close-degree and so on.Choosing the more better similarity measure formula in the actual problems to solve the actual problem will be more useful.We was inspired by the Hamming similarity measure formula,and obtained a new similarity measure formula from improving the Hamming similarity measure,and proved it was reasonable.3.New formula's applicationCompared with the beforehand kinds of similarity measure formulas,the new formula has solved the problem which other similarity measure formulas cannot solve,and the resolution of formula enhanced obviously.We gave the special example to explain strongpoint and the generalized example to explain this new formula is reasonable.This new formula induced another new similarity measure formula which accord with similarity measure axiom definition.Finally,We study the two similarity measure formulas' application in the pattern recognition.