title: [The establishment of the model for differential diagnosis of borderline cases with anterior crossbite using fuzzy set theory].
abstract: OBJECTIVE
  To introduce the fuzzy set theory to orthodontics by using the diagnostic information drawn out from the diagnosed cases to solve the problem of borderline- case diagnosis.
  
  
  METHODS
  Lateral cephalometric radiographs of 107 anterior crossbite patients in early permanent dentition were traced, measured, and 31 variables calculated. Diagnosis was made by experienced specialists and the cases were divided into three groups: dental anterior crossbite (52 cases), borderline cases (22 cases) and skeletal anterior crossbite (33 cases). Among 85 cases with accurate diagnosis we selected 70 cases to establish 6-factor model using stepwise discriminant analysis. This afforded 100 percent correct respective check and the predictive diagnosis of the other 15 cases showed that its correction rate was 93.3 percent which proved that most useful information was included. Then the contributions of the six variables were calculated and we established two sets: skeletal anterior crossbite set and dental anterior crossbite set with skeletal and dental means to be their thresholds. For each case the individual measurements of the six variables were standardized and afterwards transferred into constituent ratio and at the same time their degrees of membership of these two sets were calculated according to the distance between its location and the two thresholds. Using this fuzzy model we got the individual scores of the two sets. The diagnosis of the patient was coincident with the set of higher scores. This model was testified by 85 cases with accurate diagnosis and its correction was absolute.
  
  
  RESULTS
  22 borderline cases were diagnosed by this model.
  
  
  CONCLUSIONS
  The two-set difference were far less than that of the cases with accurate diagnosis which prove the model was reasonable.
authors.affiliation: Department of Orthodontics, School of Stomatology, Shanghai Second Medical University, Shanghai 200011, China.
authors.forename: L
authors.initials: L
authors.lastname: Chen
authors.forename: S
authors.initials: S
authors.lastname: Peng
authors.forename: Y
authors.initials: Y
authors.lastname: Zheng
mesh_terms: D019229:Dentition, Permanent; D003937:Diagnosis, Differential; D016002:Discriminant Analysis; D006801:Humans; D008310:Malocclusion / Q000175:diagnosis*; D008962:Models, Theoretical