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A Kind of Quantitative Method Based on Camberra Fuzzy Distance in Multiple-Valued Logic

ZHAO Bin;YU Peng;College of Mathematics and Information Science,Shaanxi Normal University;School of Arts and Sciences,Shaanxi University of Science and Technology;  
In this paper,by using Camberra fuzzy distance on fuzzy set,we propose the notions of Camberra-distance,Camberra-similarity degree between two formulas and Camberra-truth degree of one formula in multiple-valued Lukasiewicz logic system,and discuss the properties of Camberra-similarity degree and Camberra-truth degree,prove that the Camberratruth degree of formula φ is equal to the sum of Camberra-truth degrees of some incompatible formulas. And then,based on Camberra-truth degree,we study some properties of Lukasiewicz logic metric space,prove that there is no isolated point,and arbitrarily sphere neighbourhood is an inconsistent theory in three valued Lukasiewicz logic metric space and so on. Which provides a newmethod for expand the grade reasoning on formula set F(S).
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