Fuzzy Measures of Symmetry Breaking of Conditions, Similarity and Comparison: Non Statistical Information for the Single Patient

ABSTRACT

Science relies on experimentation to find truth. It demands that conditions remain unchanged for each repetition of an experiment. Thus, medicine relies on ‘probability theory’ based statistics and large double blind controlled randomized clinical trials. The purpose of this study is to discover measures that account for different and changing conditions of individual patients. These measures allow experiments to be performed without uniform conditions. They also allow precise prediction for the individual case. Methods: Variables of different patients or the same patient at different times are measured and normalized or expertly assigned a value in the unit interval to form the elements of a fuzzy “set as point” in the unit hypercube. Measures of breaking of symmetry of conditions, similarity, and comparison for different patient states are defined by fuzzy Subsethood measured in fuzzy cardinality. Fuzzy entropy measures for similarity and symmetry are discovered through the fuzzy Entropy theorem. Results and Conclusion: Measures of precise prediction for the single case and comparison of individual patient states capture the non linear dynamic between changing measured variables and symmetry of conditions. Non statistical information measures for this dynamic are discovered using the unifying structure of fuzzy theory and its measure space.