Toward Theory and Practice of Continuous Imprecise Numbers and Categories

We extend Hemanta Baruah's theory of imprecise sets which are fuzzy sets that obey the law of non-contradiction and excluded middle. For empirical observations mapped onto the real domain, we find the parameters of k imprecise numbers based on logistic distributions by gradient descent to derive k+1 category schema. Moreover, we recover the estimated cumulative (logistic) distribution in the process. The mapping between the forward and reverse distribution of an imprecise number and its distribution and density functions is direct. We define the operation of “imposition” which gives a positive partial presence across the full domain and also use imposition to derive imprecise categories from adjacent imprecise numbers. We present sample results from actual datasets. Results should generalize to other suitable distribution functions. We close with questions directed toward future work.