Refined Neutrosophic Information Based on Truth, Falsity, Ignorance, Contradiction and Hesitation

Abstract

In this article, starting from primary representation of neutrosophic information, namely the triplet (μ,ω,ν) made up of the degree of truth μ, degree of indeterminacy ω and degree of falsity ν, we define a refined representation in a penta-valued fuzzy space, described by the index of truth t, index of falsity f, index of ignorance u, index of contradiction c and index of hesitation h. In the proposed penta-valued refined representation the in-determinacy was split into three sub-indeterminacies such as ignorance, contradiction and hesitation. The set of the proposed five indexes represents the similarities of the neutrosophic information (μ,ω,ν) with these particular values: T=(1,0,0), F=(0,0,1), U=(0,0,0), C=(1,0,1) and H=(0.5,1,0.5). This representation can be useful when the neutrosophic information is obtained from bipolar information which is defined by the degree of truth and the degree of falsity to which is added the third parameter, its cumulative degree of imprecision.