New measures of consistency and coverage for social research based on neutrosophic logic

The mathematical methods systematically used in social sciences often rely on statistical tools like correlation, which may not optimally model social phenomena, frequently described using words. Set theory, as proposed by C.C. Ragin, provides a more suitable tool, leveraging set asymmetry to measure set-theoretic consistency and coverage, which were later generalized to fuzzy sets. Subsequent extensions into the neutrosophic field are significant because the underlying binary logic in traditional models often fails to capture the complexities and nuances of social realities, such as those found in Afro-Latin American and Caribbean cosmovisions that encompass ambiguity and indeterminacy. This paper proposes new, logically grounded measures for consistency and coverage, derived naturally from logical operators known as neutrosophic R-implications (generalizations of fuzzy R-implications). By explicitly incorporating Indeterminacy alongside Truth and Falsity, these new measures gain a deeper theoretical connotation, emphasize the logical relationships central to Ragin's methods, and offer tools better aligned with complex, non-exclusive realities.