An Introduction to Neutrosophic Possibility Theory: Modal Perspectives and Applications

Abstract

Possibility theory focuses on quantifying the degree to which a statement or proposition is possible. It deals with the measurement of possibility and necessity in a similar manner to how probability theory deals with likelihood. While the concept of fuzzy logic has proven valuable in addressing uncertainties and imprecision, its main drawback arises when dealing with situations that involve not only uncertainty but also indeterminacy, as well as the coexistence of truth, falsity, and indeterminacy within a single statement.  In this paper, we suggest using neutrosophic logic as a mathematical framework for reasoning with ambiguity and vagueness. We propose utilizing Kripke structures for neutrosophic propositions as conceptual abstract models, providing an alternative method to describe possibility theory in a neutrosophic environment. An illustrative scenario in the context of medical diagnosis is presented in order to demonstrate the efficacy and flexibility of our method. This novel approach not only enriches our knowledge of uncertainty, but it also provides pathways for more comprehensive and nuanced analysis in other domains such as in artificial intelligence, decision support systems, knowledge representation, cognitive computing etc., thus highlighting the potential benefit of merging neutrosophic logic with possibility and modal structures.