An Extension to Zadeh's Truth Qualification Principle for Resolution of Self-Referential Sentences: Towards a Comprehensive Theory of Type-2 Fuzzy Possibility

Abstract

The purpose of this paper is to formulate truth-value assignment to self-referential sentences via Zadeh's truth qualification principle and to present new methods to assign truth-values to them. Therefore, based on the truth qualification process, a new interpretation of possibilities and truth-values is suggested by means of type-2 fuzzy sets and then, the qualification process is modified such that it results in type-2 fuzzy sets. Finally, an idea of a comprehensive theory of type-2 fuzzy possibility is proposed. This approach may be unified with Zadeh's Generalized Theory of Uncertainty (GTU) in the future.