SAVAGE AXIOMS, ELLSBERG’S PARADOX AND FUZZY OPTIMAL DECISION-CHOICE RATIONALITY

Abstract

This essay is devoted to epistemics of Savage axioms and Ellsberg’s paradox in decision-choice actions in relation to fuzzy optimal decision-choice rationality in the space of uncertainties. The uncertainty space is partitioned into non-fuzzy stochastic sub-space and fuzzy-stochastic sub-space. The Savage axioms are argued to emerge from the former which is vagueness-free while Ellsberg thought experiment leading to his paradox takes place in the latter that contains vagueness. The explanation of the rise of the paradox is shown to be the result of non-comparable decision-choice sub-spaces in which both of them work. The topologies of the two sub-spaces and the required mathematics and logic are considered in their epistemic forms. Criticisms are offered on some attempts to explain and resolve the paradox. The paradox, it is argued, cannot be logically resolved in the space in which the Savage axioms are created. It can not either be resolved in the fuzzy-stochastic space with classical paradigm under Aristotelian logic where all propositions are either true or false, it is argued. A resolution of the paradox as it is related to probability estimates is offered through fuzzy logic, mathematics and computational methods of optimal fuzzy decision-choice rationality. The essay is concluded with an epistemic reflection.