A study on operations in interval and paired probabilities

Statements in fuzzy logic and probability theory both take values in the unit interval of [0, 1]. The difference between the treatments of uncertainties in fuzzy logic and probability theory give effects to the truth functionalities in their operations. In this paper, the difference between operations in fuzzy logic and probability theory is discussed and the interval and paired probabilities are introduced. Operations for these models are defined truth-functionally and generalized so that the domains of the probabilities are closed in interval or paired interval values under these operations