Probability theory and fuzzy logic have been presented as quite distinct theoretical foundations for reasoning and decision making in situations of uncertainty. This paper establishes a common basis for both forms of logic of uncertainty in which a basic uncertainty logic is defined in terms of a valuation on a lattice of propositions. The (non-truth-functional) connectives for conjunction, dis...

Uncertainty and vagueness are pervasive phenomena in real-life knowledge. They are supported in extended description logics that adapt classical description logics to deal with numerical probabilities or fuzzy truth values. While the two concepts are distinguished for good reasons, they combine in the notion of probably, which is ultimately a fuzzy qualification of probabilities. Here, we devel...

In the present investigation, we deal with the reliability characteristics of a repairable system consisting of two independent operating units, by incorporating the coverage factor. The probability of the successful detection, location and recovery from a failure is known as the coverage probability. The reboot delay and common cause shock failure are also considered. The times to failure of t...

In this paper, a model of probability fuzzy support vector machines (PFSVMs) based on the consideration both for fuzzy clustering and probability distributions is proposed. In many applications of traditional support vector machines (SVMs), there are over-fitting problems due to the fact that SVM is sensitive to outliers or noises. In order to solve the problem, the fuzzy support vector machine...

Probability judgment is essential to navigating through life, from understanding risks to making decisions under uncertainty. However, probability theory is relatively recent. How has humanity managed to get along before this development? In PNAS, Fontanari et al. (1) provide exciting new evidence of probabilistic cognition among Mayan indigenous groups, both adults and children, whose performa...

This paper presents a mathematical model for a flow shop scheduling problem consisting of m machine and n jobs with fuzzy processing times that can be estimated as independent stochastic or fuzzy numbers. In the traditional flow shop scheduling problem, the typical objective is to minimize the makespan). However,, two significant criteria for each schedule in stochastic models are: expectable m...

Aphasia diagnosis is a challenging medical diagnostic task due to the linguistic uncertainty and vagueness, large number of measurements with imprecision, inconsistencies in the definition of Aphasic syndromes, natural diversity and subjectivity in test objects as well as in options of experts who diagnose the disease. In this paper we present a new self-organized multi agent system that diagno...