Probabilistic logic and credibilistic logic are two branches of multi-valued logic for dealing with random knowledge and fuzzy knowledge, respectively. In this paper, a hybrid logic is introduced for dealing with random knowledge and fuzzy knowledge simultaneously. First, a hybrid formula is introduced on the basis of random proposition and fuzzy proposition. Furthermore, a hybrid truth value i...

Uncertainty theory is a branchof axiomaticmathematics formodelingbelief degrees. This theory provides a new mathematical tool for indeterminacy phenomena. Uncertain variable is a fundamental concept in uncertainty theory and used to represent quantities with uncertainty. There are some important characteristics about uncertain variables. The expected value of uncertain variable is its average v...

It is doubtless that intuitionistic fuzzy set (IFS) theory plays an increasingly important role in solving the problems under uncertain situation. As one of the most critical members in the theory, distance measure is widely used in many aspects. Nevertheless, it is a pity that part of the existing distance measures has some drawbacks in practical significance and accuracy. To make up for their...

Unlike the classical deterministic digital circuit analysis, we consider the analysis of uncertain digital circuits defined as follows. Given a binary function of n uncertain input binary variables, we express the probability of this binary function in terms of the probabilities of the corresponding input binary variables. This in turn, allows us to estimate appropriate probabilistic measure of...

In this paper, we study the linear fractional transportation problem with uncertain arameters. After recalling some definitions, concepts and theorems in uncertainty theory we present three approaches for solving this problem. First we consider the expected value of the objective function together with the expectation of satisfying constraints. Optimizing the expected value of the objective fun...

Unlike the classical deterministic digital circuit analysis, we consider a Monte Carlo simulation in the context of uncertain digital circuits. In other words, given a binary function of n uncertain input binary variables, we express the probability of this binary function in terms of the probabilities of the corresponding input binary variables. This in turn, allows us to estimate appropriate ...

This paper is concerned with optimization of uncertain stochastic systems, in which uncertainty is described by a total variation distance constraint between the measures induced by the uncertain systems and the measure induced by the nominal system, while the pay-off is a linear functional of the uncertain measure. Robustness at the abstract setting is formulated as a minimax game, in which th...

Shannnon entropy is an efficient tool to measure uncertain information. However, it cannot handle the more uncertain situation when the uncertainty is represented by basic probability assignment (BPA), instead of probability distribution, under the framework of Dempster Shafer evidence theory. To address this issue, a new entropy, named as Deng entropy, is proposed. The proposed Deng entropy is...

Description Logic Programs (DLP) is an expressive but tractable subset of OWL. In this paper, we study a rising but under-researched problem of learning DLP from uncertain data. Current research rarely explores the plentiful uncertain data populating the Semantic Web. We handle uncertain data in Inductive Logic Programming (ILP) framework by modifying the performance evaluation criteria. We ado...