The belief noisy-or model applied to network reliability analysis

One difficulty faced in knowledge engineering for Bayesian Network (BN) is the quan-tification step where the Conditional Probability Tables (CPTs) are determined. The number of parameters included in CPTs increases exponentially with the number of parent variables. The most common solution is the application of the so-called canonical gates. The Noisy-OR (NOR) gate, which takes advantage of the independence of causal interactions, provides a logarithmic reduction of the number of parameters required to specify a CPT. In this paper, an extension of NOR model based on the theory of belief functions, named Belief Noisy-OR (BNOR), is proposed. BNOR is capable of dealing with both aleatory and epistemic uncertainty of the network. Compared with NOR, more rich information which is of great value for making decisions can be got when the available knowledge is uncertain. Specially, when there is no epistemic uncertainty, BNOR degrades into NOR. Additionally, different structures of BNOR are presented in this paper in order to meet various needs of engineers. The application of BNOR model on the reliability evaluation problem of networked systems demonstrates its effectiveness

GRANULAR-INFORMATION-BASED RISK ANALYSIS IN UNCERTAIN SITUATIONS

In the real life almost all of the decisions that we have to make incorporate uncertainty about the future events. Assessment of the uncertainty and, thus, the risk that is inherent in these decisions models can be critical. It is even truer if we are talking about the possibility of negative impact on the environment. It is very important to assess all the environmental risks in a project if there is any hazard to the environment. In this paper the possibility of using granular information is considered. The main advantage of the granular information is that it can be used to assess risks in situations when information about future events is incomplete and imprecise. Moreover, we can use natural language to describe the problem area, as granular information paradigm uses both fuzzy and probabilistic information. We propose to use entropy as the measure of uncertainty. However, the definition of entropy should be generalised, as values of probabilities, upon which the calculation of entropy is based on, are interval-valued. We propose several possibilities of generalizing the definition of entropy. Furthermore, we analyse these approaches to see whether the additivity feature holds for the generalized entropy

INTRODUCTION TO NEUTROSOPHIC MEASURE, NEUTROSOPHIC INTEGRAL, AND NEUTROSOPHIC PROBABILITY

Neutrosophic Science means development and applications of neutrosophic logic/set/measure/integral/probability etc. and their applications in any field

Fusion of imprecise qualitative information

In this paper, we present a new 2-tuple linguistic representation model, i.e. Distribution Function Model (DFM), for combining imprecise qualitative information using fusion rules drawn from Dezert-Smarandache Theory (DSmT) framework. Such new approach allows to preserve the precision and efficiency of the combination of linguistic information in the case of either equidistant or unbalanced label model. Some basic operators on imprecise 2-tuple labels are presented together with their extensions for imprecise 2-tuple labels. We also give simple examples to show how precise and imprecise qualitative information can be combined for reasoning under uncertainty. It is concluded that DSmT can deal efficiently with both precise and imprecise quantitative and qualitative beliefs, which extends the scope of this theory

A Fuzzy Petri Nets Model for Computing With Words

Motivated by Zadeh's paradigm of computing with words rather than numbers, several formal models of computing with words have recently been proposed. These models are based on automata and thus are not well-suited for concurrent computing. In this paper, we incorporate the well-known model of concurrent computing, Petri nets, together with fuzzy set theory and thereby establish a concurrency model of computing with words--fuzzy Petri nets for computing with words (FPNCWs). The new feature of such fuzzy Petri nets is that the labels of transitions are some special words modeled by fuzzy sets. By employing the methodology of fuzzy reasoning, we give a faithful extension of an FPNCW which makes it possible for computing with more words. The language expressiveness of the two formal models of computing with words, fuzzy automata for computing with words and FPNCWs, is compared as well. A few small examples are provided to illustrate the theoretical development.Comment: double columns 14 pages, 8 figure