Data are frequently not precise numbers but more or less non-precise, also called fuzzy. Moreover a-priori information in Bayesian inference is usually not available as a precise probability distribution. In case of fuzzy data and fuzzy a-priori information Bayes' theorem has to be generalized. There are different approaches for a generalization of Bayes' theorem but most of them don't keep the...

Recently Burusco introduced interval-valued fuzzy formal contexts into fuzzy formal concept analysis. The most interesting work mainly including fuzzy attribute implications from fuzzy formal context, however, were presented under the framework of residuated lattice. In this paper, we first show that the study of interval-valued fuzzy set can be fitted into the framework of residuated lattice. ...

In order to improve the approximation property of the past fuzzy clustering algorithms when identifying systems, a fuzzy clustering neural network (FCNN) is proposed and is applied to conjunction speech recognition system. Based on the fuzzy system model, FCNN presents every state as a fuzzy system and uses continuous frames as the system input. With improving fuzzy clustering identification al...

the traditional event tree analysis uses a single probability to represent each top event. however, it is unrealistic to evaluate the occurrence of each event by using a crisp value without considering the inherent uncertainty and imprecision a state has. the fuzzy set theory is universally applied to deal with this kind of phenomena. the main purpose of this study is to construct an easy metho...

This paper discusses some models of Imprecise Probability Theory obtained by propagating uncertainty in risk analysis when some input parameters are stochastic and perfectly observable, while others are either random or deterministic, but the information about them is partial and is represented by possibility distributions. Our knowledge about the probability of events pertaining to the output ...

Based on the point of view of geometrical representation of an intuitionistic fuzzy set, we take into account all three parameters describing intuitionistic fuzzy set, propose a kind of new method to calculate correlation and correlation coefficient of intuitionistic fuzzy sets which is similar to the cosine of the intersectional angle in finite sets and probability space, respectively. Further...

This paper considers the testing of fuzzy hypotheses on the basis of a Bayesian approach. For this, using a notion of prior distribution with interval or fuzzy-valued parameters, we extend a concept of posterior probability of a fuzzy hypothesis. Some of its properties are also put into investigation. The feasibility and effectiveness of the proposed methods are also cla...

The notion of fuzzy sets has proven useful in the context of control theory, pattern recognition, and medical diagnosis. However, it has also spawned the view that classical probability theory is unable to deal with uncertainties in natural language and machine learning, so that alternatives to probability are needed. One such alternative is what is known as “possibility theory.” Such alternati...

We prove that three independent fuzzy systems can uniformly approximate Bayesian posterior probability density functions by approximating the prior and likelihood probability densities as well as the hyperprior probability densities that underly the priors. This triply fuzzy function approximation extends the recent theorem for uniformly approximating the posterior density by approximating just...