Additive fuzzy systems can filter impulsive noise from signals. Alpha-stable statistics model the impulsiveness as a parametrized family of probability density functions or unit-area bell curves. The bell-curve parameter ct ranges through the interval (0, 2] and gives the Gaussian bell curve when 0t = 2 and gives the Cauchy bell curve when ~t = 1. The impulsiveness grows as ~ falls and the bell...

We propose an additive "semantic measure" theory based on the model of a perception based fuzzy truthoods in analogy to probability measure. Probability measure, which is the subject of the probability theory, is a special case of the fuzzy measure in the Dempster-Shafer theory when the focal sets are singletons. In the literature, the fuzzy measure is considered an extension of the probability...

To describe expert uncertainty, it is often useful to go beyond additive probability measures and use non-additive (fuzzy) measures. One of the most widely and successfully used class of such measures is the class of Sugeno λ-measures. Their success is somewhat paradoxical, since from the purely mathematical viewpoint, these measures are – in some reasonable sense – equivalent to probability me...

In this paper, we present a new fuzzy risk analysis method based on generalized fuzzy numbers. Firstly, we define new arithmetic operations between generalized fuzzy numbers. Then, we propose a new method to measure the degree of similarity between generalized fuzzy numbers. Finally, we apply the new arithmetic operations between generalized fuzzy numbers and proposed similarity measure to deve...

Both the fuzzy measure and integral have been widely studied for multi-source information fusion. A number of researchers have proposed optimization techniques to learn a fuzzy measure from training data. In part, this task is difficult as the fuzzy measure can have a large number of free parameters (2 − 2 for N sources) and it has many (monotonicity) constraints. In this paper, a new genetic a...

The main aim of this paper is to connect R-Fuzzy sets and type-2 fuzzy sets, so as to provide a practical means to express complex uncertainty without the associated difficulty of a type-2 fuzzy set. The paper puts forward a significance measure, to provide a means for understanding the importance of the membership values contained within an R-fuzzy set. The pairing of an R-fuzzy set and the si...

2 Zadeh-type fuzzy probability The paper deals with two methods of a fuzzification of the Borel field of events and too the probability measure. The first approach generalizes the Zadeh definition of a crisp probability of fuzzy event. The second method is based on the Yager definition of a fuzzy probability of fuzzy event. The theoretical results obtained can be applied to modeling stochastic ...