A neural network classifier is presented, which is based on geometrical fuzzy sets. Starting from the construction of the Voronoi diagram of the training patterns, an aggregation of Voronoi regions is performed leading to the identification of larger regions belonging exclusively to one of the pattern classes. The resulting scheme is a constructive algorithm that defines fuzzy clusters of patte...

In this paper, we use the interior-outer-set model to calculate the risk of crop flood and order farming alternatives for Huarong County, China, where only a small sample of eight observations is available. Any risk assessment from the data must be imprecise. The risk calculated by this suggested model is a particular case among imprecise probabilities, called possibility–probability distributi...

Multiplayer feedforward networks trained by minimizing the mean squared error and by using a one of c teaching function yield network outputs that estimate posterior class probabilities. This provides a sound basis for combining the results from multiple networks to get more accurate classification. This paper presents a method for combining multiple networks based on fuzzy logic, especially th...

—Let f be an interval-valued fuzzy subset of a nite set U of size n. This yields n closed intervals inside the unit interval. Picking a point in each interval and dividing by the sum of the points gives rise to a probability density on the set of intervals. For a given measure of dispersion, such as entropy, the problem is to pick points that maximize (or minimize) this dispersion. The particul...

What is fuzzy logic? Fuzzy logic is an extension of Boolean logic which allows intermediate values between True and False. As in Boolean logic, a true statement is expressed by the value “1” and a false statement by the value “0”. However, unlike in probability theory, the value must not be interpreted as a confidence level but rather as a Membership Function (MF). Therefore, every statement is...

In this paper we deal with the problem of obtaining the set of k-additive measures dominating a fuzzy measure. This problem extends the problem of deriving the set of probabilities dominating a fuzzy measure, an important problem appearing in Decision Making and Game Theory. The solution proposed in the paper follows the line developed by Chateauneuf and Jaffray for dominating probabilities and...

Hellinger distance is a distance between two additive measures defined in terms of the RadonNikodym derivative of these two measures. This measure proposed in 1909 has been used in a large variety of contexts. In this paper we define an analogous measure for fuzzy measures. We discuss them for distorted probabilities and give two examples.

Following [9] some properties of Q-probability and Q-states are studied. Representation theorem of Q-probabilities and Q-states, the existence of the joint observable and The central limit theorem are proved. Keywords—Q-probability, Q-state, representation theorem, intuitionistic fuzzy events, joint Q-observable, Central limit theorem.

The paper discusses integration in possibility theory, both in an ordinal and in a numerical (behavioral) context. It is shown that in an ordinal context, the fuzzy integral has an important part in at least three areas: the extension of possibility measures to larger domains, the construction of product measures from marginals and the definition of conditional possibilities. In a numerical (be...