In this paper we present a simple belief updating system using recurrent fuzzy rules which improves class prediction in ordered datasets. The recurrent fuzzy rule builds up belief in a class for each point in a sample-ordered or timeordered dataset. Belief in each class is represented by a fuzzy set predicted class defined on the class universe. Belief in a class increases as positive cases are...

Since fuzzy numbers are not linearly ordered a median of a fuzzy sample cannot be determined directly as it happens with crisp observations. Even the very notion of a median of a fuzzy sample is not well established. Therefore we propose some definitions of the fixed-shape fuzzy median of a fuzzy sample as a member of a given class of fuzzy numbers which minimizes the distance to the sample. We...

The immune system has unique defense mechanisms such as innate, humoral and cellular immunity. These mechanisms are closely related to prevent pathogens from spreading in the host and to clear them effectively. To get a comprehensive understanding of the immune system, it is necessary to integrate the knowledge through modeling. Many immune models have been developed based on differential equat...

In one-class classification, the problem is to distinguish one class of data from the rest of the feature space. It is important in many applications where one of the classes is characterized well, while no measurements are available for the other class. Schölkopf et al. first introduced a method of adapting the support vector machine (SVM) methodology to the one-class classification problem, c...

In this article, we propose a fuzzy class relation assigning to each pair of finite fuzzy sets a degree to which they are equipollent, which indicates that they have the same number of elements. The concepts of fuzzy sets and fuzzy classes in the class of all countable sets are introduced, and several standard relations and constructions, such as the fuzzy power set and exponentiation, are defi...

We introduce the notion of an equational lifting monad: a commutative strong monad satisfying one additional equation (valid for monads arising from partial map classifiers). We prove that any equational lifting monad has a representation by a partial map classifier such that the Kleisli category of the former fully embeds in the partial category of the latter. Thus equational lifting monads pr...

The paper introduces a simple, yet powerful axiomatization of Zadeh’s notion of fuzzy set, based on formal fuzzy logic. The presented formalism is strong enough to serve as foundations of a large part of fuzzy mathematics. Its essence is elementary fuzzy set theory, cast as two-sorted first-order theory over fuzzy logic, which is generalized to simple type theory. We show a reduction of the ele...

Part I of this paper proposes a definition of the adaptive resonance theory (ART) class of constructive unsupervised on-line learning clustering networks. Class ART generalizes several well-known clustering models, e.g., ART 1, improved ART 1, adaptive Hamming net (AHN), and Fuzzy ART, which are optimized in terms of memory storage and/or computation time. Next, the symmetric Fuzzy ART (S-Fuzzy...

In this paper we present a new fuzzy reasoning method in which the Choquet integral is used as aggregation function. In this manner, we can take into account the interaction among the rules of the system. For this reason, we consider several fuzzy measures, since it is a key point on the subsequent success of the Choquet integral, and we apply the new method with the same fuzzy measure for all ...