In an earlier companion paper [56] a supervised learning neural network pattern classifier called the fuzzy min-max classification neural network was described. In this sequel, the unsupervised learning pattern clustering sibling called the fuzzy min-max clustering neural network is presented. Pattern clusters are implemented here as fuzzy sets using a membership function with a hyperbox core t...

Genetic algorithms are powerful tools that allow engineers and scientists to find good solutions to hard computational problems using evolutionary principles. The classic genetic algorithm has several disadvantages, however. Foremost among these drawbacks is the difficulty of choosing optimal parameter settings. Genetic algorithm literature is full of empirical tricks, techniques, and rules of ...

The real life problems deal with imperfectly specified knowledge and some degree of imprecision, uncertainty or inconsistency is embedded in the problem specification. The well-founded theory of fuzzy sets is a special way to model the uncertainty. The rules in a fuzzy model contain a set of propositions, each of which restricts a fuzzy variable to a single fuzzy value by means of the predicate...

The general fuzzy min-max neural network (GFMMN) is capable to perform the classification as well as clustering of the data. In addition to this it has the ability of learning in a very few passes with a very short training time. But like other artificial neural networks, GFMMN is also like a black box and expressed in terms of min-max values and associated class label. So the justification of ...

Fuzzy Description Logics (FDLs) combine classical Description Logics with the semantics of Fuzzy Logics in order to represent and reason with vague knowledge. Most FDLs using truth values from the interval [0, 1] have been shown to be undecidable in the presence of a negation constructor and general concept inclusions. One exception are those FDLs whose semantics is based on the infinitely valu...

Fuzzy Description Logics (FDLs) combine classical Description Logics with the semantics of Fuzzy Logics in order to represent and reason with vague knowledge. Most FDLs using truth values from the interval [0, 1] have been shown to be undecidable in the presence of a negation constructor and general concept inclusions. One exception are those FDLs whose semantics is based on the infinitely valu...

Fuzzy extractors (Dodis et al., Eurocrypt 2004) convert repeated noisy readings of a high-entropy secret into the same uniformly distributed key. A minimum condition for the security of the key is the hardness of guessing a value that is similar to the secret, because the fuzzy extractor converts such a guess to the key. We define fuzzy min-entropy to quantify this property of a noisy source of...

In this paper we introduce the Max-Min intuitionistic fuzzy matrix M (G) of an intuitionistic fuzzy graph. And the extreme energy of M (G) is defined. And also we give the explicit expression for the coefficients of the characteristic polynomial of M (G) . These concepts are illustrated with real time example. AMS Subject Classification: 03E72, 05C50

We consider the effect of the underlying logical structure on the asymptotic behavior of space-time diagrams of elementary Boolean cellular automata by focussing on the important case of Rule 110 and its counterparts under various many-valued logics. In particular we show that for a (continuous) probabilistic logic the corresponding rule, dubbed PCA 110, appears to have space-time diagrams with...

In 1965, in his pioneer paper L.A. Zadeh [9] introduced the concept of fuzzy set to handle the uncertainties in our daily life. After that many generalizations of fuzzy sets are presented, for example, interval valued fuzzy sets [10] and intuitionistic fuzzy sets [1]. Fuzzy sets are extremely useful to solve many problems in applied mathematics, information sciences and theory of automata [2]. ...