A jilzzy layered neural network/or classification and rule generation is proposed using logical neurons. II can handle uncertainty and/or impreciseness in the input as well as the output. Logical operators, namely, t­ norm T and t-conorm S involving And and Or neurons, are employed in place of the weighted sum and sigmoid functions. Various/uzzy implication operators are introduced to incorpora...

We introduce a new way to visualize the behavior of aggregation operators based on the analogy with a balance. The use of an analogy permits an intuitive representation of the operator. This metaphor is enough general to include operators of the most common aggregation families. So we obtain a general framework, that allows us to compare the different existing operators. In this paper we will s...

In the traditional (static) fuzzy logic approach, we select an “and”-operation (tnorm) and an “or”-operation (t-conorm). The result of applying these selected operations may be somewhat different from the actual expert’s degrees of belief in the corresponding logical combinations A&B and A∨B of the original statements – since these degrees depend not only on the expert’s degrees of belief in st...

As a natural generalization of a probability space, Butnariu and Klement introduced T-tribes of fuzzy sets with probability T-measures. Their complete characterization was found for the case when T is a Frank t-norm. Here we characterize T-measures with respect to non-Frank strict t-norms. We show that Frank t-norms play a special role in these questions. 1 Generalization of probability spaces ...

is obvious, and then what always hold in the Mamdani's case is the equivalence (p 2 q ! r) = (p ! r) ^ (q ! r): (14) Consequently, if I is a Mamdani–Larsen's implication (8) never holds, but (14) is always true. IV. CONCLUSION After remembering the four main types of implications used in Fuzzy Logic, the equality [p ^ q ! r] = [(p ! r) _ (q ! r)] (*) is analyzed bot in complemented lattices and...

In this note, we show that if all Lyapunov exponents of a matrix cocycle vanish, then it can be perturbed to become cohomologous to a cocycle taking values in the orthogonal group. This extends a result of Avila, Bochi and Damanik to general base dynamics and arbitrary dimension. We actually prove a fibered version of this result, and apply it to study the existence of dominated splittings into...

In this report, we give an overview of a certain class of attacks on elliptic and hyperelliptic curve cryptography. The attacks we will discuss are only applicable if one considers discrete logarithms in class groups of elliptic or hyperelliptic curves over finite non-prime fields. Let us state the general idea of the class of attacks we will consider: Let H/K be a elliptic or hyperelliptic cur...

This paper is expository. It is mainly a survey of some of our work on the algebraic systems that arise in fuzzy set theory and logic. We include some of the proofs here and refer to the papers [18, 19, 20, 21, 22] for further details. Our point of view is the algebraic one: when are the various systems that arise isomorphic, and what are their symmetries (automorphisms)? The bulk of the materi...

At present time configurable wireless sensor networks are given special consideration. Wireless sensor networks are now a static elements union. To make such a network a powerful system that is able to replace traditional computers, research is required of the application of different theories and technologies for sensor network development. However, building models of approximate reasoning and...

Hyers-Ulam-Rassias stability have been studied in the contexts of several areas of mathematics. The concept of fuzziness and its extensions have been introduced to almost all branches of mathematics in recent times.Here we define the cubic functional equation in 2-variables and establish that Hyers-Ulam-Rassias stability holds for such equations in intuitionistic fuzzy Banach spaces.