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Publication# Lukasiewicz fuzzy logic networks and their ultra low power hardware implementation

Abstract

In this paper, we propose a new category of current-mode Łukasiewicz OR and AND logic neurons and ensuing logic networks along with their ultra-low power realization. The introduced circuits can operate in a wide range of the input signals varying in-between 10 nA and 10 mA. For low current values the operating point of transistors is set in the under threshold region. In this region, the mismatch between transistors exhibits a far stronger impact on the current mirror precision than the one observed in case of the strong inversion region. The proposed design alleviates this problem by reducing the number of current mirrors between the input and the output of the neuron and of the overall network to only one. Łukasiewicz operators require only summation and subtraction operations, which make them suitable for realization in analog current-mode technique. In this case even large number of input signals can be summed in a simple junction in a single step. This is the reason of choosing Łukasiewicz operations in the proposed circuit. Using other t-norm and t-conorm operations with multiplication and division operations would make the realization of the circuit very difficult and inefficient.

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Related concepts (37)

Related publications (35)

Related MOOCs (4)

Łukasiewicz logic

In mathematics and philosophy, Łukasiewicz logic (ˌluːkəˈʃɛvɪtʃ , wukaˈɕɛvitʂ) is a non-classical, many-valued logic. It was originally defined in the early 20th century by Jan Łukasiewicz as a three-valued modal logic; it was later generalized to n-valued (for all finite n) as well as infinitely-many-valued (א0-valued) variants, both propositional and first order. The א0-valued version was published in 1930 by Łukasiewicz and Alfred Tarski; consequently it is sometimes called the ŁukasiewiczTarski logic.

T-norm

In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary operation used in the framework of probabilistic metric spaces and in multi-valued logic, specifically in fuzzy logic. A t-norm generalizes intersection in a lattice and conjunction in logic. The name triangular norm refers to the fact that in the framework of probabilistic metric spaces t-norms are used to generalize the triangle inequality of ordinary metric spaces.

Order of operations

In mathematics and computer programming, the order of operations (or operator precedence) is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression. For example, in mathematics and most computer languages, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. Thus, the expression 1 + 2 × 3 is interpreted to have the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9.

Electronics

Introduction à l’électronique analogique- seconde partie. Fonctions linéaires de base réalisée à l’aide de transistor bipolaire.

Electronics

Introduction à l’électronique analogique- seconde partie. Fonctions linéaires de base réalisée à l’aide de transistor bipolaire.

Electrical Engineering I

Découvrez les circuits électriques linéaires. Apprenez à les maîtriser et à les résoudre, dans un premier temps en régime continu puis en régime alternatif.

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