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Towards an extension of the 2-tuple linguistic model to deal with unbalanced linguistic term sets

Mohammed-Amine Abchir, Isis Truck (2013)

Kybernetika

In the domain of Computing with words (CW), fuzzy linguistic approaches are known to be relevant in many decision-making problems. Indeed, they allow us to model the human reasoning in replacing words, assessments, preferences, choices, wishes... by ad hoc variables, such as fuzzy sets or more sophisticated variables. This paper focuses on a particular model: Herrera and Martínez' 2-tuple linguistic model and their approach to deal with unbalanced linguistic term sets. It is interesting since the...

Towards the automated synthesis of a Gröbner bases algorithm.

Bruno Buchberger (2004)

RACSAM

We discuss the question of whether the central result of algorithmic Gröbner bases theory, namely the notion of S?polynomials together with the algorithm for constructing Gröbner bases using S?polynomials, can be obtained by ?artificial intelligence?, i.e. a systematic (algorithmic) algorithm synthesis method. We present the ?lazy thinking? method for theorem and algorithm invention and apply it to the ?critical pair / completion? algorithm scheme. We present a road map that demonstrates that, with...

Trajectory tracking for a mobile robot with skid-slip compensation in the Vector-Field-Orientation control system

Maciej Michałek, Piotr Dutkiewicz, Marcin Kiełczewski, Dariusz Pazderski (2009)

International Journal of Applied Mathematics and Computer Science

The article is devoted to a motion control problem for a differentially driven mobile robot in the task of trajectory tracking in the presence of skid-slip effects. The kinematic control concept presented in the paper is the Vector Field Orientation (VFO) feedback approach with a nonlinear feed-forward skid-slip influence compensation scheme. The VFO control law guarantees asymptotic convergence of the position tracking error to zero in spite of the disturbing influence of skid-slip phenomena. The...

Transition of Consistency and Satisfiability under Language Extensions

Julian J. Schlöder, Peter Koepke (2012)

Formalized Mathematics

This article is the first in a series of two Mizar articles constituting a formal proof of the Gödel Completeness theorem [17] for uncountably large languages. We follow the proof given in [18]. The present article contains the techniques required to expand formal languages. We prove that consistent or satisfiable theories retain these properties under changes to the language they are formulated in.

Transitive decomposition of fuzzy preference relations: the case of nilpotent minimum

Susana Díaz, Susana Montes, Bernard De Baets (2004)

Kybernetika

Transitivity is a fundamental notion in preference modelling. In this work we study this property in the framework of additive fuzzy preference structures. In particular, we depart from a large preference relation that is transitive w.r.t. the nilpotent minimum t-norm and decompose it into an indifference and strict preference relation by means of generators based on t-norms, i. e. using a Frank t-norm as indifference generator. We identify the strongest type of transitivity these indifference and...

Two operations of merging and splitting components in a chain graph

Milan Studený, Alberto Roverato, Šárka Štěpánová (2009)

Kybernetika

In this paper we study two operations of merging components in a chain graph, which appear to be elementary operations yielding an equivalent graph in the respective sense. At first, we recall basic results on the operation of feasible merging components, which is related to classic LWF (Lauritzen, Wermuth and Frydenberg) Markov equivalence of chain graphs. These results are used to get a graphical characterisation of factorisation equivalence of classic chain graphs. As another example of the use...

Twofold integral and multi-step Choquet integral

Yasuo Narukawa, Vicenç Torra (2004)

Kybernetika

In this work we study some properties of the twofold integral and, in particular, its relation with the 2-step Choquet integral. First, we prove that the Sugeno integral can be represented as a 2-step Choquet integral. Then, we turn into the twofold integral studying some of its properties, establishing relationships between this integral and the Choquet and Sugeno ones and proving that it can be represented in terms of 2-step Choquet integral.

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