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Program for generating fuzzy logical operations and its use in mathematical proofs

Tomáš Bartušek, Mirko Navara (2002)

Kybernetika

Fuzzy logic is one of the tools for management of uncertainty; it works with more than two values, usually with a continuous scale, the real interval [ 0 , 1 ] . Implementation restrictions in applications force us to use in fact a finite scale (finite chain) of truth degrees. In this paper, we study logical operations on finite chains, in particular conjunctions. We describe a computer program generating all finitely-valued fuzzy conjunctions ( t -norms). It allows also to select these t -norms according to...

(Pure) logic out of probability.

Ton Sales (1996)

Mathware and Soft Computing

Today, Logic and Probability are mostly seen as independent fields with a separate history and set of foundations. Against this dominating perception, only a very few people (Laplace, Boole, Peirce) have suspected there was some affinity or relation between them. The truth is they have a considerable common ground which underlies the historical foundation of both disciplines and, in this century, has prompted notable thinkers as Reichenbach [14], Carnap [2] [3] or Popper [12] [13] (and Gaifman [5],...

Qualitative reasoning in Bayesian networks.

Paolo Garbolino (1996)

Mathware and Soft Computing

Some probabilistic inference rules which can be compared with the inference rules of preferential logic are given and it will be shown how they work in graphical models, allowing qualitative plausible reasoning in Bayesian networks.

Quasi-hierarchical evolution algorithm for flow assignment in survivable connection-oriented networks

Michal Przewozniczek, Krzysztof Walkowiak (2006)

International Journal of Applied Mathematics and Computer Science

The main objective of this paper is to develop an effective evolutionary algorithm (EA) for the path-assignment problem in survivable connection-oriented networks. We assume a single-link failure scenario, which is the most common and frequently reported failure event. Since the network flow is modeled as a non-bifurcated multicommodity flow, the discussed optimization problem is NP-complete. Thus, we develop an effective heuristic algorithm based on an evolutionary algorithm. The main novelty of...

Rank of tensors of ℓ -out-of- k functions: An application in probabilistic inference

Jiří Vomlel (2011)

Kybernetika

Bayesian networks are a popular model for reasoning under uncertainty. We study the problem of efficient probabilistic inference with these models when some of the conditional probability tables represent deterministic or noisy ℓ -out-of- k functions. These tables appear naturally in real-world applications when we observe a state of a variable that depends on its parents via an addition or noisy addition relation. We provide a lower bound of the rank and an upper bound for the symmetric border rank...

Rationality of induced ordered weighted operators based on the reliability of the source of information in group decision-making

Francisco Chiclana, Francisco Herrera, Enrique Herrera-Viedma (2004)

Kybernetika

The aggregation of preference relations in group decision-making (GDM) problems can be carried out based on either the reliability of the preference values to be aggregated, as is the case with ordered weighted averaging operators, or on the reliability of the source of information that provided the preferences, as is the case with weighted mean operators. In this paper, we address the problem of aggregation based on the reliability of the source of information, with a double aim: a) To provide...

Realizations of Loops and Groups defined by short identities

Anthony Donald Keedwell (2009)

Commentationes Mathematicae Universitatis Carolinae

In a recent paper, those quasigroup identities involving at most three variables and of “length” six which force the quasigroup to be a loop or group have been enumerated by computer. We separate these identities into subsets according to what classes of loops they define and also provide humanly-comprehensible proofs for most of the computer-generated results.

Recherche à voisinage variable de graphes extrémaux 13. A propos de la maille

Mustapha Aouchiche, Pierre Hansen (2005)

RAIRO - Operations Research - Recherche Opérationnelle

Le système AutoGraphiX (AGX1 et AGX2) permet, parmi d’autres fonctions, la génération automatique de conjectures en théorie des graphes et, dans une version plus récente, la preuve automatique de conjectures simples. Afin d’illustrer ces fonctions et le type de résultats obtenus, nous étudions systématiquement ici des conjectures obtenues par ce système et de la forme b ̲ n ≤ g ⊕ i ≤ b ¯ n où g désigne la maille (ou longueur du plus petit cycle) du graphe G = ( V , E ) , i un autre invariant choisi parmi le nombre de stabilité,...

Recherche à voisinage variable de graphes extrémaux 13. à propos de la maille*

Mustapha Aouchiche, Pierre Hansen (2006)

RAIRO - Operations Research

Le système AutoGraphiX (AGX1 et AGX2) permet, parmi d'autres fonctions, la génération automatique de conjectures en théorie des graphes et, dans une version plus récente, la preuve automatique de conjectures simples. Afin d'illustrer ces fonctions et le type de résultats obtenus, nous étudions systématiquement ici des conjectures obtenues par ce système et de la forme b ̲ n ≤ g ⊕ i ≤ b ¯ n où g désigne la maille (ou longueur du plus petit cycle) du graphe G=(V, E), i un autre invariant choisi parmi le nombre...

Recognizing when heuristics can approximate minimum vertex covers is complete for parallel access to NP

Edith Hemaspaandra, Jörg Rothe, Holger Spakowski (2006)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

For both the edge deletion heuristic and the maximum-degree greedy heuristic, we study the problem of recognizing those graphs for which that heuristic can approximate the size of a minimum vertex cover within a constant factor of r , where r is a fixed rational number. Our main results are that these problems are complete for the class of problems solvable via parallel access to NP . To achieve these main results, we also show that the restriction of the vertex cover problem to those graphs for which...

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