From 0705dd41d0c66269b8b97d2144064e58423b489c Mon Sep 17 00:00:00 2001 From: couturie Date: Thu, 28 Feb 2019 13:35:00 +0100 Subject: [PATCH] new --- book.tex | 1 + chapter2.tex | 103 +++++++++++++++++++++++++++++++++++++++++++++++++ references.tex | 14 ++++++- 3 files changed, 117 insertions(+), 1 deletion(-) create mode 100644 chapter2.tex diff --git a/book.tex b/book.tex index a63de23..e7afb00 100644 --- a/book.tex +++ b/book.tex @@ -62,6 +62,7 @@ \mainmatter%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \include{part} \include{chapter1} +\include{chapter2} \include{references} diff --git a/chapter2.tex b/chapter2.tex new file mode 100644 index 0000000..f3a2509 --- /dev/null +++ b/chapter2.tex @@ -0,0 +1,103 @@ +%%%%%%%%%%%%%%%%%%%%% chapter.tex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +% sample chapter +% +% Use this file as a template for your own input. +% +%%%%%%%%%%%%%%%%%%%%%%%% Springer-Verlag %%%%%%%%%%%%%%%%%%%%%%%%%% +%\motto{Use the template \emph{chapter.tex} to style the various elements of your chapter content.} +\chapter{From the founding situations of the SIA to its formalization} +\label{intro} % Always give a unique label +% use \chaptermark{} +% to alter or adjust the chapter heading in the running head + + + +\abstract{ +Starting from mathematical didactic situations, the implicitative +statistical analysis method develops as problems are encountered and +questions are asked. +Its main objective is to structure data crossing subjects and +variables, to extract inductive rules between variables and, based on +the contingency of these rules, to explain and therefore forecast in +various fields: psychology, sociology, biology, etc. +It is for this purpose that the concepts of intensity of implication, +class cohesion, implication-inclusion, significance of hierarchical +levels, contribution of additional variables, etc., are based. +Similarly, the processing of binary variables (e.g., descriptors) is +gradually being supplemented by the processing of modal, frequency +and, recently, interval and fuzzy variables. +} + +\section{Preamble} + +Human operative knowledge is mainly composed of two components: that +of facts and that of rules between facts or between rules themselves. +It is his learning that, through his culture and his personal +experiences, allows him to gradually develop these forms of knowledge, +despite the regressions, the questioning, the ruptures that arise at +the turn of decisive information. +However, we know that these dialectically contribute to ensuring a +balanced operation. +However, the rules are inductively formed in a relatively stable way +as soon as the number of successes, in terms of their explanatory or +anticipatory quality, reaches a certain level (of confidence) from +which they are likely to be implemented. +On the other hand, if this (subjective) level is not reached, the +individual's economy will make him resist, in the first instance, his +abandonment or criticism. +Indeed, it is costly to replace the initial rule with another rule +when a small number of infirmations appear, since it would have been +reinforced by a large number of confirmations. +An increase in this number of negative instances, depending on the +robustness of the level of confidence in the rule, may lead to its +readjustment or even abandonment. +Laurent Fleury~\cite{Fleury}, in his thesis, correctly cites the +example - which Régis repeats - of the highly admissible rule: "all +Ferraris are red". +This very robust rule will not be abandoned when observing a single or +two counter-examples. +Especially since it would not fail to be quickly +re-comforted. + +Thus, contrary to what is legitimate in mathematics, where not all +rules (theorem) suffer from exception, where determinism is total, +rules in the human sciences, more generally in the so-called "soft" +sciences, are acceptable and therefore operative as long as the number +of counter-examples remains "bearable" in view of the frequency of +situations where they will be positive and effective. +The problem in data analysis is then to establish a relatively +consensual numerical criterion to define the notion of a level of +confidence that can be adjusted to the level of requirement of the +rule user. +The fact that it is based on statistics is not surprising. +That it has a property of non-linear resistance to noise (weakness of +the first counter-example(s)) may also seem natural, in line with the +"economic" meaning mentioned above. +That it collapses if counter-examples are repeated also seems to have +to guide our choice in the modeling of the desired criterion. +This text presents the epistemological choice we have made. +As such it is therefore refutable, but the number of situations and +applications where it has proved relevant and fruitful leads us to +reproduce its genesis here. + +\section{Introduction} + +Different theoretical approaches have been adopted to model the +extraction and representation of imprecise (or partial) inference +rules between binary variables (or attributes or characters) +describing a population of individuals (or subjects or objects). +But the initial situations and the nature of the data do not change +the initial problem. +It is a question of discovering non-symmetrical inductive rules to +model relationships of the type "if a then almost b". +This is, for example, the option of Bayesian networks~\cite{Amarger} +or Galois lattices~\cite{Simon}. +But more often than not, however, since the correlation and the +${\chi}^2$ test are unsuitable because of their symmetric nature, +conditional probability~\cite{Loevinger, Agrawal,Grasn} remains the +driving force behind the definition of the association, even when the +index of this selected association is multivariate~\cite{Bernard}. + + + diff --git a/references.tex b/references.tex index 26edca9..cf0b0c2 100644 --- a/references.tex +++ b/references.tex @@ -33,6 +33,9 @@ \bibitem{Agrawal}Agrawal R., Imielinsky T. et Swami A (1993) Mining association rules between sets of items in large databases, Proc. of the ACM SIGMOD'93. + +\bibitem{Amarger} Amarger S., Dubois D. and Prade H. (1991) Imprecise quantifiers and conditional probabilities - in Symbolic and quantitative approaches to uncertainty (R. KRUSE, P. SIEGEL), Springer-Verlag, 33-37. + \bibitem{Atlana} Atlan H. (1986), A tort et à raison, Seuil. \bibitem{Atlanb} Atlan H. (2014) Croyances, Paris, Autrement. @@ -49,7 +52,7 @@ \bibitem{Benzecri} Benzecri, J.P. (1973) L’analyse des données (vol 1), Dunod, Paris. - +\bibitem{Bernard} Bernard J.-M. and Poitrenaud S. (1999) L'analyse implicative bayesienne d'un questionnaire binaire : quasi-implications et treillis de Galois simplifié", Mathématiques, Informatique et Sciences Humaines, n° 147, 1999, 25-46 \bibitem{Blanchard} Blanchard J., Guillet F. et Gras R. (2009) Analyse Implicative Séquentielle, Analyse Statistique Implicative, Une méthode d’analyse de données pour la recherche de causalités, dir. R.Gras, eds R.Gras, J.-C. Régnier, Guillet F. Cépaduès, Toulouse, p. 183-194. @@ -87,6 +90,9 @@ \bibitem{Espagnat} d’Espagnat B. (1981) A la recherche du réel, Le regard d’un physicien, Paris. + +\bibitem{Fleury} Fleury L. (1996) Extraction de connaissances dasn une base de données pour la gestion de ressources humaines, Thèse d’Université, Université de Nantes, 22 novembre 1996. + \bibitem{Foucault} Foucault M. (1966) Les mots et les choses, Éditions Gallimard, Paris. @@ -193,6 +199,9 @@ Cépaduès Ed. Toulouse, p. 195-208, ISBN: 978.2.36493.577.8. \bibitem{Levi-strauss} Lévi-Strauss C. (1967) Structures élémentaires de la parenté, De Gruyter Mouton. +\bibitem{Loevinger} Loevinger J. (1947), A systematic approach to the + construction and evaluation of tests of abilities, Psychological Monographs, 61, n° 4. + \bibitem{Marx} Marx K. (1857-1858) Manuscrits de 1857-1858. @@ -229,6 +238,9 @@ Cépaduès Ed. Toulouse, p. 195-208, ISBN: 978.2.36493.577.8. \bibitem{Schelling} Schelling F.-W. (1994) Philosophie de la mythologie, p.361, Paris, J. Millon \bibitem{Seve} Sève L. (2005) Émergence, complexité et dialectique, Paris. + + +\bibitem{Simon} Simon A. (2001),Outils classificatoires par objets pour l'extraction de connaissances dans des bases de données, Thèse de l'Université de Nancy 1. \bibitem{Shapin} Shapin S. (2014) Une histoire sociale de la vérité, La Découverte, Paris. -- 2.39.5