The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform

Hichem Benelmechaiekh - One of the best experts on this subject based on the ideXlab platform.

  • the ran reurings fixed point theorem without partial order a simple proof
    Journal of Fixed Point Theory and Applications, 2014
    Co-Authors: Hichem Benelmechaiekh
    Abstract:

    The purpose of this note is to generalize the celebrated Ran–Reurings fixed point theorem to the setting of a space with a Binary Relation that is only transitive (and not necessarily a partial order) and a Relation-complete metric. The arguments presented here are simple and straightforward. It is also shown that extensions by Rakotch and by Hu and Kirk of Edelstein’s generalization of the Banach contraction principle to local contractions on chainable complete metric spaces are derived from the Ran–Reurings theorem.

  • the ran reurings fixed point theorem without partial order a simple proof
    arXiv: General Topology, 2014
    Co-Authors: Hichem Benelmechaiekh
    Abstract:

    The purpose of this note is to generalize the celebrated Ran and Reurings fixed point theorem to the setting of a space with a Binary Relation that is only transitive (and not necessarily a partial order) and a Relation-complete metric. The arguments presented here are simple and straightforward. It is also shown that extensions by Rakotch and Hu-Kirk of Edelstein's generalization of the Banach contraction principle to local contractions on chainable complete metric spaces derive from the theorem of Ran-Reurings.

Petros Hadjicostas - One of the best experts on this subject based on the ideXlab platform.

Samir Elloumi - One of the best experts on this subject based on the ideXlab platform.

  • using minimal generators for composite isolated point extraction and conceptual Binary Relation coverage
    Information Sciences, 2016
    Co-Authors: Samir Elloumi, Fethi Ferjani, Ali Jaoua
    Abstract:

    We present a new approach called "MinGenCoverage" for conceptual Binary Relation covering.We start by locating the isolated points and we extract their corresponding mandatory concepts.In case of properties composition, we consider only the minimal generators as candidates for isolated point extraction.We applied our approach for textual data and we considered the concept's labels associated to isolated points as the selected textual features. In recent years, several mathematical concepts have been successfully explored in the computer science domain as a basis for finding original solutions for complex problems related to knowledge engineering, data mining, and information retrieval. Hence, Relational algebra (RA) and formal concept analysis (FCA) may be considered as useful mathematical foundations that unify data and knowledge into information retrieval systems. For example, some elements in a fringe Relation (related to the (RA) domain) called isolated points have been successfully used in FCA as formal concept labels or composite labels. Once associated with words in a textual document, these labels constitute relevant features of a text. This paper proposes the MinGenCoverage algorithm for covering a Formal Context (as a formal representation of a text) based on isolated labels and using these labels (or text features) for categorization, corpus structuring, and micro-macro browsing as an advanced information retrieval functionality. The main thrust of the approach introduced here relies heavily on the close connection between isolated points and minimal generators (MGs). MGs stand at the antipodes of the closures within their respective equivalence classes. By using the fact that the minimal generators are the smallest elements within an equivalence class, their detection and traversal is greatly eased and the coverage can be swiftly built. Extensive experiments provide empirical evidence for the performance of the proposed approach.

  • formal context coverage based on isolated labels an efficient solution for text feature extraction
    Information Sciences, 2012
    Co-Authors: Fethi Ferjani, Sahar Ismail, Samir Elloumi, Sadok Ben Yahia, Ali Jaoua, Sheikha Ravan
    Abstract:

    Different available data as images, texts, or database may be mapped into an equivalent or approximate Binary Relation. A text may be considered as a Binary Relation relating sentences to words, while a numerical table may be represented by a Binary Relation after using some scaling approach. A social network may be also represented by a formal context. The objective of this paper is to present an original approach for covering a Binary Relation by formal concepts based on isolated single or multiple properties, i.e., those belonging to only one concept. As a matter of fact, isolated properties are efficiently used for discriminating and labeling concepts. The latter are used for browsing in a corpora, or in a document by navigating through associated labels. By using fringe Relations, the presented approach compared to those of the literature has the advantage of offering a relevant feature of a context by significant labels. Carried out experiments show the benefits of the introduced approach.

  • galois connection formal concepts and galois lattice in real Relations application in a real classifier
    Journal of Systems and Software, 2002
    Co-Authors: Ali Jaoua, Samir Elloumi
    Abstract:

    In this paper, we introduce the notion of a real set as an extension of a crisp and a fuzzy set by using sequences of intervals as membership degrees, instead of a single value in [0,1]. We also propose, to extend the notion of Galois connection in a real Binary Relation as well as the notions of rectangular Relation, formal concept and Galois lattice. We present finally a real classifier based on this mathematical foundation.

  • galois connection in fuzzy Binary Relations applications for discovering association rules and decision making
    RelMiCS, 2000
    Co-Authors: Ali Jaoua, Samir Elloumi, Faisal Alvi, Sadok Ben Yahia
    Abstract:

    Galois connection in crisp Binary Relations has proved to be useful for several applications in computer science. Unfortunately, data is not always presented as a crisp Binary Relation but may be composed of fuzzy values, thus forming a fuzzy Binary Relation. This paper aims at defining the notion of fuzzy galois connection corresponding to a fuzzy Binary Relation in two steps: firstly by defining the term fuzzy maximal rectangle and secondly, by extending the galois lattice structure to fuzzy Binary Relations. Applications concerning discovery of fuzzy association rules and decision making are also presented.

Ali Jaoua - One of the best experts on this subject based on the ideXlab platform.

  • using minimal generators for composite isolated point extraction and conceptual Binary Relation coverage
    Information Sciences, 2016
    Co-Authors: Samir Elloumi, Fethi Ferjani, Ali Jaoua
    Abstract:

    We present a new approach called "MinGenCoverage" for conceptual Binary Relation covering.We start by locating the isolated points and we extract their corresponding mandatory concepts.In case of properties composition, we consider only the minimal generators as candidates for isolated point extraction.We applied our approach for textual data and we considered the concept's labels associated to isolated points as the selected textual features. In recent years, several mathematical concepts have been successfully explored in the computer science domain as a basis for finding original solutions for complex problems related to knowledge engineering, data mining, and information retrieval. Hence, Relational algebra (RA) and formal concept analysis (FCA) may be considered as useful mathematical foundations that unify data and knowledge into information retrieval systems. For example, some elements in a fringe Relation (related to the (RA) domain) called isolated points have been successfully used in FCA as formal concept labels or composite labels. Once associated with words in a textual document, these labels constitute relevant features of a text. This paper proposes the MinGenCoverage algorithm for covering a Formal Context (as a formal representation of a text) based on isolated labels and using these labels (or text features) for categorization, corpus structuring, and micro-macro browsing as an advanced information retrieval functionality. The main thrust of the approach introduced here relies heavily on the close connection between isolated points and minimal generators (MGs). MGs stand at the antipodes of the closures within their respective equivalence classes. By using the fact that the minimal generators are the smallest elements within an equivalence class, their detection and traversal is greatly eased and the coverage can be swiftly built. Extensive experiments provide empirical evidence for the performance of the proposed approach.

  • formal context coverage based on isolated labels an efficient solution for text feature extraction
    Information Sciences, 2012
    Co-Authors: Fethi Ferjani, Sahar Ismail, Samir Elloumi, Sadok Ben Yahia, Ali Jaoua, Sheikha Ravan
    Abstract:

    Different available data as images, texts, or database may be mapped into an equivalent or approximate Binary Relation. A text may be considered as a Binary Relation relating sentences to words, while a numerical table may be represented by a Binary Relation after using some scaling approach. A social network may be also represented by a formal context. The objective of this paper is to present an original approach for covering a Binary Relation by formal concepts based on isolated single or multiple properties, i.e., those belonging to only one concept. As a matter of fact, isolated properties are efficiently used for discriminating and labeling concepts. The latter are used for browsing in a corpora, or in a document by navigating through associated labels. By using fringe Relations, the presented approach compared to those of the literature has the advantage of offering a relevant feature of a context by significant labels. Carried out experiments show the benefits of the introduced approach.

  • galois connection formal concepts and galois lattice in real Relations application in a real classifier
    Journal of Systems and Software, 2002
    Co-Authors: Ali Jaoua, Samir Elloumi
    Abstract:

    In this paper, we introduce the notion of a real set as an extension of a crisp and a fuzzy set by using sequences of intervals as membership degrees, instead of a single value in [0,1]. We also propose, to extend the notion of Galois connection in a real Binary Relation as well as the notions of rectangular Relation, formal concept and Galois lattice. We present finally a real classifier based on this mathematical foundation.

  • galois connection in fuzzy Binary Relations applications for discovering association rules and decision making
    RelMiCS, 2000
    Co-Authors: Ali Jaoua, Samir Elloumi, Faisal Alvi, Sadok Ben Yahia
    Abstract:

    Galois connection in crisp Binary Relations has proved to be useful for several applications in computer science. Unfortunately, data is not always presented as a crisp Binary Relation but may be composed of fuzzy values, thus forming a fuzzy Binary Relation. This paper aims at defining the notion of fuzzy galois connection corresponding to a fuzzy Binary Relation in two steps: firstly by defining the term fuzzy maximal rectangle and secondly, by extending the galois lattice structure to fuzzy Binary Relations. Applications concerning discovery of fuzzy association rules and decision making are also presented.

Phayap Katchang - One of the best experts on this subject based on the ideXlab platform.

  • fixed point result and applications on a b metric space endowed with an arbitrary Binary Relation
    Fixed Point Theory and Applications, 2013
    Co-Authors: Wutiphol Sintunavarat, Somyot Plubtieng, Phayap Katchang
    Abstract:

    In this paper, we introduce the concept of q-set-valued α-quasi-contraction mapping and establish the existence of a fixed point theorem for this mapping in b-metric spaces. Our results are generalizations and extensions of the result of Aydi et al. (Fixed Point Theory Appl. 2012:88, 2012) and some recent results. We also state some illustrative examples to claim that our results properly generalize some results in the literature. Further, by applying the main results, we investigate a fixed point theorem in a b-metric space endowed with an arbitrary Binary Relation. At the end of this paper, we give open problems for further investigation. MSC: 47H10; 54H25