Topic outline

  • General

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    • Faculty: Mathematics and Computer Science
    • Department: Mathematics
    • Target Audience : 2nd year Master 

    • Course title: Logique Algèbrique

    • Credit : 04

    • Coefficient : 02
    • Duration : 14 seasons
    • Hour: 1H30 courses and 1h30 TD
    • Instructor :  Dr Kheir Saadaoui
    • Contact : kheir.saadaoui@univ-msila.dz




  • Course objectives


    This course is designed to provide a deep dive into some of the foundational and advanced topics in mathematics that are essential for understanding complex systems and decision-making processes


  • Chapter I : Generalities on ordered sets and lattices.

    This chapter explores the foundational concepts of ordered sets and lattices. You'll learn about the structure of sets where order matters, such as how elements relate to each other in a hierarchy. We'll also delve into lattices, which are special ordered sets that allow us to find common ancestors and descendants of elements

  • Chapter II: Logic and Lukasiewicz Trivalent Algebras

    In this chapter, we investigate the fascinating world of logic beyond true and false. Łukasiewicz trivalent algebras introduce a third value: undetermined. This extension of classical logic helps us model scenarios where information is incomplete or uncertain

  • Chapter III: Generalities on fuzzy sets

    This chapter introduces fuzzy sets, which allow for a more nuanced classification of elements. Unlike classical sets with strict boundaries, fuzzy sets handle degrees of membership, making them ideal for dealing with uncertainty and imprecision in real-world situations.

  • Chapter IV: Tringular norms and triangular conorms

    Here, we delve into triangular norms (T-norms) and conorms (T-conorms), essential tools in fuzzy logic and probability theory. These operations extend the concepts of logical AND and OR to the realm of fuzzy sets

  • Chapter V: Representation of Lukasiewicz trivalent algebras by fuzzy sets.

    This chapter focuses on how fuzzy sets can represent the structures and operations of Łukasiewicz trivalent algebras

  • Tutorial Sessions