Fuzzy sets and fuzzy relations 02 2024
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- Faculty: Mathematics and Computer Science
- Department: Mathematics
- Target Audience: 1st year Master
Course title: Fuzzy sets and fuzzy relations
Coefficient : 03
- Instructor: Dr Kheir Saadaoui
- Contact : kheir.saadaoui@univ-msila.dz
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The course aims to provide students with a solid understanding of fuzzy sets and fuzzy relations. Starting with classical sets, students will grasp fundamental set theory principles before transitioning to fuzzy sets, where degrees of membership introduce a new dimension of uncertainty. Building on this, the course delves into fuzzy relations, which extend binary relations to accommodate degrees of truthfulness
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This chapter serves as a foundational introduction to the concept of sets in classical mathematics. Classical sets are defined by crisp boundaries, where an element either belongs or does not belong to a set. Students will explore set notation, operations (union, intersection, complement), Venn diagrams, and basic set theory principles such as subsets and the universal set.
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In this chapter, students transition from classical sets to fuzzy sets, which allow for degrees of membership between 0 and 1. Fuzzy sets are characterized by their membership functions, which assign a degree of membership to each element in the universe of discourse. Students will learn about the representation, operations, and properties of fuzzy sets
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Building upon the concept of fuzzy sets, this chapter introduces fuzzy relations, which generalize binary relations to allow for degrees of truthfulness. Students will learn how to represent and define fuzzy relations, including equivalence relations, partial orders, and composition of fuzzy relations
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