CourseSpecifications
Valid as from the academic year 2024-2025

Capita Selecta in Soft Computing (C001719)

Course size
Credits 6.0(nominal values; actual values may depend on programme)
Study time 165 h

Course offerings and teaching methods in academic year 2024-2025
A (semester 2)
Dutch
Gent
Lecturers in academic year 2024-2025
Cornelis, Chris

lectureWE02

lecturer-in-charge

Offered in the following programmes in 2024-2025
Master of Science in Teaching in Science and Technology(main subject Mathematics)
Master of Science in Mathematics

crdts
66offeringAA

Teaching languages
Dutch
KeywordsFuzzy relations, fuzzy relational calculus, fuzzy topology, rough sets, machine learning
Position of the course
The concept of a relation is fundamental, in a sense that sometimes science is described as
the discovery of relations between objects, systems and structures. In this course we will givean overview of the recent developments in the classical relational calculus and its extension toimprecise relationships, the so-called fuzzy relational calculus. In parallel to defining andstudying the theoretical concepts, we will illustrate them in a number of practical contexts,including machine learning. The term soft computing refers to a collection of models forrepresenting and processing imprecise information. We will focus on two of them in particular,
namely fuzzy set theory and rough set theory.
Contents
1. Classical relational calculus
1.1 Basic concepts
1.2 Operations
1.3 Classical images
1.4 New images and their properties
1.5 Special relations
1.6 Classical composition
1.7 New compositions and their properties
1.8 Application: formal concept analysis and rough set theory, and their use for machinelearning and data analysis
2. Fuzzy relational calculus
2.1 Basic concepts
2.2 Operations
2.3 Classical fuzzy images
2.4 New images and their properties
2.5 Approximate equality and similarity
2.6 Classical fuzzy composition
2.7 New compositions and their properties
2.8 Application: fuzzy rough set theory, and their use for machine learning and data analysis
2.9 Other applications, for example in recommender systems, temporal reasoning, ...
3. Introduction to fuzzy topology
Initial competences(Approved)1A positive attitude w.r.t. a mathematical approach. Basic notions of fuzzy set theory are
introduced at the start of the course.
Final competences
1 The students should be familiar with fuzzy relational calculus and its applications.
2 They should be capable of initiating independent research in this area.
Conditions for credit contract
Access to this course unit via a credit contract is determined after successful competences assessment
Conditions for exam contract
This course unit cannot be taken via an exam contract
Teaching methods
LectureExtra information on the teaching methods
The learning material is provided in English.
Study material
Type: Slides
Name: Slides'
Indicative price: Free or paid by faculty
Optional: noAdditional information: The learning material is electronically available (free of charge), using the Ufora website.
References
E.E. Kerre, Fuzzy Sets and Approximate Reasoning, Xian Jiaotong University Press, 1998.
E.E. Kerre, Introduction to the Basic Principles of Fuzzy Set Theory and Some of its
Applications, Communication and Cognition, 1993.
S. Vluymans, Dealing with Imbalanced and Weakly Labelled Data in Machine Learning using
Fuzzy and Rough Set Methods, PhD thesis, 2018.
Course content-related study coachingStudents can ask questions during lectures or via e-mail.
Assessment moments
continuous assessment
Examination methods in case of periodic assessment during the first examination period
Examination methods in case of periodic assessment during the second examination period
Examination methods in case of permanent assessment
Participation, Assignment
Possibilities of retake in case of permanent assessment
examination during the second examination period is possible
Extra information on the examination methods
Project: individual or in group, in which the theory is applied to a specific application domain,with written report and oral presentation
Participation: presence and participation in discussions during class, preparing and presenting
selected exercises on the blackboard
Calculation of the examination markThe project counts for 10 points out of 20, just like the participation. A student should obtain atleast 50% for each part to be able to pass.

(Approved)2