CourseSpecifications
Valid as from the academic year 2024-2025

Mathematical Modelling of Fuzziness (C004370)

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 1)
Dutch
Gent

Lecturers in academic year 2024-2025
Cornelis, Chris

lectureseminar

WE02

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

lecturer-in-charge
crdts
66offeringAA

Teaching languagesDutch
Keywords
Order structures, algebraic structures for many-valued logics, fuzzy logic, fuzzy sets, calculusof fuzzy quantities, fuzzy inference
Position of the course
Many complex problems cannot be solved by a sharp analysis based on classical logic and thecorresponding set theory. In case of increasing complexity a level is quickly reached above
which accuracy and relevance counteract each other. A possible solution to these problems isto abandon the idea of accuracy and allow imprecision and partial certainties. The scientific
literature of the last decade introduces many new models for representing imprecision anduncertainty. The most important of these is the theory of fuzzy sets. The usefulness of thistheory is confirmed by the massive demand for patents by Japanese companies for products
based on fuzzy set theory. In this course we will introduce the basic principles and discuss
some applications of this new theory, and thus introduce the student to a recent domain of
applicable mathematics.
Contents• Auxiliary order and algebraic structures (poset, lattice, Boolean algebra, Morgan algebra, ...)
• Logical operators on the unit interval (negators, triangular norms and conorms, implicators)• Algebraic structures for many-valued logic calculi (residuated lattices, MTL algebra's, BL• algebra's, MV algebra's, Heyting algebra's)• Formal fuzzy logic• Fuzzy sets, flou sets and L-fuzzy sets
• Calculus of fuzzy quantities and fuzzy numbers• Degree of inclusion, similarity and fuzziness• Fuzzy quantifiers• Possibility theory and fuzzy inference
Initial competences
No particular mathematical prerequisites. Obviously a positive attitude towards mathematics
and formal logic is needed.
Final competences
1 Students should be familiar with the basic concepts and techniques from fuzzy set theory
1 and related models of uncertainty among them L-fuzzy set theory and flou set theory.
2 Students should be ready to start more advanced courses offered in the master of computer1 science and the master of applied mathematics.
(Approved)

1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
Seminar, Lecture
Extra information on the teaching methods
The theory is taught during the lectures. During the labs, the students solve exercises with thehelp of a teaching assistant. For the independent work, the students prepare an exercise or atheoretical topic and present it during class.
Study material
Type: Syllabus
Name: Fuzziness and Uncertainty Modelling: course notes
Indicative price: Free or paid by faculty
Optional: noReferences• E.E. Kerre: Introduction to the Basic Principles of Fuzzy Set Theory and Some of its• Applications, second revised edition. Communication & Cognition, Gent (1993).
• E.P. Klement, R. Mesiar, E. Pap, Triangular Norms, Kluwer Academic Publishers (2000).
Course content-related study coachingStudents actively process the learning material while making exercises in the presence of ateaching assistant. Furthermore students can submit their solutions for additional exercises toget feedback from the assistant or the instructor. The assistant and the instructor are alsoavailable to students for additional individual explanation outside of the scheduled class times.
Assessment moments
end-of-term and continuous assessment
Examination methods in case of periodic assessment during the first examination period
Written assessment
Examination methods in case of periodic assessment during the second examination period
Written assessment
Examination methods in case of permanent assessment
Assignment
Possibilities of retake in case of permanent assessment
not applicableCalculation of the examination mark
Combination of non-periodical evaluation (written report and oral presentation of theassignment, i.e. 40% of the final score) and periodical evaluation (written exam, i.e. 60% of thefinal score).
To be able to pass, a student should obtain a score of at least 10/20 for the exam.

(Approved)2