Course: Fuzzy Logic

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Course title Fuzzy Logic
Course code KMI/PGSFL
Organizational form of instruction Lecture
Level of course Doctoral
Year of study not specified
Semester Winter and summer
Number of ECTS credits 12
Language of instruction Czech, English
Status of course unspecified
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • Vychodil Vilém, doc. RNDr. Ph.D.
Course content
Structures of truth degrees: Residuated lattices and their properties. Subclasses of residuated lattices given by identities: MTL-algebras, BL-algebras, MV-algebras, G-algebras, Pi-algebras, and others. Filters on residuated lattices. Subdirect representation of MTL and BL-algebras. Propositional BL-logic and its schematic extensions: Language of BL-logic, formulas, axiomatic systems. Derived logical connectives. Provability, deduction theorem. Soundness and completeness of BL-logic. Schematic extensions, Lukasiewicz logic, Goedel logic, product logic, and their standard completeness. Pavelka's abstract logic: Logic with truth-weighted syntax. Theories as fuzzy sets of formulas. Truth-weighted proofs and provability degrees. General concepts of soundness and completeness in Pavelka-style logics. Examples of Pavelka-complete calculi: propositional Pavelka Rational Logic (RPL) and its completeness (via BL). Predicate BL-logic and further logics: Fuzzy structures and safe interpretations. Completeness of predicate BL-logic. Propositional and predicate MTL-logic. Extension of fuzzy logics by unary connectives (Baaz's delta connective). Fuzzy logic vs. modalities and generalized quantifiers. Fuzzy logic calculi over restricted types of formulas: fuzzy equational logic, fuzzy horn logic, logic of fuzzy attribute implications. Fuzzy structures and their properties: Fuzzy sets and fuzzy relations (in naive sense) as particular fuzzy structures. Properties of fuzzy structures. Representation of fuzzy structures by classical sets (cutlike representation). Special fuzzy relations: similarity and fuzzy equality. Compatibility and similarity preservation. Cutlike semantics.

Learning activities and teaching methods
Lecture, Demonstration
  • Preparation for the Exam - 120 hours per semester
Learning outcomes
The students become familiar with basic concepts of fuzzy logic.
1. Knowledge Describe and understand comprehensively principles and methods of fuzzy logic.

Assessment methods and criteria
Oral exam, Written exam

Active participation in class. Completion of assigned homeworks. Passing the oral (or written) exam.
Recommended literature
  • Bělohlávek R. (2002). Fuzzy Relational Systems: Foundations and Principles. NY: Kluwer Academic/Plenum Press (Vol.20 of IFSR Int. Series on Systems Science and Engineering).
  • Bělohlávek R., Vychodil V. (2005). Fuzzy Equational Logic. Springer-Verlag.
  • Gerla G. (2001). Fuzzy Logic. Mathematical Tools for Approximate Reasoning. Kluwer, Dordrecht.
  • Gottwald S. (2001). A Treatise on Many-Valued Logics. Taylor & Francis Group.
  • Hájek P. (1998). Metamathematics of Fuzzy Logic. Kluwer, Dordrecht.
  • Klement E. P., Mesiar R., Pap E. (2000). Triangular Norms. Kluwer, Dordrecht.
  • Klir G. J., Yuan B. (1995). Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester