Fuzzy real numbers as Dedekind cuts with respect to a multiple-valued logic
Fuzzy Sets and Systems - Fuzzy Numbers
Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view
Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view
A similarity-based generalization of fuzzy orderings preserving the classical axioms
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
A development of set theory in fuzzy logic
Beyond two
From fuzzy logic to fuzzy mathematics: A methodological manifesto
Fuzzy Sets and Systems
Mathematical fuzzy logic as a tool for the treatment of vague information
Information Sciences—Informatics and Computer Science: An International Journal
On the difference between traditional and deductive fuzzy logic
Fuzzy Sets and Systems
A formal theory of intermediate quantifiers
Fuzzy Sets and Systems
Mathematical Fuzzy Logic: An Invitation to Interesting Research Areas
Fundamenta Informaticae - Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science. In Recognition of Professor Andrzej Grzegorczyk
Relations in Fuzzy Class Theory
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Solution of a system of linear equations with fuzzy numbers
Fuzzy Sets and Systems
Topology in Fuzzy Class Theory: Basic Notions
IFSA '07 Proceedings of the 12th international Fuzzy Systems Association world congress on Foundations of Fuzzy Logic and Soft Computing
Features of Mathematical Theories in Formal Fuzzy Logic
IFSA '07 Proceedings of the 12th international Fuzzy Systems Association world congress on Foundations of Fuzzy Logic and Soft Computing
Accuracy statistics for judging soft classification
International Journal of Remote Sensing
Relational compositions in Fuzzy Class Theory
Fuzzy Sets and Systems
From (Deductive) Fuzzy Logic to (Logic-Based) Fuzzy Mathematics
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Triangular norm based predicate fuzzy logics
Fuzzy Sets and Systems
Fuzzy logics with an additional involutive negation
Fuzzy Sets and Systems
Logical foundations of rule-based systems
Fuzzy Sets and Systems
Which logic is the real fuzzy logic?
Fuzzy Sets and Systems
From fuzzy logic to fuzzy mathematics: A methodological manifesto
Fuzzy Sets and Systems
Are fuzzy sets a reasonable tool for modeling vague phenomena?
Fuzzy Sets and Systems
Mathematical aspects of fuzzy sets and fuzzy logic
Fuzzy Sets and Systems
Mathematical fuzzy logic as a tool for the treatment of vague information
Information Sciences: an International Journal
Łukasiewicz logic and weighted logics over MV-semirings
Journal of Automata, Languages and Combinatorics
Reasoning about mathematical fuzzy logic and its future
Fuzzy Sets and Systems
Graded properties of unary and binary fuzzy connectives
Fuzzy Sets and Systems
Mathematical Fuzzy Logic: An Invitation to Interesting Research Areas
Fundamenta Informaticae - Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science. In Recognition of Professor Andrzej Grzegorczyk
| Hi-index | 0.21 |
The paper introduces a simple, yet powerful axiomatization of Zadeh's notion of fuzzy set, based on formal fuzzy logic. The presented formalism is strong enough to serve as foundations of a large part of fuzzy mathematics. Its essence is elementary fuzzy set theory, cast as two-sorted first-order theory over fuzzy logic, which is generalized to simple type theory. We show a reduction of the elementary fuzzy set theory to fuzzy propositional calculus and a general method of fuzzification of classical mathematical theories within this formalism. In this paper we restrict ourselves to set relations and operations that are definable without any structure on the universe of objects presupposed; however, we also demonstrate how to add structure to the universe of discourse within our framework.