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
Fuzzy Sets and Systems
On approximate reasoning with graded rules
Fuzzy Sets and Systems
On the difference between traditional and deductive fuzzy logic
Fuzzy Sets and Systems
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
IFSA '07 Proceedings of the 12th international Fuzzy Systems Association world congress on Foundations of Fuzzy Logic and Soft Computing
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
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 Sets and Systems
Reasoning about mathematical fuzzy logic and its future
Fuzzy Sets and Systems
Graded properties of unary and binary fuzzy connectives
Fuzzy Sets and Systems
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The paper states the problem of fragmentation of contemporary fuzzy mathematics and the need of a unified methodology and formalism. We formulate several guidelines based on Hajek's methodology in fuzzy logic, which enable us to follow closely the constructions and methods of classical mathematics recast in a fuzzy setting. As a particular solution we propose a three-layer architecture of fuzzy mathematics, with the layers of formal fuzzy logic, a foundational theory, and individual mathematical disciplines developed within its framework. The ground level of logic being sufficiently advanced, we focus on the foundational level; the theory we propose for the foundations of fuzzy mathematics can be characterized as Henkin-style higher-order fuzzy logic. Finally, we give some hints on the further development of individual mathematical disciplines in the proposed framework, and proclaim it a research programme in formal fuzzy mathematics.