From fuzzy logic to fuzzy mathematics: A methodological manifesto

Libor Běhounek, Petr Cintula
2006 Fuzzy sets and systems (Print)  
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 Hájek'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
more » ... 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.
doi:10.1016/j.fss.2005.10.011 fatcat:4zezmbqspzdbzhjx5qrhbeea5a