Abstract
Both parts of this paper form a survey on the close relationship between enriched category and fuzzy set theory and focuses on such fundamental axioms as reflexivity, transitivity, symmetry, antisymmetry. Part I (this is the present paper) deals with reflexivity and transitivity and develops the algebraic basis of many-valued preordered sets including their Cauchy completion. Further the change of base is explained which plays a fundamental role in many-valued mathematics. Part II (Hohle, Many-valued preorders II: the symmetry axiom and probabilistic geometry (in this volume) [1]) will treat the symmetry axiom and its applications to probabilistic geometry—a theory which can be viewed as a predecessor of fuzzy set theory.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
