Monadic Power Set Theories in Kleisli Categories

DOI

10.2991/asum.k.210827.002How to use a DOI?

Keywords

Lattice-valued fuzzy sets, categoris, monad theory, Kleisli categories

Abstract

In this paper, we follow up on the well-known interpretation of fuzzy relations as morphisms in Kleisli category defined in the category of sets using a suitable monad. This Kleisli category thus becomes a relational variant of the classical category of fuzzy sets. This interpretation and the associated construction of, e.g., various transformation operators, is often used not only in fuzzy set theory but also in computer science. Using this principle we create in the paper a relational variant of a given Kleisli category which will be defined again using a suitable monad in the original Kleisli category.

Copyright

© 2021, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Jiří Močkoř
PY  - 2021
DA  - 2021/08/30
TI  - Monadic Power Set Theories in Kleisli Categories
BT  - Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)
PB  - Atlantis Press
SP  - 9
EP  - 16
SN  - 2589-6644
UR  - https://doi.org/10.2991/asum.k.210827.002
DO  - 10.2991/asum.k.210827.002
ID  - Močkoř2021
ER  -