At-least At-most Modifications in a Space with Fuzzy Preoreder

DOI

10.2991/eusflat.2013.97How to use a DOI?

Keywords

monotonous fuzzy rule base system of fuzzy relation equations ``at least'' (``at most'') quantifiers fuzzy preorder criterion of solvability

Abstract

In this paper, we utilize the theory of solvability of systems of fuzzy relation equations in a space with fuzzy preorder and propose a justification of solvability of the systems that are modified with ``at least'' (``at most'') quantifiers. We show that the respectively modified fuzzy sets are upper (lower) sets of a fuzzy preorder on the space of reals. On the basis of this, we show that the systems with the sup-* composition and with the same type of modifications on both sides are solvable. Moreover, we explain why the solvability of the similarly modified systems with the inf-> composition cannot be established. Last but not least we show that only opposite modifications on the left and right-hand sides of the modified system with the inf-> composition guarantee its solvability.

Copyright

© 2013, 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  - Irina Perfilieva
PY  - 2013/08
DA  - 2013/08
TI  - At-least At-most Modifications in a Space with Fuzzy Preoreder
BT  - Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13)
PB  - Atlantis Press
SP  - 682
EP  - 687
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2013.97
DO  - 10.2991/eusflat.2013.97
ID  - Perfilieva2013/08
ER  -