At-least At-most Modifications in a Space with Fuzzy Preoreder
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- monotonous fuzzy rule base system of fuzzy relation equations ``at least'' (``at most'') quantifiers fuzzy preorder criterion of solvability
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.
- © 2013, the Authors. Published by Atlantis Press.
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Cite this article
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 - https://doi.org/10.2991/eusflat.2013.97 ID - Perfilieva2013/08 ER -