Abstract
A multi-adjoint fuzzy relation equation is defined from a sup-composition operator, which combines different conjunctions. The choice of such compositions has a direct impact on the resolution of the equation. This paper presents a first approach to the consequences of modifying the sup-composition associated with a multi-adjoint fuzzy relation equation in its solution set. Firstly, we show that greater conjunctions lead to lower greatest solutions. Then, two counterexamples are presented to highlight that, in general, an existing ordering in the conjunctions does not lead to comparable minimal solutions. Nevertheless, if the minimal solutions are comparable, we show that greater conjunctions lead to lower minimal solutions.
Supported by the 2014–2020 ERDF Operational Programme in collaboration with the State Research Agency (AEI) in project PID2019-108991GB-I00, and with the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia in project FEDER-UCA18-108612, and by the European Cooperation in Science & Technology (COST) Action CA17124.
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Notes
- 1.
\([0,1]_m\) denotes a regular partitions of [0, 1] into m pieces, for example, \([0,1]_4=\{0,0.25,0.5,0,75,1\}\) divides the unit interval into four pieces.
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Lobo, D., López-Marchante, V., Medina, J. (2022). On the Effects of Conjunctions in the Solution Set of Multi-adjoint Fuzzy Relation Equations. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1601. Springer, Cham. https://doi.org/10.1007/978-3-031-08971-8_12
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