Journal
COMPUTATIONAL & APPLIED MATHEMATICS
Volume 41, Issue 5, Pages -Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s40314-022-01920-4
Keywords
Directional monotonic fuzzy implication functions; Directional increasing quasi-grouping functions; Pre-aggregation functions; (g, N)-operations
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Funding
- National Natural Science Foundation of China [62166037, 11901465]
- Science and Technology Program of Gansu Province [20JR10RA101]
- China Postdoctoral Science Foundation [2021M692561]
- Scientific Research Fund for Young Teachers of Northwest Normal University [NWNU-LKQN-18-28]
- Doctoral Research Fund of Northwest Normal University [6014/0002020202]
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This paper presents the basic properties of directional monotonic fuzzy implication functions and proposes construction methods. The concept of (G, N)-operations is introduced based on binary functions G and fuzzy negations N, and the conditions for (G, N)-operations to be directional monotonic fuzzy implication functions are investigated when using directional increasing quasi-grouping functions g.
In this paper, first we give some basic properties of directional monotonic fuzzy implication functions proposed by Bustince et al. (Fuzzy Sets Syst 386:161-178, 2020) by relaxing the monotonicity of fuzzy implication functions to the directional monotonicity lately. And then, we propose several construction methods of directional monotonic fuzzy implication functions. Finally, we introduce the concept of (G, N)-operations on the basis of binary functions G and fuzzy negations N and investigate the conditions under which (G, N)-operations can be directional monotonic fuzzy implication functions when the binary functions G are taken as directional increasing quasi-grouping functions g proposed by Qiao recently.
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