| Fuzzy mathematics is a mathematical theory and method for studying and dealing with fuzzy phenomena.It has important applications in clustering analysis,pattern recognition,comprehensive evaluation,decision-making and prediction,control and information processing,and embodies the speculative thinking of mathematics Rough set theory is another mathematical tool for dealing with uncertain phenomena after probability theory,fuzzy set theory,and evidence theory.As a relatively new soft computing method,rough set theory has received increasing attention in recent years,and its effectiveness has been confirmed in many scientific and engineering fields.It is currently one of the research hotspots in the field of artificial intelligence theory and its application in the international community.In the article[Real valued semi metric based fuzzy rough sets and an application to contour extraction of digital surfaces.Fuzzy Sets and Systems.2023(459):201-219],the authors constructed fuzzy rough set models based on semi metric functions and real number addition and subtraction methods,and studied their related properties and applications in contour extraction of digital surfaces On the basis of the above,this paper first replaces semi metrics with fuzzy pre ordering,defines and studies a pair of fuzzy rough approximation operators using real number multiplication and division,then studies the properties and topological structure of definable sets under this model,and finally studies the application of this model in the acquisition of the closest gradient graph of digital images. |
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