Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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COMPLETELY V-REGULAR ALGEBRA ON SEMIRING AND ITS APPLICATION IN EDGE DETECTION

  • G.E. CHATZARAKIS (Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education (ASPETE)) ;
  • S. DICKSON (Department of Mathematics, Periyar University) ;
  • S. PADMASEKARAN (Department of Mathematics, Periyar University) ;
  • J. RAVI (School of Management Studies, REVA University)
  • Received : 2022.10.06
  • Accepted : 2022.11.17
  • Published : 2023.05.30
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Abstract

In this paper, Completely V-Regular on semiring is defined and used to derive new theorems with some of its properties. This paper also illustrates V-Regular algebra and Completely V-Regular Algebra with examples and properties. By extending completely V-Regular to fuzzy, a new concept, fuzzy V-Regular is brought out and fuzzy completely V-Regular algebra is introduced too. It is also developed by defining the ideals of Completely V -Regular Algebra and fuzzy completely V-Regular algebra. Finally, this fuzzy algebra concept is applied in image processing to detect edges. This V-Regular Algebra is novel in the research area.

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Acknowledgement

The first author was supported by the Special Account for Research of ASPETE through the funding program "Strengthening research of ASPETE faculty members". The second author is partially supported by the University Research Fellowship (PU/AD-3/URF/ 21F37237/2021 dated 09.11.2021) of Periyar University, Salem. The third author is supported by the fund for improvement of Science and Technology Infrastructure (FIST) of DST (SR/FST/MSI-115/2016).

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