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A Picture Fuzzy Based Approach Using Proximal Relator Spaces

Year 2025, Volume: 17 Issue: 1, 232 - 242, 30.06.2025
https://doi.org/10.47000/tjmcs.1579906

Abstract

Picture fuzzy sets are extensions of the fuzzy sets and the intuitonistic fuzzy sets
which consist of membership, a neutral membership and a non-membership degrees.
In this paper, we define the picture fuzzy proximity relations which are extension of picture fuzzy sets
and fuzzy proximity relations, and give some examples. Also, we give the definition of picture fuzzy spatial and
descriptive Lodato proximity space.

References

  • Atanassov, K.T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986), 87–96.
  • Concilio, A.D., Guadagni, C., Peters, J.F., Ramanna, S., Descriptive proximities. properties and interplay between classical proximities and overlap, Mat. Comput. Sci., 12(2018), 91–106.
  • Cuong, B.C., Kreinovich, V., Picture fuzzy sets-a new concept for computational intelligence problems. Third World Congress on Information and Communication Technologies. IEEE, 2013, 1-6.
  • Cuong, B.C., Picture fuzzy sets, J. Comput. Sci. Cybern., 30(4)(2015), 409–420.
  • Efremovic, V.A, The geometry of proximity, Mat. Sb. N.S., 31(73)(1952), 189–200 .
  • Kumar, S., Arya, V., Kumar, S., Dahiya, A., A new picture fuzzy entropy and its application based on combined picture fuzzy methodology with partial weight information Int. J. Fuzzy Syst. 24(2022), 3208–3225 .
  • Li, L., Chen, Z., Jiang, X., A hybrid picture fuzzy similarity measure and improved VIKOR method, Int J Comput Intell Syst, 15(2022), 113.
  • Lodato, M.W., On topologically induced generalized proximity relations I Proc. Amer. Math. Soc., 15(3)(1964), 417–422 .
  • Lodato, M.W., On topologically induced generalized proximity relations II Pacific J. Math., 17(1)(1966), 131–135 .
  • Luo, M., Li, W., Some new similarity measures on picture fuzzy sets and their applications, Soft Comput, 27(10)(2023), 6049-6067.
  • Naimpally, S.A., Warrack, B.D., Proximity Spaces. Cambridge Tract. 59, England, 1970.
  • Öztürk, M.A., İnan, E., Tekin, Ö., Peters, J.F.Fuzzy proximal relator spaces, Neural Comput. Appl., 31(7)(2019), 3201–3210 .
  • Öztürk, M.A., Intuitionistic fuzzy proximal relator spaces, Southeast Asian Bull. Math., (2025), (Accepted).
  • Peters, J.F., Naimpally, S.A., Applications of near sets, Notices of the Amer. Math. Soc., 59(4)(2012), 536–542.
  • Peters, J.F., Local near sets: pattern discovery in proximity spaces, Mat. Comput. Sci., 7(1)(2013), 87–106.
  • Peters, J.F., Near sets: an introduction, Math. Comput. Sci., 7(1)(2013), 3–9.
  • Peters, J.F., Proximal relator spaces, Filomat, 30(2)(2016), 469–472.
  • Peters, J.F., Computational Proximity. Excursions in the Topology of Digital Images, Intelligent Systems Reference Library, Springer, 2016.
  • Singh, S., Ganie, A.H., On a new picture fuzzy correlation coefficient with its applications to pattern recognition and identification of an investment sector. Comput. Appl. Math., 41(1)(2022), 1–35.
  • Szas, A., Basic tools and mild continuties in relator spaces. Acta Math. Hungar., 50(3-4)(1987), 177–201.
  • Tekin, Ö., Öztürk, M.A., İnan, E., L-Fuzzy relations via proximal spaces, Thai J. Math. 19(2)(2021), 557–570.
  • Tekin, Ö., Öztürk, M.A., Complex fuzzy proximal relator spaces, J. Mult.-Val. Log. Soft Comput., 38(3-4)(2022), 355–385.
  • Tekin, Ö., An approach for spherical fuzzy relations via relator spaces, J. Intell. Fuzzy Systems, 45(4)(2023), 6875–6886.
  • Verma, R., Rohtagi, B., Novel similarity measures between picture fuzzy sets and their applications to pattern recognition and medical diagnosis, Granul. Comput., 7(2022), 761–777.
  • Zadeh, L.A., Fuzzy sets, Inform. and Control, 8(1965), 338-353.

Year 2025, Volume: 17 Issue: 1, 232 - 242, 30.06.2025
https://doi.org/10.47000/tjmcs.1579906

Abstract

References

  • Atanassov, K.T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986), 87–96.
  • Concilio, A.D., Guadagni, C., Peters, J.F., Ramanna, S., Descriptive proximities. properties and interplay between classical proximities and overlap, Mat. Comput. Sci., 12(2018), 91–106.
  • Cuong, B.C., Kreinovich, V., Picture fuzzy sets-a new concept for computational intelligence problems. Third World Congress on Information and Communication Technologies. IEEE, 2013, 1-6.
  • Cuong, B.C., Picture fuzzy sets, J. Comput. Sci. Cybern., 30(4)(2015), 409–420.
  • Efremovic, V.A, The geometry of proximity, Mat. Sb. N.S., 31(73)(1952), 189–200 .
  • Kumar, S., Arya, V., Kumar, S., Dahiya, A., A new picture fuzzy entropy and its application based on combined picture fuzzy methodology with partial weight information Int. J. Fuzzy Syst. 24(2022), 3208–3225 .
  • Li, L., Chen, Z., Jiang, X., A hybrid picture fuzzy similarity measure and improved VIKOR method, Int J Comput Intell Syst, 15(2022), 113.
  • Lodato, M.W., On topologically induced generalized proximity relations I Proc. Amer. Math. Soc., 15(3)(1964), 417–422 .
  • Lodato, M.W., On topologically induced generalized proximity relations II Pacific J. Math., 17(1)(1966), 131–135 .
  • Luo, M., Li, W., Some new similarity measures on picture fuzzy sets and their applications, Soft Comput, 27(10)(2023), 6049-6067.
  • Naimpally, S.A., Warrack, B.D., Proximity Spaces. Cambridge Tract. 59, England, 1970.
  • Öztürk, M.A., İnan, E., Tekin, Ö., Peters, J.F.Fuzzy proximal relator spaces, Neural Comput. Appl., 31(7)(2019), 3201–3210 .
  • Öztürk, M.A., Intuitionistic fuzzy proximal relator spaces, Southeast Asian Bull. Math., (2025), (Accepted).
  • Peters, J.F., Naimpally, S.A., Applications of near sets, Notices of the Amer. Math. Soc., 59(4)(2012), 536–542.
  • Peters, J.F., Local near sets: pattern discovery in proximity spaces, Mat. Comput. Sci., 7(1)(2013), 87–106.
  • Peters, J.F., Near sets: an introduction, Math. Comput. Sci., 7(1)(2013), 3–9.
  • Peters, J.F., Proximal relator spaces, Filomat, 30(2)(2016), 469–472.
  • Peters, J.F., Computational Proximity. Excursions in the Topology of Digital Images, Intelligent Systems Reference Library, Springer, 2016.
  • Singh, S., Ganie, A.H., On a new picture fuzzy correlation coefficient with its applications to pattern recognition and identification of an investment sector. Comput. Appl. Math., 41(1)(2022), 1–35.
  • Szas, A., Basic tools and mild continuties in relator spaces. Acta Math. Hungar., 50(3-4)(1987), 177–201.
  • Tekin, Ö., Öztürk, M.A., İnan, E., L-Fuzzy relations via proximal spaces, Thai J. Math. 19(2)(2021), 557–570.
  • Tekin, Ö., Öztürk, M.A., Complex fuzzy proximal relator spaces, J. Mult.-Val. Log. Soft Comput., 38(3-4)(2022), 355–385.
  • Tekin, Ö., An approach for spherical fuzzy relations via relator spaces, J. Intell. Fuzzy Systems, 45(4)(2023), 6875–6886.
  • Verma, R., Rohtagi, B., Novel similarity measures between picture fuzzy sets and their applications to pattern recognition and medical diagnosis, Granul. Comput., 7(2022), 761–777.
  • Zadeh, L.A., Fuzzy sets, Inform. and Control, 8(1965), 338-353.
There are 25 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory, Pure Mathematics (Other)
Journal Section Articles
Authors

Özlem Tekin 0000-0001-9223-6149

Publication Date June 30, 2025
Submission Date November 5, 2024
Acceptance Date June 12, 2025
Published in Issue Year 2025 Volume: 17 Issue: 1

Cite

APA Tekin, Ö. (2025). A Picture Fuzzy Based Approach Using Proximal Relator Spaces. Turkish Journal of Mathematics and Computer Science, 17(1), 232-242. https://doi.org/10.47000/tjmcs.1579906
AMA Tekin Ö. A Picture Fuzzy Based Approach Using Proximal Relator Spaces. TJMCS. June 2025;17(1):232-242. doi:10.47000/tjmcs.1579906
Chicago Tekin, Özlem. “A Picture Fuzzy Based Approach Using Proximal Relator Spaces”. Turkish Journal of Mathematics and Computer Science 17, no. 1 (June 2025): 232-42. https://doi.org/10.47000/tjmcs.1579906.
EndNote Tekin Ö (June 1, 2025) A Picture Fuzzy Based Approach Using Proximal Relator Spaces. Turkish Journal of Mathematics and Computer Science 17 1 232–242.
IEEE Ö. Tekin, “A Picture Fuzzy Based Approach Using Proximal Relator Spaces”, TJMCS, vol. 17, no. 1, pp. 232–242, 2025, doi: 10.47000/tjmcs.1579906.
ISNAD Tekin, Özlem. “A Picture Fuzzy Based Approach Using Proximal Relator Spaces”. Turkish Journal of Mathematics and Computer Science 17/1 (June2025), 232-242. https://doi.org/10.47000/tjmcs.1579906.
JAMA Tekin Ö. A Picture Fuzzy Based Approach Using Proximal Relator Spaces. TJMCS. 2025;17:232–242.
MLA Tekin, Özlem. “A Picture Fuzzy Based Approach Using Proximal Relator Spaces”. Turkish Journal of Mathematics and Computer Science, vol. 17, no. 1, 2025, pp. 232-4, doi:10.47000/tjmcs.1579906.
Vancouver Tekin Ö. A Picture Fuzzy Based Approach Using Proximal Relator Spaces. TJMCS. 2025;17(1):232-4.