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A New Approach to Near Approximation in Fuzzy Ideals of an MV-Algebras Cover

A New Approach to Near Approximation in Fuzzy Ideals of an MV-Algebras

By: Fatemeh Jokar and  Bijan Davvaz  
Open Access
|Mar 2025

References

  1. Al-shami T.M., (2,1)-Fuzzy sets: properties, weighted aggregated operators and their applications to multi-criteria decision-making methods, Complex Intell. Syst. 9 (2023) 1687-1705.
  2. Al-Shami T.M., Alshammari I., Rough sets models inspired by supra-topology structures, Artif. Intell. Rev., 56 (7) (2023) 6855-6883.
  3. Al-Shami T.M., Mhemdi A., Approximation operators and accuracy measures of rough sets from an infra-topology view, Soft Comput. 27 (2023) 1317-1330.
  4. Al-shami T.M., Mhemdi A., Generalized frame for orthopair fuzzy sets: (m,n)-Fuzzy sets and their applications to multi-criteria decision-making methods, Information, 4 (1) (2023) p56.
  5. Bağirmaz N., Near ideals in near semigroups, Eur. J. Pure Appl. Math., 11 (2018), 505-516.
  6. Bagirmaz N., Near approximations in groups, Appl. Algebra Eng. Commun.Comput, 30(4) (2019), 285-297.
  7. Chang C. C., Algebraic analysis of many valued logics, Transactions of the American Mathematical Society, 88 (1958), 467-490.
  8. Chang C. C., A new proof of the completeness of the Lukasiewicz axioms, Transactions of the American Mathematical society, 93 (1959), 74-80.
  9. Cignoli R., D’Ottavaviano I., Mundici D., Algebraic Foundation of Many-Valued-Reasoning, Kluwer, Dorderecht, 2000.
  10. Davvaz B., Roughness based on fuzzy ideals, Information Sciences, 176 (2006), 2417-2437.
  11. Davvaz B., Roughness in rings, Information Sciences, 164 (2004), 147-163.
  12. Davvaz B., Mahdavipour M., Rough approximations in a general approximation space and their fundamental properties, International Journal General System, 37(3) (2008), 373-386.
  13. Davvaz B., Rough sets in a fundamental ring, Bull. Iranian Math. Soc. 24 (2) (1998), 49-61.
  14. Davvaz B., Soleha D.,Setyawati W., Mukhlash I., Near approximations in modules, Foundation of Computing and Decision Science, 46(4) (2021), 319-337.
  15. Hasankhani A., Saadat H., Some quotients on a BCK-algebra generated by a fuzzy set, Iranian Journal of Fuzzy Systems, 1(2) (2004) 33-43.
  16. Hoo C. S., Fuzzy ideals of BCI and MV -algebras, Fuzzy Sets and Systems, 62 (1994), 111-114.
  17. Ibrahim H.Z.,Al-shami T.M.,Arar M., Hosny M., Knm-Rung picture fuzzy information in a modern approach to multi-attribute group decision-making, Complex Intell. Syst., 10 (2) (2023) 2605-2625.
  18. ˙Inan E.,Öztürk M.A., Near semigroups on nearness approximation spaces, Ann. Fuzzy Math. Inform., 10(2) (2015), 287-297.
  19. ˙Inan E.,Öztürk M.A., Near groups on nearness approximation spaces, Hacet. J. Math. Stat., 41(4) (2012), 545-558.
  20. Kondo M., On the structure of generalized rough sets, Information Sciences, 176 (2006), 589-600.
  21. Kuroki N., Rough ideals in semigroups, Information Sciences, 100 (1997), 139-163.
  22. Kuroki N., Wang P.P., The lower and upper approximations in a fuzzy group, Information Sciences, 90 (1996), 203-220.
  23. Li F., Yin Y., Lu L., ( θ, T )-fuzzy rough approximation operators and TL-fuzzy rough ideals on a ring, Information Sciences, 177 (2007), 4711-4726.
  24. Liu W.J., Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets Syst., 8 (1982), 133-139.
  25. Liu W.J., Operations on fuzzy ideals, Fuzzy Sets Syst., 11 (1983), 31-41.
  26. Lin T. Y., Topological and fuzzy rough sets, in: R. Slowinski (Ed.), Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory, Kluwer Academic Publishers, Boston, 1992, pp. 287-304.
  27. Mukherjee T.K., Sen M.K., On fuzzy ideals in rings 1, Fuzzy Sets Syst. 21 (1987), 99-104.
  28. Mostafavi M., Davvaz B., Near polygroups on nearness approximation spaces, New Mathematics and Natural Computation, 18(3) (2022), 593-613.
  29. Mostafavi M., Davvaz B., Near semihypergroups on nearness approximation spaces, Computational and Applied Mathematics, 42 (2023), 344.
  30. Pawlak Z., Rough sets: Theoretical aspects of reasoning about data, Kluwer academic Publishers, Dordrecht, 1991.
  31. Pawlak Z., Rough sets, International Journal of Computer Sciences, 11 (1982), 341-356.
  32. Peters J. F., Su ciently near sets of neighbourhoods, in: J. Yao, S. Ramanna, G. Wang, Z. Suraj (eds.), Rough Sets and Knowledge Technology, LNCS 6954, Springer, Berlin, 1724, 2011.
  33. Peters J. F., Classification of perceptual objects by means of features, International Journal of Information Technology and Intelligent Computing, 3(2) (2008), 1-35
  34. Peters J. F., Naimpally S., Approach spaces for near filters, Gen. Math. Notes, 2(1) (2011), 159-164.
  35. Peters J.F., Tiwari S., Approach merotopies and near filters, Gen. Math. Notes, 3(1) (2011), 1-15.
  36. Peters J. F., Near sets, general theory about nearness of objects, Appl. Math. Sci., 1(53) (2007), 2609-2629.
  37. Peters J. F., Wasilewski P., Foundations of near sets, Information Sciences,, 179 (2009), 3091-3109.
  38. Piciu D., Algebras of fuzzy logic, Universitaria Craiova, 2007.
  39. Rasouli S., Davvaz B., Roughness in MV -algebras, Information Sciences, 180 (2010), 737-747.
  40. Rosenfeld A., Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
  41. Setyawati D. W., Soleha, Subiono, Mukhlash I., Rinwati, Davvaz B., Application of near approximations in Cayley graphs, Discrete Mathematics, Algorithms and Applications, 15(8) (2023), 2250180 (31 pages).
  42. Wang C., Wu C., Chen D., A systematic study on attribute reduction with rough sets based on general binary relations, Information Sciences, 178 (2008), 2237-2261.
  43. Yang X. -P., Minimization of axiom sets on fuzzy approximation operators, Information Sciences, 177 (2007), 3840-3854.
  44. Yang Y., John R., Roughness bounds in rough set operations, Information Sciences, 176 (2007), 4997-5011.
  45. Yao Y. Y., Two views of the theory of rough sets in finite universes, International Journal of Approximation Reasoning, 15 (1996), 291-317.
  46. Zadeh L.A., The concept of linguistic variable and its applications to approximate reasoning, Part I, Information Sciences, 8 (1975), 199-249 Part II, Information Sciences, 8 (1975), 301-357 Part III, Information Sciences, 9 (1976), 43-80.
  47. Zadeh L.A., Fuzzy sets, Inform. Cont., 8 (1965), 338-353.
  48. Zhu W., Generalized rough sets based on relations, Information Sciences, 177 (2007), 1499-1508.
DOI: https://doi.org/10.2478/fcds-2025-0003 | Journal eISSN: 2300-3405 | Journal ISSN: 0867-6356
Language: English
Page range: 57 - 86
Submitted on: May 31, 2024
Accepted on: Dec 16, 2024
Published on: Mar 8, 2025
Published by: Poznan University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2025 Fatemeh Jokar, Bijan Davvaz, published by Poznan University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.