Open Journal Systems

Applications of intuitionistic fuzzy sets to assessment, decision making and to topological spaces

Michael Gr. Voskoglou

Abstract

The intuitionistic fuzzy sets, in which the elements of the universe have their membership and non-membership degrees in [0, 1], is a generalization of Zadeh’s fuzzy set. In this paper intuitionistic fuzzy sets are used as tools for assessment and decision making. This is useful in cases where one is not sure about the suitability of the linguistic characterizations assigned to each element of the universal set. Further, it is described how the notions of convergence, continuity, compactness, and of Hausdorff topological space are extended to intuitionistic fuzzy topological spaces. Applications illustrating our results are also presented.

Keywords

fuzzy set; intuitionistic FS; soft set; fuzzy assessment; decision making in fuzzy environment; intuitionistic fuzzy topological space

Full Text:

PDF

References

1. Voskoglou M. Methods for Assessing Human–Machine Performance under Fuzzy Conditions. Mathematics. 2019, 7(3): 230. doi: 10.3390/math7030230

2. Berger JO. Statistical Decision Theory. Springer New York; 1980. doi: 10.1007/978-1-4757-1727-3

3. Zadeh LA. Fuzzy sets. Information and Control. 1965, 8(3): 338-353. doi: 10.1016/s0019-9958(65)90241-x

4. Bellman RE, Zadeh LA. Decision-Making in a Fuzzy Environment. Management Science. 1970, 17(4): B-141-B-164. doi: 10.1287/mnsc.17.4.b141

5. Alcantud JCR. Fuzzy Techniques for Decision Making, reprint of the special issue published in Symmetry, MDPI, Basel, Switzerland, 2018.

6. Zhu B, Ren P. Type-2 fuzzy numbers made simple in decision making. Fuzzy Optimization and Decision Making. 2021, 21(2): 175-195. doi: 10.1007/s10700-021-09363-y

7. Voskoglou MGr. An Application of Neutrosophic Sets to Decision Making. Neutrosophic Sets and Systems. 2023, 53: 1-9.

8. Atanassov KT. Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 1986, 20(1): 87-96. doi: 10.1016/s0165-0114(86)80034-3

9. Ejegwa PA, Akubo AJ, Joshua OM. Intuitionistic Fuzzy Set and its Application in Career Determination via Normalized Euclidean Distance Method, European Scientific Journal. 2014, 10(15): 529-536.

10. Annamalai C. Intuitionistic Fuzzy Sets: New Approach and Applications. Available online: https://www.researchgate.net/publication/360395248 (accessed on 19 December 2023).

11. Atanassov KT. Intuitionistic Fuzzy Sets. Physica-Verlag HD, 1999. doi: 10.1007/978-3-7908-1870-3

12. Szmidt E, Kacprzyk J. Intuitionistic fuzzy sets in group decision making. Notes on Intuitionistic Fuzzy Sets. 1996, 2(1): 11–14.

13. Szmitd E, Kacprzyk J. Remarks on some applications of intuitionistic fuzzy sets in decision making. Notes on Intuitionistic Fuzzy Sets. 1996, 2(3): 22-31.

14. De SK, Biswas R, Roy AR. An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets and Systems. 2001, 117(2): 209-213. doi: 10.1016/s0165-0114(98)00235-8

15. Szmitd E, Kacprzyk J. Intuitionistic fuzzy sets in same medical applications. Notes on Intuitionistic Fuzzy Sets. 2001, 7(4): 58–64.

16. Davvaz B, Hassani Sadrabadi E. An application of intuitionistic fuzzy sets in medicine. International Journal of Biomathematics. 2016, 9(3): 1650037. doi: 10.1142/s1793524516500376

17. Mohamed Kozae A, Shokry M, Omran M. Intuitionistic Fuzzy Set and Its Application in Corona Covid-19. Applied and Computational Mathematics. 2020, 9(5): 146. doi: 10.11648/j.acm.20200905.11

18. Atanassov K, Gargov G. Intuitionistic fuzzy logic. C.R. Acad. Bulgare sc. 1990, 43(3): 9–12.

19. Atanassov K, Georgiev C. Intuitionistic fuzzy prolog. Fuzzy Sets and Systems. 1993, 53(2): 121-128. doi: 10.1016/0165-0114(93)90166-f

20. Meena K, Ponnappen L. An Application of Intuitionistic Fuzzy Sets in Choice of Discipline of Study. Global J. of Pure and Applied Mathematics. 2018, 14(6): 867-871.

21. Molodtsov D. Soft set theory—First results. Computers & Mathematics with Applications. 1999, 37(4-5): 19-31. doi: 10.1016/s0898-1221(99)00056-5

22. Zadeh LA. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems. 1978, 1(1): 3-28. doi: 10.1016/0165-0114(78)90029-5

23. Klir GJ, Folger TA. Fuzzy sets, Uncertainty and Information. Prentice-Hall, London; 1988.

24. Voskoglou MGr. Generalizations of Fuzzy Sets and Related Theories. In: Voskoglou M (editor). An Essential Guide to Fuzzy Systems. Nova Science Publishers, NY; 2019. pp. 345-352.

25. Atanassov KT. 25 years of Intuitionistic Fuzzy Sets or: The most important mistakes and results of mine. In: Proceedings of the 7th International Workshop on Intuitionistic Fuzzy Sets and Generalizations, Warsaw, Poland, 2008.

26. Atanassova V. Intuitionistic Fuzzy Sets and Applications, Special Issue, Mathematics. Available online: https://www.mdpi.com/journal/mathematics/special_issues/intuitionistic_fuzzy_sets (accessed on 19 December 2023).

27. Smarandache F. Neutrosophy/Neutrosophic Probability, Set, and Logic, Proquest, Michigan, USA, 1998.

28. Mendel JM. Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions. Prentice-Hall, Upper-Saddle River, NJ, 2001.

29. Zadeh LA. The concept of a linguistic variable and its application to approximate reasoning—I. Information Sciences. 1975, 8(3): 199-249. doi: 10.1016/0020-0255(75)90036-5

30. Mohammadzadeh A, Zhang C, Alattas KA, et al. Fourier-based type-2 fuzzy neural network: Simple and effective for high dimensional problems. Neurocomputing. 2023, 547: 126316. doi: 10.1016/j.neucom.2023.126316

31. Cao Y, Raise A, Mohammadzadeh A, et al. Deep learned recurrent type-3 fuzzy system: Application for renewable energy modeling/prediction. Energy Reports. 2021, 7: 8115-8127. doi: 10.1016/j.egyr.2021.07.004

32. Mohammadzadeh A, Sabzalian MH, Zhang W. An Interval Type-3 Fuzzy System and a New Online Fractional-Order Learning Algorithm: Theory and Practice. IEEE Transactions on Fuzzy Systems. 2020, 28(9): 1940-1950. doi: 10.1109/tfuzz.2019.2928509

33. Kaufmann A, Gupta M. Introduction to Fuzzy Arithmetic; Van Nostrand Reinhold Company. New York, NY, USA, 1991.

34. Dubois D, Prade H. Interval-Valued Fuzzy Sets, Possibility Theory and Imprecise Probability, Proceedings EUSFLAT-LFA, 2005. pp. 314-319.

35. Pawlak Z. Rough Sets: Aspects of Reasoning about Data, Kluer Academic Publishers, Dordrecht, 1991.

36. Deng J. Control Problems of Grey Systems. Systems and Control Letters. 1982. 288-294.

37. Maji PK, Biswas R, Roy AR. Soft set theory. Computers & Mathematics with Applications. 2003, 45(4-5): 555-562. doi: 10.1016/s0898-1221(03)00016-6

38. Maji PK, Roy AR, Biswas R. An application of soft sets in a decision making problem. Computers & Mathematics with Applications. 2002, 44(8-9): 1077-1083. doi: 10.1016/s0898-1221(02)00216-x

39. Voskoglou MGr. Fuzziness, Indeterminacy and Soft Sets: Frontiers and Perspectives. Mathematics. 2022, 10(20): 3909. doi: 10.3390/math10203909

40. Voskoglou MGr. Neutrosophic Assessment and Decision Making. Equations. 2023, 3: 68-72.

41. Willard S. General Topology, Dover Publ. Inc., N.Y. 2004.

42. Chang CL. Fuzzy topological spaces. Journal of Mathematical Analysis and Applications. 1968, 24(1): 182-190. doi: 10.1016/0022-247x(68)90057-7

43. Luplanlez FG. On Intuitionistic Fuzzy Topological Spaces, Kybernetes. 2006, 35(5): 743-747.

44. Salama AA, Alblowi SA. Neutrosophic Sets and Neutrosophic Topological Spaces. IOSR Journal of Mathematics. 2013, 3(4): 31-35.

45. Shabir M, Naz M. On soft topological spaces. Computers & Mathematics with Applications. 2011, 61(7): 1786-1799. doi: 10.1016/j.camwa.2011.02.006

46. Dan S, et al. Intuitionistic Type-2 Fuzzy Set and Its Properties. Symmetry. 2019, 11: 808.

47. Castillo O, Melin P. Towards Interval Type-3 Intuitionistic Fuzzy Sets and Systems. Mathematics. 2022, 10(21): 4091. doi: 10.3390/math10214091

48. Castillo O, Castro JR, Melin P. Interval Type-3 Fuzzy Control for Automated Tuning of Image Quality in Televisions. Axioms. 2022, 11(6): 276. doi: 10.3390/axioms11060276


DOI: https://doi.org/10.59400/jam.v1i4.325
(79 Abstract Views, 45 PDF Downloads)

Refbacks

  • There are currently no refbacks.


Copyright (c) 2023 Michael Gr. Voskoglou

License URL: http://creativecommons.org/licenses/by/4.0/


This site is licensed under a Creative Commons Attribution 4.0 International License.