Career determination is a vital decision-making process that often involves significant uncertainty and indecision. This paper introduces a new distance measure and a similarity measure based on picture fuzzy multisets. Also, it is shown that the distance measure satisfies the metric properties and the new similarity measure satisfies the conditions for the similarity measure. Lastly, using a hypothetical dataset, the new similarity measure was applied to decision-making problem in career determination. The new similarity measure evaluates the similarities between students and potential career paths by computing the highest similarity values between their respective picture fuzzy multisets. The results demonstrate the effectiveness of the proposed measure in identifying optimal career choices, thereby providing a more robust framework for decision-making under uncertainty.
- Open Access
- Article
Picture Fuzzy Multisets with Application in Career Determination
Author Information
Received: 10 Apr 2026 | Revised: 18 Aug 2026 | Accepted: 14 Sep 2026 | Published: 30 Sep 2026
Abstract
Keywords
multiset | fuzzy multiset | picture fuzzy set | picture fuzzy multiset
References
- 1.
Kapes, J.T.; Mastie, M.M.; Whitfield, E.A. A Counselor’s Guide to Career Assessment Instruments; National Career Development Association: Alexandria, VA, USA, 1994.
- 2.
Zadeh, L.A. Fuzzy Sets. Inf. Control 1965, 8, 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.
- 3.
Atanassov, K.T. Intuitionistic Fuzzy Sets. Fuzzy Sets Syst. 1986, 20, 87–96. https://doi.org/10.1016/s0165-0114(86)80034-3.
- 4.
Wang, W.; Xin, X. Distance Measure Between Intuitionistic Fuzzy sets. Pattern Recognit. Lett. 2005, 26, 2063–2069. https://doi.org/10.1016/j.patrec.2005.03.018.
- 5.
Cuong, B.C.; Kreinovich, V. Picture Fuzzy Sets—A new concept for Computational intelligence problems. In Proceedings of the Third World Congress on Information and Communication Technologies, Hanoi, Vietnam, 15–18 December 2013; pp. 1–6. https://doi.org/10.1109/wict.2013.7113099.
- 6.
Cuong, B.C. Pythagorean Picture Fuzzy Sets, part 1—Basic notions. J. Comput. Sci. Cybern. 2019, 35, 293–304. https://doi.org/10.15625/1813-9663/35/4/13898.
- 7.
Cuong, B.C.; Pham, V.H. Some Fuzzy Logic Operators for Picture Fuzzy Sets. In Proceedings of the 2015 Seventh International Conference on Knowledge and Systems Engineering (KSE), Ho Chi Minh City, Vietnam, 8–10 October 2015; pp. 132–137. https://doi.org/10.1109/kse.2015.20.
- 8.
Cuong, B.C.; Ngan, R.T.; Hai, B.D. An Involutive Picture Fuzzy Negator on Picture Fuzzy Sets and Some De Morgan Triples. In Proceedings of the Seventh International Conference on Knowledge and Systems Engineering, Ho Chi Minh City, Vietnam, 8–10 October 2015; pp. 126–131. https://doi.org/10.1109/kse.2015.21.
- 9.
Cuong, B.C.; Kreinovich, V.; Ngan, R.T. A Classification of Representable t‑norm Operators for Picture Fuzzy Sets. In Proceedings of the 2016 Eighth International Conference on Knowledge and Systems Engineering (KSE), Hanoi, Vietnam, 6–8 October 2016. https://doi.org/10.1109/kse.2016.7758023.
- 10.
Hasan, M.K.; Sultana, A.; Mitra, N.K. Compositions of Picture Fuzzy Relations with Application in Decision Making. Eur. J. Math. Stat. 2023, 4, 19–28. https://doi.org/10.24018/ejmath.2023.4.2.188.
- 11.
Hasan, M.K.; Sultana, A.; Mitra, N.K. Picture Fuzzy Relations Over Picture Fuzzy Sets. Am. J. Comput. Math. 2023, 13, 161–184. https://doi.org/10.4236/ajcm.2023.131008.
- 12.
Nguyen, V.D.; Nguyen, X.T. Some Measures of Picture Fuzzy Sets and Their Application in Multi‑attribute Decision Making. Int. J. Math. Sci. Comput. 2018, 4, 23–41. https://doi.org/10.5815/ijmsc.2018.03.03.
- 13.
Son, L.H. Generalized picture distance measure and applications to picture fuzzy clustering. Appl. Soft Comput. 2016, 46, 284–295. https://doi.org/10.1016/j.asoc.2016.05.009.
- 14.
Dutta, P. Medical Diagnosis Based on Distance Measures between Picture Fuzzy Sets. Int. J. Fuzzy Syst. Appl. 2018, 7, 15–36. https://doi.org/10.4018/ijfsa.2018100102.
- 15.
Rozy; Kaur, G. Similarity Measure between Picture Fuzzy sets and its Applications in Medical Diagnosis. J. Adv. Sch. Res. Allied Educ. 2022, 19, 210–212.
- 16.
Wei, G. Some Similarity Measures for Picture Fuzzy Sets and Their Applications. Iran. J. Fuzzy Syst. 2018, 15, 77–89.
- 17.
Yager, R.R. On the Theory of Bags. Int. J. Gen. Syst. 1986, 13, 23–37. https://doi.org/10.1080/03081078608934952.
- 18.
Kim, K.S.; Miyamoto, S. Application of Fuzzy Multisets to Fuzzy Database Systems. In Soft Computing in Intelligent Systems and Information Processing, Proceedings of the 1996 Asian Fuzzy Systems Symposium, Kenting, Taiwan, 11–14 December 1996; IEEE: New York, NY, USA, 1996; pp. 115–120. https://doi.org/10.1109/afss.1996.583573.
- 19.
Onasanya, B.O.; Sholabomi, A.S. Fuzzy multiset operations in applications. Ann. Fuzzy Math. Inform. 2019, 17, 279–288. https://doi.org/10.30948/afmi.2019.17.3.279.
- 20.
Shinoj, T.K.; John, S.J. Intuitionistic Fuzzy Multisets. Int. J. Eng. Sci. Innov. Technol. 2013, 2, 1–24.
- 21.
Rajarajeswari, P.; Uma, N. Normalized Hamming Similarity Measure for Intuitionistic Fuzzy Multi Sets and Its Application in Medical Diagnosis. Int. J. Math. Trends Technol. 2014, 5, 219–225.
- 22.
Shinoj, T.K.; John, S.J. Intuitionistic Fuzzy Multisets and its Application in Medical Diagnosis. World Acad. Sci. Eng. Technol. 2012, 6, 1418–1421.
- 23.
Ejegwa, P.A.; Kwarkar, L.N.; Ihuoma, K.N. Application of Intuitionistic Fuzzy Multisets in Appointment Process. Int. J. Comput. Appl. 2016, 135, 1–4. https://doi.org/10.5120/ijca2016908167.
- 24.
Ejegwa, P.A.; Onyeke, I.C.; Adah, V. Recognition Principle for Course Allocation in Higher Institution Based on Intuitionistic fuzzy Correlation Coefficient. J. Fuzzy Ext. Appl. 2025, 6, 94–108.
- 25.
Ejegwa, P.A.; Onyeke, I.C. A novel Intuitionistic Fuzzy Correlation Algorithm and its Application in Pattern recognition and Student admission process. Int. J. Fuzzy Syst. Appl. 2022, 11, 1–20. https://doi.org/10.4018/ijfsa.285984.
- 26.
Shinoj, T.K.; Sunil, J.J. Accuracy in Collaborative Robotics: An Intuitionistic Fuzzy Multisets Approach. Glob. J. Sci. Front. Res. Math. Decis. Sci. 2013, 13, 21–28.
- 27.
Usman, A.; Isah, A.; Adeyinka, A.S. An Application of Intuitionistic Fuzzy Multiset Distance Measure to Radiological Finding and Climate Change. Sci. World J. 2025, 20, 1700–1705. https://doi.org/10.4314/swj.v20i4.51.
- 28.
Cao, L.; Feng, Y.; Sangodapo, T.O. Picture Fuzzy Multisets. Ital. J. Pure Appl. Math. 2024, 51, 64–76.
- 29.
Feng, Y.; Sangodapo, T.O. Distance Measures between Picture Fuzzy Multisets and Their Application to Medical Diagnosis. Ital. J. Pure Appl. Math. 2025, 54, 113–125.
- 30.
Ejegwa, P.A. Pythagorean fuzzy set and its application in career placements based on academic performance using max–min–max composition. Complex Intell. Syst. 2019, 5, 165–175. https://doi.org/10.1007/s40747-019-0091-6.
- 31.
Yager, R.R. Pythagorean fuzzy subsets. In Proceedings of the Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, AB, Canada, 24–28 June 2013; pp. 57–61. https://doi.org/10.1109/ifsa‑nafips.2013.6608375.
- 32.
Yager, R.R. Pythagorean Membership Grades in Multicriteria Decision Making. IEEE Trans. Fuzzy Syst. 2014, 22, 958–965. https://doi.org/10.1109/tfuzz.2013.2278989.
- 33.
Johnson, T. Applications of intuitionistic fuzzy sets in the Academic Career of the Students. Indian J. Sci. Technol. 2017, 10, 23–25.
- 34.
Ejegwa, P.A.; Tyongi, B.B.; Osuwa, S.C.; et al. Career Determination Using Intuitionistic fuzzy Multisets Approach. MAYFEB J. Math. 2016, 1, 1–10.
- 35.
Ejegwa, P.A.; Akubo, A.J.; Joshua, O.M. Intuitionistic fuzzy sets in career determination. J. Inf. Comput. Sci. 2014, 9, 285–288.
- 36.
Sangodapo, T.O.; Kausar, N.; Chreif, M.Y. A New Decision‑Making Analysis Model Based on the Transformation of Picture Fuzzy Sets into Fuzzy Sets. In Analytical Decision Making and Data Envelopment Analysis: Advances and Challenges; Springer Nature: Singapore, 2024; pp. 455–464. https://doi.org/10.1007/978‑981‑97‑6972‑8_20.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Suite 4002 Level 4, 447 Collins Street, Melbourne, Victoria 3000, Australia
General Inquiries: info@sciltp.com