INTERVAL-VALUED INTUITIONISTIC QUADRI-PARTITIONED NEUTROSOPHIC SETS IN PSYCHOLOGICAL RESEARCH WITH EXAMPLES AND THEORETICAL INSIGHTS

P. Sai Anu; A. Arulselvam

INTERVAL-VALUED INTUITIONISTIC QUADRI-PARTITIONED NEUTROSOPHIC SETS IN PSYCHOLOGICAL RESEARCH WITH EXAMPLES AND THEORETICAL INSIGHTS

Abstract

This manuscript presents a comprehensive study of interval-valued intuitionistic quadri-partitioned neutrosophic sets (IVIQPNSs) and their combination with soft sets (IVIQPNSSs), focusing on the relationships between the membership grades of truth, falsity, contradiction, and indeterminacy. Specifically, the sum of the truth and falsity membership grades is constrained such that it does not exceed unity, while the sum of all four membership grades (truth, indeterminacy, contradiction, and falsity) is bounded by three. The manuscript also explores operators such as necessity and possibility, establishing several key properties. Given that many psychiatric disorders exhibit ambivalent behavior, representing membership grades with IVIQPNSs is essential. This work give effective approach to diagnose psychiatric disorder with robust flexible framework in fuzzy environment.

Keywords

References

Abdel-Basset, M., Mohamed, M., Elhoseny, M. et al., (2019), Cosine similarity measures of bipolar neutrosophic set for diagnosis of bipolar disorder diseases. Artificial Intelligence in Medicine, DOI: 10.1016/j.artmed.2019.101735.
Atanassov, K. T., (1986), Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 20, pp.87-96.
Atanassov, K. T., (1989), More on Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 33(01), pp.37-45.
Atanassov, K. T., (1994), New Operations Defined Over the Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 61(02), pp.137-142.
Atanassov, K. T., Gargov, G., (1989), Interval Valued Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 31(03), pp.343-349.
Bhowmik, M., Pal, M., (2008), Intuitionistic Neutrosophic Set, Journal of Information and Computing Science, 04,(02), pp.142-152.
Broumi, S., Smarandache, F., (2013), Several Similarity Measures of Neutrosophic Sets. Neutrosophic Sets System, 01(01), pp.54-62.
Broumi, S., Smarandache, F., (2013), Intuitionistic Neutrosophic Soft Set, Journal of Information and Computing Science, 08(02), pp.130-140.

Broumi, S., Smarandache, F., (2014), Cosine Similarity Measure of Interval Valued Neutrosophic Sets, Neutrosophic Sets and Systems, 05, pp.28-32.
Broumi, S., Smarandache, F., (2014), New distance and similarity measures of interval neutrosophic sets, 17th International Conference on Information Fusion (FUSION), Salamanca, Spain, pp.1-7.
Chahhtterjee, R., Majumdar, P., Samanta, S. K., (2019), Similarity Measures in Neutrosophic Sets-I, Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets. Stud. Fuzziness Soft Computing, 369, pp.249-294.
Zhou J., Wu X, Chen C. (2025), Investigating Various Intuitonistic Fuzzy Information Measures and their Relationships, Appl. Comput. Math., Vol.24, No.4, pp.579-607 DOI: 10.30546/1683-6154.24.4.2025.579
Toktoshov G.Y., Yurgenson A.N., Migov D.A., (2025), An Approach for the Topology DEsign and Optimization of a Utility Network with Unreliable Elements, TWMS J. Pure Appl. Math. V.16, N.1, pp.71-83, DOI: 10.30546/2219-1259.16.1.2025.71.
Chicaiza, C., Paspuel,O., Cuesta,P., Hernandez, S., (2020), Neutrosophic Psychology for Emotional Intelligence Analysis in Students of the Autonomous University of Los Andes, Ecuador, Neutrosophic Sets and Systems, 34, pp.1-8.
Chinnadurai, V., Smarandache, F., Bobin, A., (2020), Multi-Aspect Decision-Making Process in Equity Investment Using Neutrosophic Soft Matrices, Neutrosophic Sets and Systems, 31, pp.224-241.
Chinnadurai, V., Bobin, A., (2020), Multiple-criteria Decision Analysis Process by Using Prospect Decision Theory in Interval-valued Neutrosophic Environment, CAAI Transactions on Intelligence Technology, 05(03), pp.209-221.
Christianto, V., Smarandache, F., (2019), A Review of Seven Applications of Neutrosophic Logic: In Cultural Psychology, Economics Theorizing, Conflict Resolution, Philosophy of Science, etc. J- Multidisciplinary Scientific Journal, 02(02), pp.128-137.
De, S.K., Biswas, R., Roy, A. R., (2000), Some operations on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 114(03), pp.477-484.
Hamidi, M., Borumand Saeid, A., (2018), Achievable single-valued neutrosophic graphs in Wireless sensor networks, New Mathematics and Natural Computation, 14(02), pp.157-185.
Jiang, Y., Yong, T., Qimai,C., Hai,L., Jianchao,T., (2010), Interval-valued intuitionistic fuzzy soft sets and their properties, Comput. Math. Appl., 60, pp.906-918.
Liu, D., Liu, G., Liu, Z., (2018), Some Similarity Measures of Neutrosophic Sets Based on the Euclidean Distance and Their Application in Medical Diagnosis. Computational and Mathematical Methods in Medicine, 2018, pp.01-09.
Pramanik, S., (2022), Interval Quadripartitioned Neutrosophic Sets, Neutrosophic Sets and Systems, 51, pp.1-10.
Saranya, S., Vigneshwaran, M., Jafari, S., (2020), C # Application to Deal with Neutrosophic g α-Closed Sets In Neutrosophic Topology, Applications and Applied Mathematics: An International Journal (AAM), 15(01), pp. 226-239.
Shahzadi, G., Akram, M., Borumand Saeid, A., (2017), An application of single-valued neutrosophic sets in medical diagnosis, Neutrosophic Sets and Systems, 18, pp.80-88.
Smarandache, F., (1999), A Unifying Field in Logics: Neutrosophic Logic, American Research Press.
Smarandache, F., (2018), Neutropsychic Personality / A mathematical approach to psychology (third enlarged edition).
Smarandache, F., (2019), Introduction to Neutrosophic Sociology (Neutrosociology), Infinite Study, SSRN: https://ssrn.com/abstract=3405436
Wang, H., Smarandache, F., Zhang, Y., Sunderraman, R., (2010), Single Valued Neutrosophic Sets, Rev. Air Force Acad., 01, pp.10-14.
Wang, H., Smarandache, F., Zhang, Y., Sunderraman, R., (2005), Interval Neutrosophic Sets and Logic: Theory and Applications in Computing, Hexis, Phoenix, Ariz, USA.
Wang, W., Xinwang, L., (2013), Some Operations over Atanassov’s Intuitionistic Fuzzy Sets Based on Einstein T-norm and T-Conorm, Int. J. Uncertain. Fuzziness Knowl. Based System, 21, pp. 63-276.
Jun, Ye., (2014), Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses, Artificial Intelligence in Medicine, 63, pp.171-179.
Zadeh, L.A., (1965), Fuzzy Sets, Information and Control, 08(03), pp.338-353.

Details

Primary Language

English

Subjects

Mathematical Logic, Set Theory, Lattices and Universal Algebra

Journal Section

Research Article

Authors

P. Sai Anu This is me
0009-0001-7831-0776
India

A. Arulselvam ^* This is me
0000-0001-8383-2889
India

Publication Date

February 3, 2026

Submission Date

January 9, 2025

Acceptance Date

April 10, 2025

Published in Issue

Year 2026 Volume: 16 Number: 2

IZ

https://izlik.org/JA43LH68LK

Cite

RIS / Bibtex

APA

Sai Anu, P., & Arulselvam, A. (2026). INTERVAL-VALUED INTUITIONISTIC QUADRI-PARTITIONED NEUTROSOPHIC SETS IN PSYCHOLOGICAL RESEARCH WITH EXAMPLES AND THEORETICAL INSIGHTS. TWMS Journal of Applied and Engineering Mathematics, 16(2), 169-187. https://izlik.org/JA43LH68LK

AMA

1.Sai Anu P, Arulselvam A. INTERVAL-VALUED INTUITIONISTIC QUADRI-PARTITIONED NEUTROSOPHIC SETS IN PSYCHOLOGICAL RESEARCH WITH EXAMPLES AND THEORETICAL INSIGHTS. JAEM. 2026;16(2):169-187. https://izlik.org/JA43LH68LK

Chicago

Sai Anu, P., and A. Arulselvam. 2026. “INTERVAL-VALUED INTUITIONISTIC QUADRI-PARTITIONED NEUTROSOPHIC SETS IN PSYCHOLOGICAL RESEARCH WITH EXAMPLES AND THEORETICAL INSIGHTS”. TWMS Journal of Applied and Engineering Mathematics 16 (2): 169-87. https://izlik.org/JA43LH68LK.

EndNote

Sai Anu P, Arulselvam A (February 1, 2026) INTERVAL-VALUED INTUITIONISTIC QUADRI-PARTITIONED NEUTROSOPHIC SETS IN PSYCHOLOGICAL RESEARCH WITH EXAMPLES AND THEORETICAL INSIGHTS. TWMS Journal of Applied and Engineering Mathematics 16 2 169–187.

IEEE

[1]P. Sai Anu and A. Arulselvam, “INTERVAL-VALUED INTUITIONISTIC QUADRI-PARTITIONED NEUTROSOPHIC SETS IN PSYCHOLOGICAL RESEARCH WITH EXAMPLES AND THEORETICAL INSIGHTS”, JAEM, vol. 16, no. 2, pp. 169–187, Feb. 2026, [Online]. Available: https://izlik.org/JA43LH68LK

ISNAD

Sai Anu, P. - Arulselvam, A. “INTERVAL-VALUED INTUITIONISTIC QUADRI-PARTITIONED NEUTROSOPHIC SETS IN PSYCHOLOGICAL RESEARCH WITH EXAMPLES AND THEORETICAL INSIGHTS”. TWMS Journal of Applied and Engineering Mathematics 16/2 (February 1, 2026): 169-187. https://izlik.org/JA43LH68LK.

JAMA

1.Sai Anu P, Arulselvam A. INTERVAL-VALUED INTUITIONISTIC QUADRI-PARTITIONED NEUTROSOPHIC SETS IN PSYCHOLOGICAL RESEARCH WITH EXAMPLES AND THEORETICAL INSIGHTS. JAEM. 2026;16:169–187.

MLA

Sai Anu, P., and A. Arulselvam. “INTERVAL-VALUED INTUITIONISTIC QUADRI-PARTITIONED NEUTROSOPHIC SETS IN PSYCHOLOGICAL RESEARCH WITH EXAMPLES AND THEORETICAL INSIGHTS”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 2, Feb. 2026, pp. 169-87, https://izlik.org/JA43LH68LK.

Vancouver

1.P. Sai Anu, A. Arulselvam. INTERVAL-VALUED INTUITIONISTIC QUADRI-PARTITIONED NEUTROSOPHIC SETS IN PSYCHOLOGICAL RESEARCH WITH EXAMPLES AND THEORETICAL INSIGHTS. JAEM [Internet]. 2026 Feb. 1;16(2):169-87. Available from: https://izlik.org/JA43LH68LK