MORE ON CONTINUOUS AND IRRESOLUTE MAPS IN PYTHAGOREAN FUZZY TOPOLOGICAL SPACES

Vadivel A; G Gavaskar; C John Sundar

MORE ON CONTINUOUS AND IRRESOLUTE MAPS IN PYTHAGOREAN FUZZY TOPOLOGICAL SPACES

Abstract

The new dimension of non-standard fuzzy sets called Pythagorean fuzzy sets which can handle the inaccurate data very strongly has been established in recent days. Even though intuitionistic fuzzy sets were generously used in decision making to handle the imprecise data the novelty and the voluminous of Pythagorean fuzzy environment gives motivation to use it in decision making process. The Pythagorean fuzzy topological spaces are the novel generalization of fuzzy topological spaces. In this paper, we develop the concept of Pythagorean fuzzy $\delta $ continuity which is stronger than Pythagorean fuzzy continuous function in Pythagorean fuzzy topological spaces and specialize some of their basic properties with examples. Also, we introduce and discuss about properties and characterization of Pythagorean fuzzy $\delta$ irresolute maps. Interrelations have been studied elaborately for the defined functions using various examples.

Keywords

References

Abbas, S. E., (2012), Weaker Forms of Fuzzy Contra-continuity, The Journal of Fuzzy Mathematics, 2010.
Acikgoz, A. and Esenbel, F., (2019), Neutrosophic soft $ \delta $-topology and neutrosophic soft compactness, AIP Conference Proceedings, 2183, 030002.
Adabitabar Firozja, M., Agheli, B. and Baloui Jamkhaneh, E., (2019), A new similarity measure for Pythagorean fuzzy sets, Complex and Intelligent Systems.
Aranganayagi, S., Saraswathi, M. and Chitirakala, K., (2023), More on open maps and closed maps in fuzzy hypersoft topological spaces and application in Covid-19 diagnosis using cotangent similarity measure, International Journal of Neutrosophic Science, 21 (2), 32-58.
Aranganayagi, S., Saraswathi, M., Chitirakala, K. and Vadivel, A., (2023), The $ e $-open sets in neutrosophic hypersoft topologial spaces and application in Covid-19 diagnosis using normalized hamming distance, Journal of the Indonesian Mathematical Society, 29 (2), 177-196.
Atanassov, K. T., (1983), Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia.
Atanassov, K. T., (1986), Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87-96.
Atanassov, K. T., (1999), Intuitionistic fuzzy sets: theory and applications, Physica, Heidelberg.

Atanassov, K. T., (2012), On intuitionistic fuzzy sets theory, Springer, Berlin.
Azad, K. K., (1981), On fuzzy semi continuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. App, 82, 14-32.
Chang, C. L., (1968), Fuzzy topological spaces, J. Math. Anal. Appi., 24, 182-190.
Coker, D., (1997), An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88, 81-89.
Gnanachristy, N. B. and Revathi, G. K., (2020), Analysis of Various Fuzzy Topological Spaces, Journal of Critical Reviews, 7, 2394-5125.
Gnanachristy, N. B. and Revathi, G. K., (2021), A View on Pythagorean Fuzzy Contra $\mathcal{G^{8}}$ Continuous Function, Journal of Physics Conference Series, 2115, 012041.
John Sundar, C. and Vadivel, A., (2023), Somewhat Neutrosopic $\delta$-Continuous Functions in Neutrosophic Topological Spaces, Journal of Neutrosophic and Fuzzy Systems, 6 (2), 38-48.
Murat Olgun, Mehmet Unver and Seyhmus Yardimci, (2019), Pythagorean fuzzy topological spaces, Complex $\&$ Intelligent Systems.
Necla Turanli and Dogan coker, (2000), Fuzzy connectedness in intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 116, 369-375.
Paul Augustine Ejegwa, (2019), Pythagorean fuzzy set and its application in career placements based on academic performance using max-min-max composition, Complex and Intelligent Systems.
Preethi, N. and Revathi, G. K., (2020), A conceptual View on $PFD$ functions and its Properties, Test Engineering and Management, 0913-4120.
Rana Muhammad Zulqarnain, (2021), Development of TOPSIS Technique under Pythagorean Fuzzy Hypersoft Environment Based on Correlation Coefficient and Its Application towards the Selection of Antivirus Mask in COVID-19 Pandemic, Hindawi Complexity.
Revathi, G. K., Roja, E. and Uma, M. K., (2010), Fuzzy Contra G continuous functions, International Review of Fuzzy mathematics, 5, 81-91.
Saha, S., (1987), Fuzzy $ \delta $-continuous mappings, Journal of Mathematical Analysis and Applications, 126, 130-142.
Santhi, R. and Arul Prakash, K., (2011), Intuitionistic fuzzy contra semi-generalised continuous mappings, 3, 30-40.
Surendra, P., Chitirakala, K. and Vadivel, A., (2023), $\delta$-open sets in neutrosophic hypersoft topological spaces, International Journal of Neutrosophic Science, 20 (4), 93-105.
Surendra, P., Vadivel, A. and Chitirakala, K., (2024), $\delta$-separation axioms on fuzzy hypersoft topological spaces, International Journal of Neutrosophic Science, 23 (1), 17-26.
Shukla, M., (2013), On Fuzzy Contra $g^{*}$ Semi-Continuous Functions, International Journal of Scientific and Engineering Research, 4.
Udhaya Shalini, M. and Stanis Arul Mary, A., (2022), Generalized pre-closed sets in Pythagorean fuzzy topological spaces, International Journal of Creative Research Thoughts (IJCRT), 10 (30), e142-e147.
Vadivel, A. and John Sundar, C., (2022), $ N_{nc} \delta $-Open Sets, South East Asian Journal of Mathematics and Mathematical Sciences, 18 (3), 207-216.
Vadivel, A. and John Sundar, C., (2023), Somewhat neutrosophic $\delta$-irresolute continuous mappings in neutrosophic topological spaces, TWMS Journal of Applied and Engineering Mathematics, 13 (2), 773-781.
Vadivel, A., John Sundar, C., Kirubadevi, K. and Tamilselvan, S., (2022), More on Neutrosophic Nano Open Sets, International Journal of Neutrosophic Science (IJNS), 18 (4), 204-222.
Vadivel, A., Seenivasan, M. and John Sundar, C., (2021), An Introduction to $ \delta $-open sets in a Neutrosophic Topological Spaces, Journal of Physics: Conference Series, 1724, 012011.
Warren, R. H., (1978), Neighborhoods, Bases and Continuity in Fuzzy Topological Spaces, Rocky Mountain Journal of Mathematics, 8.
Yager, R. R., (2013), Pythagorean membership grades in multicriteria decision making, In: Technical report $MII$-3301. Machine Intelligence Institute, Iona College, New Rochelle.
Yager, R. R. (2013), Pythagorean fuzzy subsets, In: Proceedings of the joint $IFSA$ world congress $NAFIPS$ annual meeting, 57-61.
Yager, R. R. and Abbasov, A. M., (2013), Pythagorean membership grades, complex numbers, and decision making, Int J Intell Syst., 28, 436-452.
Yager, R. R., (2014), Pythagorean membership grades in multicriteria decision making, $IEEE$ Trans Fuzzy Syst., 22 (4), 958-965.
Zadeh, L. A., (1965), Fuzzy sets, Inf. Control, 8, 338-353.

Details

Primary Language

English

Subjects

Mathematical Logic, Set Theory, Lattices and Universal Algebra

Journal Section

Research Article

Authors

Vadivel A ^*
0000-0001-5970-035X
India

G Gavaskar This is me
0009-0000-7398-5654
India

C John Sundar
0000-0002-7455-4976
India

Publication Date

November 3, 2025

Submission Date

September 3, 2024

Acceptance Date

November 22, 2024

Published in Issue

Year 2025 Volume: 15 Number: 11

IZ

https://izlik.org/JA86BG99EL

Cite

RIS / Bibtex

APA

A, V., Gavaskar, G., & John Sundar, C. (2025). MORE ON CONTINUOUS AND IRRESOLUTE MAPS IN PYTHAGOREAN FUZZY TOPOLOGICAL SPACES. TWMS Journal of Applied and Engineering Mathematics, 15(11), 2697-2708. https://izlik.org/JA86BG99EL

AMA

1.A V, Gavaskar G, John Sundar C. MORE ON CONTINUOUS AND IRRESOLUTE MAPS IN PYTHAGOREAN FUZZY TOPOLOGICAL SPACES. JAEM. 2025;15(11):2697-2708. https://izlik.org/JA86BG99EL

Chicago

A, Vadivel, G Gavaskar, and C John Sundar. 2025. “MORE ON CONTINUOUS AND IRRESOLUTE MAPS IN PYTHAGOREAN FUZZY TOPOLOGICAL SPACES”. TWMS Journal of Applied and Engineering Mathematics 15 (11): 2697-2708. https://izlik.org/JA86BG99EL.

EndNote

A V, Gavaskar G, John Sundar C (November 1, 2025) MORE ON CONTINUOUS AND IRRESOLUTE MAPS IN PYTHAGOREAN FUZZY TOPOLOGICAL SPACES. TWMS Journal of Applied and Engineering Mathematics 15 11 2697–2708.

IEEE

[1]V. A, G. Gavaskar, and C. John Sundar, “MORE ON CONTINUOUS AND IRRESOLUTE MAPS IN PYTHAGOREAN FUZZY TOPOLOGICAL SPACES”, JAEM, vol. 15, no. 11, pp. 2697–2708, Nov. 2025, [Online]. Available: https://izlik.org/JA86BG99EL

ISNAD

A, Vadivel - Gavaskar, G - John Sundar, C. “MORE ON CONTINUOUS AND IRRESOLUTE MAPS IN PYTHAGOREAN FUZZY TOPOLOGICAL SPACES”. TWMS Journal of Applied and Engineering Mathematics 15/11 (November 1, 2025): 2697-2708. https://izlik.org/JA86BG99EL.

JAMA

1.A V, Gavaskar G, John Sundar C. MORE ON CONTINUOUS AND IRRESOLUTE MAPS IN PYTHAGOREAN FUZZY TOPOLOGICAL SPACES. JAEM. 2025;15:2697–2708.

MLA

A, Vadivel, et al. “MORE ON CONTINUOUS AND IRRESOLUTE MAPS IN PYTHAGOREAN FUZZY TOPOLOGICAL SPACES”. TWMS Journal of Applied and Engineering Mathematics, vol. 15, no. 11, Nov. 2025, pp. 2697-08, https://izlik.org/JA86BG99EL.

Vancouver

1.Vadivel A, G Gavaskar, C John Sundar. MORE ON CONTINUOUS AND IRRESOLUTE MAPS IN PYTHAGOREAN FUZZY TOPOLOGICAL SPACES. JAEM [Internet]. 2025 Nov. 1;15(11):2697-708. Available from: https://izlik.org/JA86BG99EL