Construction of Intuitionistic Fuzzy Mappings with Applications

Soheyb Milles; Ergün Nart; Farhan Ismail; Abdelkrim Latreche

doi:10.32323/ujma.745248

EN

Construction of Intuitionistic Fuzzy Mappings with Applications

Abstract

In a recent paper, Ismail and Massa'deh have introduced the notion of L-fuzzy mapping and some basic operations were proved. In this paper, we generalize this notion to the setting of intuitionistic fuzzy sets. Moreover, we study the main properties related to intuitionistic fuzzy mapping. As applications, we provide properties of intuitionistic fuzzy continuous mappings in intuitionistic fuzzy topological spaces and investigate the relation among various kinds of intuitionistic fuzzy continuity.

Keywords

Intuitionistic fuzzy set, Intuitionistic fuzzy mapping, Intuitionistic fuzzy topology

References

[1] K. Atanassov, Intuitionistic fuzzy sets, VII ITKRs Scientific Session, Sofia, 1983.
[2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87–96, doi:10.1016/S0165-0114(86)80034-3
[3] K. Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications, Springer-Verlag, Heidelberg, New York, 1999, doi:10.1007/978-3-7908-1870-3-1
[4] P. Burillo and H. Bustince, Intuitionistic fuzzy relations (Part I) , Mathware and computing 2, (1995), 5–38.
[5] P. Burillo and H. Bustince, Intuitionistic fuzzy relations (Part II) , Mathware and computing 2, (1995), 117–148.
[6] H. Bustince and P. Burillo, Antisymmetrical intuitionistic fuzzy relation. Order on the referential set induced by an bi fuzzy relation , Fuzzy Sets and Systems, Fuzzy Sets and Systems, 2 (1995), 17–22.
[7] H. Bustince and P. Burillo, Structures on intuitionistic fuzzy relations , Fuzzy Sets and Systems, 3 (1996), 293–303, doi:10.1016/0165-0114(96)84610-0
[8] P. Burillo, Construction of intuitionistic fuzzy relations with predetermined properties, Fuzzy Sets and Systems, Fuzzy Sets and Systems 3 (2000), 379–403, doi:10.1016/S0165-0114(97)00381-3
[9] H. Gurc¸ay, D. C¸ oker and A.H. Es¸, On fuzzy continuity in intuitionistic fuzzy topological spaces, Journal of Fuzzy Mathematics, 2 (2003), 365–378.
[10] I. Farhan and O.M. Mourad, A new structure and constructions of L-fuzzy maps, International Journal of Computational and Applied Mathematics 1 (2013), 1–10.

[11] O. Galor, Discrete dynamical systems, Springer, 2007, doi:10.1007/3-540-36776-4
[12] G. Gomathi and D. Jayanthi, Intuitionistic fuzzy b] continuous mapping, Advances in Fuzzy Mathematics 1 (2018), 39–47.
[13] S. Heilpern, Fuzzy mappings and fixed point theorem, Journal of Mathematical Analysis and Applications, Journal of Mathematical Analysis and Applications, 83 (1981), 566–569, doi:10.1016/0022-247X(81)90141-4
[14] G.E. Hughes and M.J. Cresswell, A New Introduction to Modal Logic, London: Routledge, (2012), doi:10.4324/9780203028100
[15] K. Hur, S.Y. Jang and H.M. Kang, Intuitionistic fuzzy subgroupoids, International Journal of Fuzzy Logic and Intelligent Systems, 1 (2003), 72–77, doi:10.5391/IJFIS.2003.3.1.072
[16] D. Jayanthi, Intuitionistic Fuzzy Generalized Beta Continuous, Indian Journal of Applied Research, Mappings, 4 (2014), 1–6.
[17] A. Kandil, S. Saleh and M.M. Yakout, Fuzzy topology on fuzzy sets: regularity and separation axioms, American Academic and Scholarly Research Journal, 2 (2012).
[18] H.W. Kang, J-G. Lee and K. Hur, Intuitionistic fuzzy mappings and intuitionistic fuzzy equivalence relations, Annals of Fuzzy Mathematics and Informatics, 1 (2012), 61–87.
[19] K. Lim, G.H. Choi and H. Hur, Fuzzy mappings and fuzzy equivalence relations, International Journal of Fuzzy Logic and Intelligent Systems, 3 (2011), 750–749, doi:10.5391/IJFIS.2011.11.3.153
[20] A. Manimaran, K. A. Prakash, P. Thangaraj, Intuitionistic fuzzy totally continuous and totally semi-continuous mappings in intuitionistic fuzzy topological spaces, International journal of Advanced Scientific and Technical Research, 2 (2011), 505–509.
[21] S.K. Sardar, M. Mandal and S.K. Majumder, Intuitionistic fuzzy ideal extensions in semigroups , J. Pure Appl. Math, 1 (2015), 59–67.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Soheyb Milles ^*
Algeria

Ergün Nart
0000-0001-5049-609X
Türkiye

Farhan Ismail This is me
0000-0002-0822-8961
Türkiye

Abdelkrim Latreche This is me
0000-0003-1424-7197
Algeria

Publication Date

December 23, 2020

Submission Date

May 29, 2020

Acceptance Date

September 29, 2020

Published in Issue

Year 2020 Volume: 3 Number: 4

DOI

https://doi.org/10.32323/ujma.745248

IZ

https://izlik.org/JA74YZ87LT

APA

Milles, S., Nart, E., Ismail, F., & Latreche, A. (2020). Construction of Intuitionistic Fuzzy Mappings with Applications. Universal Journal of Mathematics and Applications, 3(4), 144-155. https://doi.org/10.32323/ujma.745248

AMA

1.Milles S, Nart E, Ismail F, Latreche A. Construction of Intuitionistic Fuzzy Mappings with Applications. Univ. J. Math. Appl. 2020;3(4):144-155. doi:10.32323/ujma.745248

Chicago

Milles, Soheyb, Ergün Nart, Farhan Ismail, and Abdelkrim Latreche. 2020. “Construction of Intuitionistic Fuzzy Mappings With Applications”. Universal Journal of Mathematics and Applications 3 (4): 144-55. https://doi.org/10.32323/ujma.745248.

EndNote

Milles S, Nart E, Ismail F, Latreche A (December 1, 2020) Construction of Intuitionistic Fuzzy Mappings with Applications. Universal Journal of Mathematics and Applications 3 4 144–155.

IEEE

[1]S. Milles, E. Nart, F. Ismail, and A. Latreche, “Construction of Intuitionistic Fuzzy Mappings with Applications”, Univ. J. Math. Appl., vol. 3, no. 4, pp. 144–155, Dec. 2020, doi: 10.32323/ujma.745248.

ISNAD

Milles, Soheyb - Nart, Ergün - Ismail, Farhan - Latreche, Abdelkrim. “Construction of Intuitionistic Fuzzy Mappings With Applications”. Universal Journal of Mathematics and Applications 3/4 (December 1, 2020): 144-155. https://doi.org/10.32323/ujma.745248.

JAMA

1.Milles S, Nart E, Ismail F, Latreche A. Construction of Intuitionistic Fuzzy Mappings with Applications. Univ. J. Math. Appl. 2020;3:144–155.

MLA

Milles, Soheyb, et al. “Construction of Intuitionistic Fuzzy Mappings With Applications”. Universal Journal of Mathematics and Applications, vol. 3, no. 4, Dec. 2020, pp. 144-55, doi:10.32323/ujma.745248.

Vancouver

1.Soheyb Milles, Ergün Nart, Farhan Ismail, Abdelkrim Latreche. Construction of Intuitionistic Fuzzy Mappings with Applications. Univ. J. Math. Appl. 2020 Dec. 1;3(4):144-55. doi:10.32323/ujma.745248