Intuitionistic fuzzy hypersoft topology and ıts applications to multi-criteria decision-making
Sigma Journal of Engineering and Natural Sciences 2023, Vol. 41, Issue 1, pp. 106-118; doi.org/10.14744/sigma.2023.00011
Abstract
The aim of this paper is to introduce the concept of intuitionistic fuzzy hypersoft topology. Certain properties of intuitionistic fuzzy hypersoft (IFH) topology like IFH basis, IFH subspace, IFH interior and IFH cloure are investigated. Furthermore, the multicriteria decision making (MCDM) algorithms with aggregation operators based on IFH topology are developed. In Algorithm 1 and Algorithm 2, MCDM problem is applied for IFH sets and IFH topology, respectively. Any real-life implementations of the proposed MCDM algorithms are demonstrated by numerical illustrations.
Keywords: Intuitionistic Fuzzy Hypersoft Set; İntuitionistic Fuzzy Hypersoft Topology; IFH İnterior(Closure); IFH Basis; MCDM
References
- Alcantud JCR. Soft open bases and a novel construc- [20] Ozturk TY, Yolcu A. On neutrosophic hypersoft tion of soft topologies from bases for topologies. topological spaces. In: Smarandache F, Abdel- Mathematics 2020;8:672. [CrossRef] Baset M, Saeed M, Saqlain M, editors. Theory and
- Atanassov KT, Intuitionistic fuzzy sets. Fuzzy Sets application of hypersoft set. 1st ed. Brussels: Pons Syst 1986;20:87–96. [CrossRef] Publishing House; 2021. pp. 215–234.
- Atanassov K, Gargov G. Interval valued intuition- [21] Ozturk TY, Gunduz Aras C, Bayramov S. A new istic fuzzy sets. Fuzzy Sets Syst 1989;31:343–349. approach to operations on neutrosophic soft sets and [CrossRef] to neutrosophic soft topological spaces. Commun
- Aygunoglu A, Aygun H. Some notes on soft topo- Math Appl 2019;10:481–493. [CrossRef] logical spaces. Neural Comput Appl 2012;21:113– [22] Ozturk TY. On bipolar soft topological spaces. J
- [CrossRef] New Theory 2018;20:64–75.
- Cagman N, Karatas S, Enginoglu S. Soft topology. [23] Ozturk TY, Yolcu A. Some structures on pythag- Comput Math Appl 2011;62:351–358. [CrossRef] orean fuzzy topological spaces. J New Theory
- Coker D. An introduction to intuitionistic fuzzy 2020;33:15–25. topological spaces. Fuzzy Sets Syst 1997;88:81–89. [24] Roy AR, Maji PK. A fuzzy soft set theoretic approach [CrossRef] to decision making problems. J Comput Appl Math
- Deli I. Hybrid Set Structures Under Uncertainly 2007;203:412–418. [CrossRef] Parameterized Hypersoft Sets: Theory and
- Saeed M, Ahsan M, Siddique MK, Ahmad MR. A Applications In: Smarandache F, Abdel-Baset M, study of the fundamentals of hypersoft set theory. Saeed M, Saqlain M, editors. Theory and application Int J Sci Eng Res 2020;11:230. of hypersoft set. 1st ed. Brussels: Pons Publishing
- Smarandache F. Extension of soft set to hypersoft set, House; 2021. pp. 24–49. and then to plithogenic hypersoft set. Neutrosophic
- Enginoglu S, Arslan B. Intuitionistic fuzzy param- Sets Syst 2018;22:168–170. eterized intuitionistic fuzzy soft matrices and their
- Simsekler Dizman T, Ozturk TY. Fuzzy bipolar application in decision-making. Comput Appl Math soft topological spaces. TWMS J App Eng Math 2020;39:325. [CrossRef] 2021;11:151–159.
- Terepeta M. On separating axioms and similarity of J. Intuitionistic fuzzy sets in multicriteria group soft topological spaces. Soft Comput 2019;23:1049– decision making problems using the characteristic 1057. [CrossRef] objects method. Symmetry 2020;12:1382. [CrossRef]
- Feng F, Zheng Y, Alcantud JCR, Wang Q. Minkowski tic fuzzy decision making: an overview. Inf Fusion weighted score functions of intuitionistic fuzzy val- 2016;28:10–23. [CrossRef] ues. Mathematics 2020;8:1143. [CrossRef]
- Garg H, Kaur G. Cubic intuitionistic fuzzy sets and fuzzy hypersoft set. Commun Fac Sci Univ Ank Ser its fundamental properties. J. Multvalued Log S A1 Math Stat 2021;70:443–455. [CrossRef] 2019;33:507–537.
- Garg H, Kumar K. Linguistic interval-valued Application to Decision-Making. In: Smarandache Atanassov intuitionistic fuzzy sets and their appli- F, Abdel-Baset M, Saeed M, Saqlain M, editors. cations to group decision-making problems. IEEE Theory and application of hypersoft set. 1st ed. Trans Fuzzy Syst 2019;27:2302–2311. [CrossRef] Brussels: Pons Publishing House; 2021. pp. 50–64.
- Zadeh LA. Fuzzy sets. Inf Control 1965;8:338–353. S, Kumar R. Introduction to plithogenic hyper- [CrossRef] soft subgroup. Neutrosophic Sets Sys 2020;33:14. [33] Zulqarnain RM, Xin XL, Saqlain M, Smarandache [CrossRef] F. Generalized aggregate operators on neutrosophic
- Hussain S. On some properties of Intuitionistic hypersoft set. Neutrosophic Sets Sys 2020;36:271– fuzzy soft boundary. Commun Fac Sci Univ Ank Ser
- [CrossRef] A1 Math Stat 2020;69:39–50. [CrossRef]
- Li Z, Cui R. On the topological structures of intu- TOPSIS method under intuitionistic fuzzy hyper- itionistic fuzzy soft sets. Ann Fuzzy Math Inform soft environment based on correlation coe_cient 2013;5:229–239. and aggregation operators to solve decision making
- Maji PK, Biswas R, Roy AR. Fuzzy soft sets. J Fuzzy problem. AIMS Mathematics 2021;6:2732–2755. Math 2001;9:589–602. [CrossRef]
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YOLCU, A. Intuitionistic fuzzy hypersoft topology and ıts applications to multi-criteria decision-making. Sigma Journal of Engineering and Natural Sciences 2023, Vol. 41, pp. 106-118. https://doi.org/10.14744/sigma.2023.00011
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