TY - JOUR T1 - Intuitionistic fuzzy hypersoft topology and ıts applications to multi-criteria decision-making AU - Yolcu, Adem PY - 2023 DA - March JF - Sigma Journal of Engineering and Natural Sciences JO - SIGMA PB - Yildiz Technical University WT - DergiPark SN - 1304-7191 SP - 106 EP - 118 VL - 41 IS - 1 LA - en AB - The aim of this paper is to introduce the concept of intuitionistic fuzzy hypersoft to pology. Certain properties of intuitionistic fuzzy hypersoft (IFH) t o pology l i ke IFH b a sis, 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. KW - Intuitionistic Fuzzy Hypersoft Set KW - İntuitionistic Fuzzy Hypersoft Topology KW - IFH İnterior(Closure) KW - IFH Basis KW - MCDM CR - REFERENCES CR - [1] Abbas M, Murtaza G, Smarandache F. Basic operations on hypersoft sets and hypersoft point. Neutrosophic Sets Sys 2020;35:407–421. CR - [2] Alcantud JCR, Khameneh AZ, Kilicman A. Aggregation of in_nite chains of intuitionistic fuzzy sets and their application to choices with temporal intuitionistic fuzzy information. Inf Sci 2020;514:106–117. [CrossRef] CR - [3] Alcantud JCR. Soft open bases and a novel construc-tion of soft topologies from bases for topologies. Mathematics 2020;8:672. [CrossRef] CR - [4] Atanassov KT, Intuitionistic fuzzy sets. Fuzzy Sets Syst 1986;20:87–96. [CrossRef] CR - [5] Atanassov K, Gargov G. Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst 1989;31:343–349. [CrossRef] CR - [6] Aygunoglu A, Aygun H. Some notes on soft topo-logical spaces. Neural Comput Appl 2012;21:113–119. [CrossRef] CR - [7] Cagman N, Karatas S, Enginoglu S. Soft topology. Comput Math Appl 2011;62:351–358. [CrossRef] CR - [8] Coker D. An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets Syst 1997;88:81–89. [CrossRef} CR - [9] Deli I. Hybrid Set Structures Under Uncertainly Parameterized Hypersoft Sets: Theory and Applications In: Smarandache F, Abdel-Baset M, Saeed M, Saqlain M, editors. Theory and application of hypersoft set. 1st ed. Brussels: Pons Publishing House; 2021. pp. 24–49. CR - [10] Enginoglu S, Arslan B. Intuitionistic fuzzy param-eterized intuitionistic fuzzy soft matrices and their application in decision-making. Comput Appl Math 2020;39:325. [CrossRef] CR - [11] Faizi S, Salabun W, Rashid T, Zafar S, Watrobski J. Intuitionistic fuzzy sets in multicriteria group decision making problems using the characteristic objects method. Symmetry 2020;12:1382. [CrossRef] CR - [12] Feng F, Zheng Y, Alcantud JCR, Wang Q. Minkowski weighted score functions of intuitionistic fuzzy val-ues. Mathematics 2020;8:1143. [CrossRef] CR - [13] Garg H, Kaur G. Cubic intuitionistic fuzzy sets and its fundamental properties. J. Multvalued Log S 2019;33:507–537. CR - [14] Garg H, Kumar K. Linguistic interval-valued Atanassov intuitionistic fuzzy sets and their appli-cations to group decision-making problem. IEEE Trans Fuzzy Syst 2019;27:2302-2311. CR - [15] Gayen S, Smarandache F, Jha S, Singh MK, Broumi S, Kumar R. Introduction to plithogenic hyper-soft subgroup. Neutrosophic Sets Sys 2020;33:14.[CrossRef] CR - [16] Hussain S. On some properties of Intuitionistic fuzzy soft boundary. Commun Fac Sci Univ Ank Ser A1 Math Stat 2020;69:39–50. [CrossRef] CR - [17] Li Z, Cui R. On the topological structures of intu-itionistic fuzzy soft sets. Ann Fuzzy Math Inform 2013;5:229–239. CR - [18] Maji PK, Biswas R, Roy AR. Fuzzy soft sets. J Fuzzy Math 2001;9:589–60. CR - [19] Molodtsov DA. Soft set theory first results. Comput Math Appl 1999;37:19–31. [CrossRef] CR - [20] Ozturk TY, Yolcu A. On neutrosophic hypersoft topological spaces. In: Smarandache F, Abdel-Baset M, Saeed M, Saqlain M, editors. Theory and application of hypersoft set. 1st ed. Brussels: Pons Publishing House; 2021. pp. 215–234. CR - [21] Ozturk TY, Gunduz Aras C, Bayramov S. A new approach to operations on neutrosophic soft sets and to neutrosophic soft topological spaces. Commun Math Appl 2019;10:481–493. [CrossRef] CR - [22] Ozturk TY. On bipolar soft topological spaces. J New Theory 2018;20:64–75. CR - [23]Ozturk TY, Yolcu A. Some structures on pythag-orean fuzzy topological spaces. J New Theory 2020;33:15–25. CR - [24]Roy AR, Maji PK. A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 2007;203:412–418. [CrossRef] CR - [25]Saeed M, Ahsan M, Siddique MK, Ahmad MR. A study of the fundamentals of hypersoft set theory. Int J Sci Eng Res 2020;11:230. CR - [26]Smarandache F. Extension of soft set to hypersoft set, and then to plithogenic hypersoft set. Neutrosophic Sets Syst 2018;22:168–170. CR - [27] Simsekler Dizman T, Ozturk TY. Fuzzy bipolar soft topological spaces. TWMS J App Eng Math 2021;11:151–159. CR - [28]Terepeta M. On separating axioms and similarity of soft topological spaces. Soft Comput 2019;23:1049–1057. [CrossRef] CR - [29]Xu ZS, Zhao N. Information fusion for intuitionis-tic fuzzy decision making: an overview. Inf Fusion 2016;28:10–23. [CrossRef] CR - [30]Yolcu A, Smarandache F, Ozturk TY. Intuitionistic fuzzy hypersoft set. Commun Fac Sci Univ Ank Ser A1 Math Stat 2021;70:443–455. [CrossRef] CR - [31] Yolcu A, Ozturk TY, Fuzzy Hypersoft Sets and It’s Application to Decision-Making. In: Smarandache F, Abdel-Baset M, Saeed M, Saqlain M, editors. Theory and application of hypersoft set. 1st ed. Brussels: Pons Publishing House; 2021. pp. 50–64. CR - [32]Zadeh LA. Fuzzy sets. Inf Control 1965;8:338–353. [CrossRef] CR - [33]Zulqarnain RM, Xin XL, Saqlain M, Smarandache F. Generalized aggregate operators on neutrosophic hypersoft set. Neutrosophic Sets Sys 2020;36:271–281. [CrossRef] CR - [34] Zulqarnain RM, Xin XL, Saeed M. Extension of TOPSIS method under intuitionistic fuzzy hyper-soft environment based on correlation coe_cient and aggregation operators to solve decision making problem. AIMS Mathematics 2021;6:2732–2755. [CrossRef] UR - https://dergipark.org.tr/en/pub/sigma/issue//1402864 L1 - https://dergipark.org.tr/en/download/article-file/3590724 ER -