Research Article
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Year 2023, Volume: 41 Issue: 1, 106 - 118, 14.03.2023

Abstract

References

  • REFERENCES
  • [1] Abbas M, Murtaza G, Smarandache F. Basic operations on hypersoft sets and hypersoft point. Neutrosophic Sets Sys 2020;35:407–421.
  • [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]
  • [3] Alcantud JCR. Soft open bases and a novel construc-tion of soft topologies from bases for topologies. Mathematics 2020;8:672. [CrossRef]
  • [4] Atanassov KT, Intuitionistic fuzzy sets. Fuzzy Sets Syst 1986;20:87–96. [CrossRef]
  • [5] Atanassov K, Gargov G. Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst 1989;31:343–349. [CrossRef]
  • [6] Aygunoglu A, Aygun H. Some notes on soft topo-logical spaces. Neural Comput Appl 2012;21:113–119. [CrossRef]
  • [7] Cagman N, Karatas S, Enginoglu S. Soft topology. Comput Math Appl 2011;62:351–358. [CrossRef]
  • [8] Coker D. An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets Syst 1997;88:81–89. [CrossRef}
  • [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.
  • [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]
  • [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]
  • [12] Feng F, Zheng Y, Alcantud JCR, Wang Q. Minkowski weighted score functions of intuitionistic fuzzy val-ues. Mathematics 2020;8:1143. [CrossRef]
  • [13] Garg H, Kaur G. Cubic intuitionistic fuzzy sets and its fundamental properties. J. Multvalued Log S 2019;33:507–537.
  • [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.
  • [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]
  • [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]
  • [17] Li Z, Cui R. On the topological structures of intu-itionistic fuzzy soft sets. Ann Fuzzy Math Inform 2013;5:229–239.
  • [18] Maji PK, Biswas R, Roy AR. Fuzzy soft sets. J Fuzzy Math 2001;9:589–60.
  • [19] Molodtsov DA. Soft set theory first results. Comput Math Appl 1999;37:19–31. [CrossRef]
  • [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.
  • [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]
  • [22] Ozturk TY. On bipolar soft topological spaces. J New Theory 2018;20:64–75.
  • [23]Ozturk TY, Yolcu A. Some structures on pythag-orean fuzzy topological spaces. J New Theory 2020;33:15–25.
  • [24]Roy AR, Maji PK. A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 2007;203:412–418. [CrossRef]
  • [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.
  • [26]Smarandache F. Extension of soft set to hypersoft set, and then to plithogenic hypersoft set. Neutrosophic Sets Syst 2018;22:168–170.
  • [27] Simsekler Dizman T, Ozturk TY. Fuzzy bipolar soft topological spaces. TWMS J App Eng Math 2021;11:151–159.
  • [28]Terepeta M. On separating axioms and similarity of soft topological spaces. Soft Comput 2019;23:1049–1057. [CrossRef]
  • [29]Xu ZS, Zhao N. Information fusion for intuitionis-tic fuzzy decision making: an overview. Inf Fusion 2016;28:10–23. [CrossRef]
  • [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]
  • [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.
  • [32]Zadeh LA. Fuzzy sets. Inf Control 1965;8:338–353. [CrossRef]
  • [33]Zulqarnain RM, Xin XL, Saqlain M, Smarandache F. Generalized aggregate operators on neutrosophic hypersoft set. Neutrosophic Sets Sys 2020;36:271–281. [CrossRef]
  • [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]

Intuitionistic fuzzy hypersoft topology and ıts applications to multi-criteria decision-making

Year 2023, Volume: 41 Issue: 1, 106 - 118, 14.03.2023

Abstract

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.

References

  • REFERENCES
  • [1] Abbas M, Murtaza G, Smarandache F. Basic operations on hypersoft sets and hypersoft point. Neutrosophic Sets Sys 2020;35:407–421.
  • [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]
  • [3] Alcantud JCR. Soft open bases and a novel construc-tion of soft topologies from bases for topologies. Mathematics 2020;8:672. [CrossRef]
  • [4] Atanassov KT, Intuitionistic fuzzy sets. Fuzzy Sets Syst 1986;20:87–96. [CrossRef]
  • [5] Atanassov K, Gargov G. Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst 1989;31:343–349. [CrossRef]
  • [6] Aygunoglu A, Aygun H. Some notes on soft topo-logical spaces. Neural Comput Appl 2012;21:113–119. [CrossRef]
  • [7] Cagman N, Karatas S, Enginoglu S. Soft topology. Comput Math Appl 2011;62:351–358. [CrossRef]
  • [8] Coker D. An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets Syst 1997;88:81–89. [CrossRef}
  • [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.
  • [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]
  • [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]
  • [12] Feng F, Zheng Y, Alcantud JCR, Wang Q. Minkowski weighted score functions of intuitionistic fuzzy val-ues. Mathematics 2020;8:1143. [CrossRef]
  • [13] Garg H, Kaur G. Cubic intuitionistic fuzzy sets and its fundamental properties. J. Multvalued Log S 2019;33:507–537.
  • [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.
  • [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]
  • [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]
  • [17] Li Z, Cui R. On the topological structures of intu-itionistic fuzzy soft sets. Ann Fuzzy Math Inform 2013;5:229–239.
  • [18] Maji PK, Biswas R, Roy AR. Fuzzy soft sets. J Fuzzy Math 2001;9:589–60.
  • [19] Molodtsov DA. Soft set theory first results. Comput Math Appl 1999;37:19–31. [CrossRef]
  • [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.
  • [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]
  • [22] Ozturk TY. On bipolar soft topological spaces. J New Theory 2018;20:64–75.
  • [23]Ozturk TY, Yolcu A. Some structures on pythag-orean fuzzy topological spaces. J New Theory 2020;33:15–25.
  • [24]Roy AR, Maji PK. A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 2007;203:412–418. [CrossRef]
  • [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.
  • [26]Smarandache F. Extension of soft set to hypersoft set, and then to plithogenic hypersoft set. Neutrosophic Sets Syst 2018;22:168–170.
  • [27] Simsekler Dizman T, Ozturk TY. Fuzzy bipolar soft topological spaces. TWMS J App Eng Math 2021;11:151–159.
  • [28]Terepeta M. On separating axioms and similarity of soft topological spaces. Soft Comput 2019;23:1049–1057. [CrossRef]
  • [29]Xu ZS, Zhao N. Information fusion for intuitionis-tic fuzzy decision making: an overview. Inf Fusion 2016;28:10–23. [CrossRef]
  • [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]
  • [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.
  • [32]Zadeh LA. Fuzzy sets. Inf Control 1965;8:338–353. [CrossRef]
  • [33]Zulqarnain RM, Xin XL, Saqlain M, Smarandache F. Generalized aggregate operators on neutrosophic hypersoft set. Neutrosophic Sets Sys 2020;36:271–281. [CrossRef]
  • [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]
There are 35 citations in total.

Details

Primary Language English
Subjects Empirical Software Engineering
Journal Section Research Articles
Authors

Adem Yolcu 0000-0002-4317-652X

Publication Date March 14, 2023
Submission Date March 1, 2021
Published in Issue Year 2023 Volume: 41 Issue: 1

Cite

Vancouver Yolcu A. Intuitionistic fuzzy hypersoft topology and ıts applications to multi-criteria decision-making. SIGMA. 2023;41(1):106-18.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/