Abstract
Although some statistical tools, such as mean and median, used for modelling a problem containing parameters or alternatives with multiple intuitionistic fuzzy values because these values are obtained in a specific period, decrease uncertainty, they lead to data loss. However, interval-valued intuitionistic fuzzy values can overcome such a concern. For this reason, the present study proposes the concept of interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft sets (d-sets) and presents several of its basic properties. Moreover, by using d-sets, we suggest a new soft decision-making method and apply it to a problem concerning the eligibility of candidates for two vacant positions in an online job advertisement. Since it is the first method proposed in relation to this structure (d-sets), it is impossible to compare this method with another in this sense. To deal with this difficulty, we introduce four new concepts, i.e. mean reduction, mean bireduction, mean bireduction-reduction, and mean reduction-bireduction. By using these concepts, we apply four state-of-the-art soft decision-making methods to the problem. We then compare the ranking performances of the proposed method with those of the four methods. Besides, we apply five methods to a real problem concerning performance-based value assignment to some filters used in image denoising and compare the ranking performances of these methods. Finally, we discuss d-sets and the proposed method for further research.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles and news from researchers in related subjects, suggested using machine learning.References
Alkhazaleh S, Salleh AR, Hassan N (2011) Fuzzy parameterized interval-valued fuzzy soft set. Appl Math Sci 5(67):3335–3346
Atanassov K, Marinov P, Atanassova V (2019) Intercriteria analysis with interval-valued intuitionistic fuzzy evaluations. In: Int conf flexible query answering syst, pp 329–338. https://doi.org/10.1007/978-3-030-27629-4_30
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
Atanassov KT (1994) Operators over interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst 64(2):159–174. https://doi.org/10.1016/0165-0114(94)90331-X
Atanassov KT (2020) Interval-valued intuitionistic fuzzy sets. Studies in fuzziness and soft computing. Springer
Atanassov KT, Gargov G (1989) Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31(3):343–349. https://doi.org/10.1016/0165-0114(89)90205-4
Atmaca S (2017) Relationship between fuzzy soft topological spaces and \(({X},\tau _{e})\) parameter spaces. Cumhuriyet Sci J 38(4):77–85. https://doi.org/10.17776/csj.340541
Çağman N, Enginoğlu S (2010a) Soft matrix theory and its decision making. Comput Math Appl 59(10):3308–3314. https://doi.org/10.1016/j.camwa.2010.03.015
Çağman N, Enginoğlu S (2010b) Soft set theory and \(uni\)-\(int\) decision making. Eur J Oper Res 207(2):848–855. https://doi.org/10.1016/j.ejor.2010.05.004
Çağman N, Enginoğlu S (2012) Fuzzy soft matrix theory and its application in decision making. Iran J Fuzzy Syst 9(1):109–119. http://ijfs.usb.ac.ir/article_229.html
Çağman N, Çıtak F, Enginoğlu S (2010) Fuzzy parameterized fuzzy soft set theory and its applications. Turk J Fuzzy Syst 1(1):21–35
Çağman N, Çıtak F, Enginoğlu S (2011a) FP-soft set theory and its applications. Ann Fuzzy Math Inf 2(2):219–226. http://www.afmi.or.kr/papers/2011/Vol-02_No-02/AFMI-2-2(219-226)-J-110329R1.pdf
Çağman N, Enginoğlu S, Çıtak F (2011b) Fuzzy soft set theory and its applications. Iran J Fuzzy Syst 8(3):137–147. http://ijfs.usb.ac.ir/article_292.html
Çıtak F, Çağman N (2015) Soft int-rings and its algebraic applications. J Intell Fuzzy Syst 28(3):1225–1233. https://doi.org/10.3233/IFS-141406
Çıtak F, Çağman N (2017) Soft k-int-ideals of semirings and its algebraic structures. Ann Fuzzy Math Inf 13(4):531–538. https://doi.org/10.30948/afmi.2017.13.4.531
Deli I, Çağman N (2015) Intuitionistic fuzzy parameterized soft set theory and its decision making. Appl Soft Comput 28:109–113. https://doi.org/10.1016/j.asoc.2014.11.053
Deli I, Karataş S (2016) Interval valued intuitionistic fuzzy parameterized soft set theory and its decision making. J Intell Fuzzy Syst 30(4):2073–2082. https://doi.org/10.3233/IFS-151920
Enginoğlu S (2012) Soft matrices. PhD dissertation, Gaziosmanpaşa University, Tokat. https://tez.yok.gov.tr/UlusalTezMerkezi
Enginoğlu S, Çağman N (n.d.) Fuzzy parameterized fuzzy soft matrices and their application in decision-making. TWMS J Appl Eng Math, In Press
Enginoğlu S, Memiş S (2018) A configuration of some soft decision-making algorithms via fpfs-matrices. Cumhuriyet Sci J 39(4):871–881. https://doi.org/10.17776/csj.409915
Enginoğlu S, Çağman N, Karataş S, Aydın T (2015) On soft topology. El-Cezerî J Sci Eng 2(3):23–38. https://doi.org/10.31202/ecjse.67135
Enginoğlu S, Memiş S, Arslan B (2018) Comment (2) on soft set theory and uni-int decision-making [European Journal of Operational Research, (2010) 207, 848–855]. J New Theory (25):84–102. https://dergipark.org.tr/download/article-file/594503
Enginoğlu S, Erkan U, Memiş S (2019) Pixel similarity-based adaptive Riesz mean filter for salt-and-pepper noise removal. Multimed Tools Appl 78:35401–35418. https://doi.org/10.1007/s11042-019-08110-1
Erkan U, Gökrem L (2018) A new method based on pixel density in salt and pepper noise removal. Turk J Electr Eng Comput Sci 26(1):162–171. https://doi.org/10.3906/elk-1705-256
Erkan U, Gökrem L, Enginoğlu S (2018) Different applied median filter in salt and pepper noise. Comput Electr Eng 70:789–798. https://doi.org/10.1016/j.compeleceng.2018.01.019
Esakkirajan S, Veerakumar T, Subramanyam AN, PremChand CH (2011) Removal of high density salt and pepper noise through modified decision based unsymmetric trimmed median filter. IEEE Signal Process Lett 18(5):287–290. https://doi.org/10.1109/LSP.2011.2122333
Garg H, Arora R (2020) Maclaurin symmetric mean aggregation operators based on t-norm operations for the dual hesitant fuzzy soft set. J Ambient Intell Humaniz Comput 11(1):375–410. https://doi.org/10.1007/s12652-019-01238-w
Gorzałczany MB (1987) A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 21(1):1–17. https://doi.org/10.1016/0165-0114(87)90148-5
Hao F, Pei Z, Park DS, Phonexay V, Seo HS (2018) Mobile cloud services recommendation: a soft set-based approach. J Ambient Intell Humaniz Comput 9(4):1235–1243. https://doi.org/10.1007/s12652-017-0572-7
Hemavathi P, Muralikrishna P, Palanivel K (2018) On interval valued intuitionistic fuzzy \(\beta\)-subalgebras. Afr Mat 29(1–2):249–262. https://doi.org/10.1007/s13370-017-0539-z
Huang B, Zhuang YL, Li HX (2013) Information granulation and uncertainty measures in interval-valued intuitionistic fuzzy information systems. Eur J Oper Res 231(1):162–170. https://doi.org/10.1016/j.ejor.2013.05.006
Iqbal MN, Rizwan U (2019) Some applications of intuitionistic fuzzy sets using new similarity measure. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-019-01516-7
Jiang Y, Tang Y, Chen Q, Liu H, Tang J (2010) Interval-valued intuitionistic fuzzy soft sets and their properties. Comput Math Appl 60(3):906–918. https://doi.org/10.1016/j.camwa.2010.05.036
Joshi R (2020) A new multi-criteria decision-making method based on intuitionistic fuzzy information and its application to fault detection in a machine. J Ambient Intell Humaniz Comput 11(2):739–753. https://doi.org/10.1007/s12652-019-01322-1
Kamacı H (2019) Interval-valued fuzzy parameterized intuitionistic fuzzy soft sets and their applications. Cumhuriyet Sci J 40(2):317–331. https://doi.org/10.17776/csj.524802
Karaaslan F (2016) Intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets with applications in decision making. Ann Fuzzy Math Inf 11(4):607–619. http://www.afmi.or.kr/papers/2016/Vol-11_No-04/PDF/AFMI-11-4(607-619)-H-150813-1R1.pdf
Kim T, Sotirova E, Shannon A, Atanassova V, Atanassov K, Jang LC (2018) Interval valued intuitionistic fuzzy evaluations for analysis of a student’s knowledge in university e-learning courses. Int J Fuzzy Logic Intell Syst 18(3):190–195. https://doi.org/10.5391/IJFIS.2018.18.3.190
Liu Y, Jiang W (2020) A new distance measure of interval-valued intuitionistic fuzzy sets and its application in decision making. Soft Comput 24(9):6987–7003. https://doi.org/10.1007/s00500-019-04332-5
Luo M, Liang J (2018) A novel similarity measure for interval-valued intuitionistic fuzzy sets and its applications. Symmetry 10(10):1–13. https://doi.org/10.3390/sym10100441
Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 9(3):589–602
Maji PK, Roy AR, Biswas R (2002) An application of soft sets in a decision making problem. Comput Math Appl 44(8–9):1077–1083. https://doi.org/10.1016/S0898-1221(02)00216-X
Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45(4–5):555–562. https://doi.org/10.1016/S0898-1221(03)00016-6
Min WK (2008) Interval-valued intuitionistic fuzzy soft sets. J Korean Inst Intell Syst 18(3):316–322. https://doi.org/10.5391/JKIIS.2008.18.3.316
Mishra AR, Rani P (2018) Interval-valued intuitionistic fuzzy WASPAS method: application in reservoir flood control management policy. Group Decis Negotiat 27(6):1047–1078. https://doi.org/10.1007/s10726-018-9593-7
Molodtsov D (1999) Soft set theory-first results. Comput Math Appl 37(4–5):19–31. https://doi.org/10.1016/S0898-1221(99)00056-5
Niewiadomski A (2013) Cylindric extensions of interval-valued fuzzy sets in data linguistic summaries. J Ambient Intell Humaniz Comput 4(3):369–376. https://doi.org/10.1007/s12652-011-0098-3
Park CK (2016) Interval-valued intuitionistic gradation of openness. Korean J Math 24(1):27–40. https://doi.org/10.11568/kjm.2016.24.1.27
Park CK (2017) \(([r, s],[t, u])\)-interval-valued intuitionistic fuzzy generalized precontinuous mappings. Korean J Math 25(1):1–18 https://doi.org/10.11568/kjm.2017.25.1.1
Pattnaik A, Agarwal S, Chand S (2012) A new and efficient method for removal of high density salt and pepper noise through cascade decision based filtering algorithm. Proc Technol 6:108–117. https://doi.org/10.1016/j.protcy.2012.10.014
Priyadharsini J, Balasubramaniam P (2019) Multi-criteria decision making method based on interval-valued intuitionistic fuzzy sets. J Anal 27(1):259–276. https://doi.org/10.1007/s41478-018-0122-5
Razak SA, Mohamad D (2011) A soft set based group decision making method with criteria weight. World Acad Sci Eng Technol 5(10):1641–1646. https://doi.org/10.5281/zenodo.1062538
Razak SA, Mohamad D (2013) A decision making method using fuzzy soft sets. Malays J Fundam Appl Sci 9(2):99–104. https://doi.org/10.11113/mjfas.v9n2.91
Riaz M, Hashmi MR (2017) Fuzzy parameterized fuzzy soft topology with applications. Ann Fuzzy Math Inf 13(5):593–613. https://doi.org/10.30948/afmi.2017.13.5.593
Riaz M, Hashmi MR, Farooq A (2018) Fuzzy parameterized fuzzy soft metric spaces. J Math Anal 9(2):25–36. http://www.ilirias.com/jma/repository/docs/JMA9-2-3.pdf
Selvachandran G, John SJ, Salleh AR (2017) Decision making based on the aggregation operator and the intuitionistic fuzzy reduction method of intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets. J Telecommun Electron Comput Eng 9(1-3):123–127. http://journal.utem.edu.my/index.php/jtec/article/view/1756
Senapati T, Shum KP (2019) Atanassov’s interval-valued intuitionistic fuzzy set theory applied in KU-subalgebras. Discrete Math Algorithms Appl 11(2):17. https://doi.org/10.1142/S179383091950023X
Şenel G (2016) A new approach to Hausdorff space theory via the soft sets. Math Probl Eng 2016:6. https://doi.org/10.1155/2016/2196743(Article ID 2196743)
Şenel G (2018) Analyzing the locus of soft spheres: illustrative cases and drawings. Eur J Pure Appl Math 11(4):946–957. https://doi.org/10.29020/nybg.ejpam.v11i4.3321
Sezgin A (2016) A new approach to semigroup theory I: Soft union semigroups, ideals and bi-ideals. Algebra Lett 2016(3):1–46, http://scik.org/index.php/abl/article/view/2989
Sezgin A, Çağman N, Çıtak F (2019) \(\alpha\)-inclusions applied to group theory via soft set and logic. Commun Fac Sci Univ Ank Ser A1 Math Stat 68(1):334–352. https://doi.org/10.31801/cfsuasmas.420457
Sotirov S, Sotirova E, Atanassova V, Atanassov K, Castillo O, Melin P, Petkov T, Surchev S (2018) A hybrid approach for modular neural network design using intercriteria analysis and intuitionistic fuzzy logic. Complexity 2018:11. https://doi.org/10.1155/2018/3927951(Article ID 3927951)
Sulukan E, Çağman N, Aydın T (2019) Fuzzy parameterized intuitionistic fuzzy soft sets and their application to a performance-based value assignment problem. J New Theory (29):79–88. https://dergipark.org.tr/tr/download/article-file/906764
Tan C (2011) A multi-criteria interval-valued intuitionistic fuzzy group decision making with choquet integral-based topsis. Expert Syst Appl 38(4):3023–3033. https://doi.org/10.1016/j.eswa.2010.08.092
Tang Z, Yang Z, Liu K, Pei Z (2016) A new adaptive weighted mean filter for removing high density impulse noise. In: Eighth international conference on digital image processing (ICDIP 2016), international society for optics and photonics, vol 10033, pp 1003353/1–5. https://doi.org/10.1117/12.2243838
Thomas J, John SJ (2016) A note on soft topology. J New Results Sci 5(11):24–29. https://dergipark.org.tr/tr/pub/jnrs/issue/27287/287227
Toh KKV, Isa NAM (2010) Noise adaptive fuzzy switching median filter for salt-and-pepper noise reduction. IEEE Signal Process Lett 17(3):281–284. https://doi.org/10.1109/LSP.2009.2038769
Ullah A, Karaaslan F, Ahmad I (2018) Soft uni-Abel-Grassmann’s groups. Eur J Pure Appl Math 11(2):517–536. https://doi.org/10.29020/nybg.ejpam.v11i2.3228
Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600–612. https://doi.org/10.1109/TIP.2003.819861
Xu Z, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35(4):417–433. https://doi.org/10.1080/03081070600574353
Xu ZS (2007) Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control Decis 22(2):215–219
Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8(3):199–249. https://doi.org/10.1016/0020-0255(75)90036-5
Zorlutuna I, Atmaca S (2016) Fuzzy parametrized fuzzy soft topology. New Trends Math Sci 4(1):142–152. https://doi.org/10.20852/ntmsci.2016115658
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Aydın, T., Enginoğlu, S. Interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft sets and their application in decision-making. J Ambient Intell Human Comput 12, 1541–1558 (2021). https://doi.org/10.1007/s12652-020-02227-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12652-020-02227-0