Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Advertisement

Springer Nature Link
Log in

Decision-making method under the interval-valued complex fuzzy soft environment

  • Published:
Computational and Applied Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we introduce some set-theoretic operations and laws of the IV-CFSSs, such as interval-valued complex fuzzy soft complement, union, intersection, t-norm, s-norm, simple product, Cartesian product, probabilistic sum, simple difference, and the convex linear sum of min and max operators. We define the distance measure of two IV-CFSSs. This distance measure is then used to define the \(\delta \)-equality of IV-CFSSs. We establish some particular examples and basic results of these operations and laws. Moreover, we use IV-CFSSs in decision-making problems. We develop a new decision-making method using the interval-valued complex fuzzy distance measures under the environments of IV-CFSSs. We discuss the real-life case based on the proposed decision-making method. A real-life example demonstrates that the decision-making method developed in the paper can be utilized to deal with problems of uncertainty. Further, the comparative study of IV-CFSSs with complex fuzzy soft sets, interval-valued fuzzy soft sets, and fuzzy soft sets is established.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Data Availability:

Our manuscript has no associated data.

References

  • Ahsan M, Saeed M, Mehmood A, Saeed MH, Asad J (2021) The study of HIV diagnosis using complex fuzzy hypersoft mapping and proposing appropriate treatment. IEEE Access 9:104405–104417

    Google Scholar 

  • Akram M, Feng F, Borumand Saeid A, Leoreanu-Fotea V (2018) A new multiple criteria decision-making method based on bipolar fuzzy soft graphs. Iran J Fuzzy Syst 15(4):73–92

    MathSciNet  Google Scholar 

  • Akram M, Shabir M, Adeel A, Al-Kenani AN (2021a) A multiattribute decision-making framework: VIKOR method with complex spherical fuzzy-soft sets. Math Problems Eng 2021:1–25

    Google Scholar 

  • Akram M, Shabir M, Al-Kenani AN, Alcantud JCR (2021b) Hybrid decision-making frameworks under complex spherical fuzzy-soft sets. J Math 2021:1–46

    MathSciNet  Google Scholar 

  • Akram M, Shumaiza, Rodríguez Alcantud JC (2023) Extended VIKOR method based with complex bipolar fuzzy sets. In: Multi-criteria decision making methods with bipolar fuzzy sets. Springer Nature Singapore, Singapore, pp 93–122

  • Ali Z (2022) Decision-making techniques based on complex intuitionistic fuzzy power interaction aggregation operators and their applications. J Innov Res Math Comput Sci 1(1):107–125

    MathSciNet  Google Scholar 

  • Ali Z, Mahmood T, Aslam M, Chinram R (2021) Another view of complex intuitionistic fuzzy soft sets based on prioritized aggregation operators and their applications to multiattribute decision making. Mathematics 9(16):1922

    Google Scholar 

  • Alkouri AUM, Massa’deh MO, Ali M (2020) On bipolar complex fuzzy sets and its application. J Intell Fuzzy Syst 39(1):383–397

    Google Scholar 

  • Atanassov K (2016) Intuitionistic fuzzy sets. Int J Bioautom 20:1

    Google Scholar 

  • Atef M, Ali MI, Al-shami TM (2021) Fuzzy soft covering-based multi-granulation fuzzy rough sets and their applications. Comput Appl Math 40(4):115

    MathSciNet  Google Scholar 

  • Beg I, Rashid T, Jamil RN (2018) Human attitude analysis based on fuzzy soft differential equations with Bonferroni mean. Comput Appl Math 37:2632–2647

    MathSciNet  Google Scholar 

  • Begam SS, Selvachandran G, Ngan TT, Sharma R (2020) Similarity measure of lattice ordered multi-fuzzy soft sets based on set theoretic approach and its application in decision making. Mathematics 8(8):1255

    Google Scholar 

  • Bhardwaj N, Sharma P (2021) An advanced uncertainty measure using fuzzy soft sets: application to decision-making problems. Big Data Min Anal 4(2):94–103

    Google Scholar 

  • Dai S, Bi L, Hu B (2019) Distance measures between the interval-valued complex fuzzy sets. Mathematics 7(6):549

    Google Scholar 

  • Fan JP, Cheng R, Wu MQ (2019) Extended EDAS methods for multi-criteria group decision-making based on IV-CFSWAA and IV-CFSWGA operators with interval-valued complex fuzzy soft information. IEEE Access 7:105546–105561

    Google Scholar 

  • Ghosh SK, Ghosh A (2021) A novel intuitionistic fuzzy soft set based colonogram enhancement for polyps localization. Int J Imaging Syst Technol 31:1486–1502

    MathSciNet  Google Scholar 

  • Ghosh SK, Mitra A, Ghosh A (2021) A novel intuitionistic fuzzy soft set entrenched mammogram segmentation under multigranulation approximation for breast cancer detection in early stages. Expert Syst Appl 169:114329

    Google Scholar 

  • Greenfield S, Chiclana F, Dick S (2016) Interval-valued complex fuzzy logic. In: 2016 IEEE international conference on fuzzy systems (FUZZ-IEEE). IEEE, pp 2014–2019

  • Gwak J, Garg H, Jan N (2023) Hybrid integrated decision-making algorithm for clustering analysis based on a bipolar complex fuzzy and soft sets. Alex Eng J 67:473–487

    Google Scholar 

  • Hayat K, Tariq Z, Lughofer E, Aslam MF (2021) New aggregation operators on group-based generalized intuitionistic fuzzy soft sets. Soft Comput 25(21):13353–13364

    Google Scholar 

  • Hu B, Bi L, Dai S, Li S (2018) Distances of complex fuzzy sets and continuity of complex fuzzy operations. J Intell Fuzzy Syst 35(2):2247–2255

    Google Scholar 

  • Hussain A, Ali S, Ullah K (2022) A novel approach of picture fuzzy sets with unknown degree of weights based on Schweizer–Sklar aggregation operators. J Innov Res Math Comput Sci 1(2):18–39

    Google Scholar 

  • Khalil AM, Li SG, Lin Y, Li HX, Ma SG (2020) A new expert system in prediction of lung cancer disease based on fuzzy soft sets. Soft Comput 24(18):14179–14207

    Google Scholar 

  • Li C, Wu T, Chan FT (2012) Self-learning complex neuro-fuzzy system with complex fuzzy sets and its application to adaptive image noise canceling. Neurocomputing 94:121–139

    Google Scholar 

  • Liu P, Ali Z, Mahmood T (2020) The distance measures and cross-entropy based on complex fuzzy sets and their application in decision making. J Intell Fuzzy Syst 39(3):3351–3374

    Google Scholar 

  • Ma X, Zhan J, Khan M, Zeeshan M, Anis S, Awan AS (2019) Complex fuzzy sets with applications in signals. Comput Appl Math 38:1–34

    MathSciNet  Google Scholar 

  • Ma X, Fei Q, Qin H, Li H, Chen W (2021) A new efficient decision making algorithm based on interval-valued fuzzy soft set. Appl Intell 51(6):3226–3240

    Google Scholar 

  • Mahmood T, Ur Rehman U, Ali Z (2021) A novel complex fuzzy N-soft sets and their decision-making algorithm. Complex Intell Syst 7:2255–2280

    Google Scholar 

  • Maji PK (2009) More on intuitionistic fuzzy soft sets. In: International workshop on rough sets, fuzzy sets, data mining, and granular-soft computing. Springer, Berlin, pp 231–240

  • Maji PK, Roy AR, Biswas R (2001) Fuzzy Soft Sets. J Fuzzy Math 9: 589–602

  • Memiş S, Enginoğlu S, Erkan U (2021a) Numerical data classification via distance-based similarity measures of fuzzy parameterized fuzzy soft matrices. IEEE Access 9:88583–88601

    Google Scholar 

  • Memiş S, Arslan B, Aydin T, Enginoğlu S, Camci Ç (2021b) A classification method based on Hamming pseudo-similarity of intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices. J New Results Sci 10(2):59–76

    Google Scholar 

  • Močkoř J (2020) Powerset theory of fuzzy soft sets. Int J Fuzzy Log Intell Syst 20(4):298–315

    Google Scholar 

  • Močkoř J, Hurtík P (2021) Approximations of fuzzy soft sets by fuzzy soft relations with image processing application. Soft Comput 25(10):6915–6925

    Google Scholar 

  • Mohanty RK, Tripathy BK (2021) Recommending turmeric variety for higher production using interval-valued fuzzy soft set model and PSO. Int J Swarm Intell Res (IJSIR) 12(2):94–110

    Google Scholar 

  • Molodtsov D (1999) Soft set theory—first results. Comput Math Appl 37(4–5):19–31

    MathSciNet  Google Scholar 

  • Patrascu V (2015) Similarity, cardinality and entropy for bipolar fuzzy set in the framework of penta-valued representation. arXiv preprint arXiv:1506.02060

  • Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):341–356

    Google Scholar 

  • Peng X, Yang Y (2015) Some results for Pythagorean fuzzy sets. Int J Intell Syst 30(11):1133–1160

    MathSciNet  Google Scholar 

  • Peng X, Krishankumar R, Ravichandran KS (2021) A novel interval-valued fuzzy soft decision-making method based on CoCoSo and CRITIC for intelligent healthcare management evaluation. Soft Comput 25(6):4213–4241

    Google Scholar 

  • Petchimuthu S, Garg H, Kamacı H, Atagün AO (2020) The mean operators and generalized products of fuzzy soft matrices and their applications in MCGDM. Comput Appl Math 39:1–32

    MathSciNet  Google Scholar 

  • Qin H, Wang Y, Ma X, Wang J (2021) A novel approach to decision making based on interval-valued fuzzy soft set. Symmetry 13(12):2274

    Google Scholar 

  • Qiyas M, Naeem M, Khan N, Khan S, Khan F (2024) Confidence levels bipolar complex fuzzy aggregation operators and their application in decision making problem. IEEE Access 12:6204–6214

    Google Scholar 

  • Rahman AU, Saeed M, Khalid A, Ahmad MR, Ayaz S (2021) Decision-making application based on aggregations of complex fuzzy hypersoft set and development of interval-valued complex fuzzy hypersoft set. Neutrosophic Sets Syst 46(1):22

    Google Scholar 

  • Ramot D, Milo R, Friedman M, Kandel A (2002) Complex fuzzy sets. IEEE Trans Fuzzy Syst 10(2):171–186

    Google Scholar 

  • Sakr HH, Muse AH, Mohamed MS, Ateya SF (2023) Applications on bipolar vague soft sets. J Math 2023:1–25

    MathSciNet  Google Scholar 

  • Sarwar M, Akram M (2017) New applications of m-polar fuzzy matroids. Symmetry 9(12):319

    Google Scholar 

  • Selvachandran G, Salleh AR (2017) Interval-valued complex fuzzy soft sets. In: AIP conference proceedings, vol 1830, no 1. AIP Publishing LLC, p 070009

  • Selvachandran G, Singh PK (2018) Interval-valued complex fuzzy soft set and its application. Int J Uncertain Quantif 8(2):101–117

    MathSciNet  Google Scholar 

  • Singh A (2021) Modified non-linear programming methodology for multi-attribute decision-making problem with interval-valued intuitionistic fuzzy soft sets information. In: 2021 2nd Global conference for advancement in technology (GCAT). IEEE, pp 1–9

  • Thirunavukarasu P, Suresh R, Ashokkumar V (2017) Theory of complex fuzzy soft set and its applications. Int J Innov Res Sci Technol 3(10):13–18

    Google Scholar 

  • Yang X, Lin TY, Yang J, Li Y, Yu D (2009) Combination of interval-valued fuzzy set and soft set. Comput Math Appl 58(3):521–527

    MathSciNet  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Google Scholar 

  • Zararsız Z, Riaz M (2022) Bipolar fuzzy metric spaces with application. Comput Math Appl 41(1):49

    MathSciNet  Google Scholar 

  • Zeeshan M, Khan M (2022) Complex fuzzy sets with applications in decision-making. Iran J Fuzzy Syst 19(4):147–163

    MathSciNet  Google Scholar 

  • Zeeshan M, Khan M, Iqbal S (2022) Distance function of complex fuzzy soft sets with application in signals. Comput Appl Math 41(3):96

    MathSciNet  Google Scholar 

  • Zhang WR (1994) Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis. In: NAFIPS/IFIS/NASA’94. Proceedings of the first international joint conference of the North American fuzzy information processing society biannual conference. The Industrial Fuzzy Control and Intelligence. IEEE, pp 305–309

  • Zhang G, Dillon TS, Cai KY, Ma J, Lu J (2009) Operation properties and \(\delta \)-equalities of complex fuzzy sets. Int J Approx Reason 50(8):1227–1249

    MathSciNet  Google Scholar 

  • Zulqarnain RM, Xin XL, Saqlain M, Khan WA (2021) TOPSIS method based on the correlation coefficient of interval-valued intuitionistic fuzzy soft sets and aggregation operators with their application in decision-making. J Math 2021:1–16

    MathSciNet  Google Scholar 

Download references

Acknowledgements

This work is financially supported by the Higher Education Commission of Pakistan (Grant No. 7750/Federal/NRPU/R &D/HEC/2017).

Author information

Authors and Affiliations

  1. Department of Mathematics, COMSATS University Islamabad, Islamabad Campus, Pakistan

    Muhammad Zeeshan

  2. Department of Mathematics, University of Agriculture, Dera Ismail Khan, Pakistan

    Muhammad Zeeshan

  3. Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Pakistan

    Madad Khan & Saima Anis

  4. Department of Computer Science, University of Agriculture, Dera Ismail Khan, Pakistan

    Muhammad Ali Abid

  5. Department of Mathematics, Gomal University, Dera Ismail Khan, Pakistan

    Zubair Ahmad

Authors
  1. Muhammad Zeeshan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Madad Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Muhammad Ali Abid
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zubair Ahmad
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Saima Anis
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors have contributed equally to this work.

Corresponding author

Correspondence to Madad Khan.

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

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zeeshan, M., Khan, M., Abid, M.A. et al. Decision-making method under the interval-valued complex fuzzy soft environment. Comp. Appl. Math. 43, 203 (2024). https://doi.org/10.1007/s40314-024-02686-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40314-024-02686-7

Keywords

Mathematics Subject Classification

Search

Navigation