Skip to main content
SpringerLink
Log in

A generalized belief interval-valued soft set with applications in decision making

  • Foundations
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

The belief interval-valued soft set (BIVSS) combines soft set theory and belief interval value (Dempster–Shafer theory). In this study, we propose a generalized belief interval-valued soft set (GBIVSS) approach and explore the associated properties of this approach in decision-making applications. Using the score function, the scoring function and similarity measure used to compare the relationships between GBIVSS are proposed. Then, we applied the GBIVSS to deal with multi-attribute decision making (MADM) problems. Furthermore, we used a case study of car purchase to illustrate the rationality of the proposed approach. In addition, we compare the effectiveness and advantages of our proposed approach and other existing models, which show superior performance in our proposed approach. GBIVSS provides a solution for multi-attribute problems.

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

Access this article

Log in via an institution

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

References

  • Agarwal M, Biswas KK, Hanmandlu M (2013) Generalized intuitionistic fuzzy soft sets with applications in decision-making. Appl Soft Comput 13(8):3552–3566

    Google Scholar 

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    MATH  Google Scholar 

  • Cai Q, Gao X, Deng Y (2020) Pignistic belief transform: a new method of conflict measurement. IEEE Access 8(1):15265–15272

    Google Scholar 

  • Cao Z, Lin CT (2018) Inherent fuzzy entropy for the improvement of EEG complexity evaluation. IEEE Trans Fuzzy Syst 26(2):1032–1035

    MathSciNet  Google Scholar 

  • Cao Z, Ding W, Wang YK, Hussain FK, Al-Jumaily A, Lin CT (2019) Effects of repetitive SSVEPs on EEG complexity using multiscale inherent fuzzy entropy. Neurocomput. https://doi.org/10.1016/j.neucom.2018.08.091

    Article  Google Scholar 

  • Cao Z, Lin CT, Lai KL, Ko LW, King JT, Liao KK, Fuh JL, Wang SJ (2019) Extraction of SSVEPs-based Inherent fuzzy entropy using a wearable headband EEG in migraine patients. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2019.2905823

    Article  Google Scholar 

  • Chen SM, Tan JM (1994) Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 67(2):163–172

    MathSciNet  MATH  Google Scholar 

  • Cheong KH, Koh JM (2019) A hybrid genetic-levenberg marquardt algorithm for automated spectrometer design optimization. Ultramicroscopy 202:100–106

    Google Scholar 

  • Cheong KH, Teo YH, Koh JM, Acharya UR, Yu SCM (2020) A simulation-aided approach in improving thermal-visual comfort and power efficiency in buildings. J Build Eng 27:100,936

    Google Scholar 

  • Cui H, Liu Q, Zhang J, Kang B (2019) An improved deng entropy and its application in pattern recognition. IEEE Access 7:18284–18292. https://doi.org/10.1109/ACCESS.2019.2896286

    Article  Google Scholar 

  • Dempster AP (1967) Upper and lower probabilities induced by a multivalued mapping. Ann Math Stat 38(2):325–339

    MathSciNet  MATH  Google Scholar 

  • Deng X, Jiang W (2019) D number theory based game-theoretic framework in adversarial decision making under a fuzzy environment. Int J Approx Reason 106:194–213

    MathSciNet  MATH  Google Scholar 

  • Deng X, Jiang W (2019) Evaluating green supply chain management practices under fuzzy environment: a novel method based on D number theory. Int J Fuzzy Syst. https://doi.org/10.1007/s40,815-019-00,639-5

    Article  Google Scholar 

  • Deng X, Jiang W, Wang Z (2019) Zero-sum polymatrix games with link uncertainty: a Dempster–Shafer theory solution. Appl Math Comput 340:101–112

    MathSciNet  MATH  Google Scholar 

  • Dinda B, Bera T, Samanta T (2010) Generalised intuitionistic fuzzy soft sets and its application in decision making. URL http://arxiv.org/pdf/1010.2468.pdf

  • Dymova L, Sevastjanov P (2010) An interpretation of intuitionistic fuzzy sets in terms of evidence theory: decision making aspect. Knowl Based Syst 23(8):772–782

    Google Scholar 

  • Dymova L, Sevastjanov P (2012) The operations on intuitionistic fuzzy values in the framework of Dempster–Shafer theory. Knowl Based Syst 35:132–143

    MATH  Google Scholar 

  • Fan CL, Song Y, Fu Q, Lei L, Wang X (2018) New operators for aggregating intuitionistic fuzzy information with their application in decision making. IEEE Access 6:27214–27238

    Google Scholar 

  • Fei L (2019) On interval-valued fuzzy decision-making using soft likelihood functions. Int J Intell Syst. https://doi.org/10.1002/int.22110

    Article  Google Scholar 

  • Feng F, Li Y (2013) Soft subsets and soft product operations. Inf Sci 232:44–57

    MathSciNet  MATH  Google Scholar 

  • Feng F, Cho J, Pedrycz W, Fujita H, Herawan T (2016) Soft set based association rule mining. Knowl Based Syst 111:268–282

    Google Scholar 

  • Feng F, Fujita H, Ali MI, Yager RR, Liu X (2019) Another view on generalized intuitionistic fuzzy soft sets and related multiattribute decision making methods. IEEE Trans Fuzzy Syst 27(3):474–488

    Google Scholar 

  • Feng F, Liang M, Fujita H, Yager RR, Liu X (2019) Lexicographic orders of intuitionistic fuzzy values and their relationships. Mathematics 7(2):166

    Google Scholar 

  • Fu C, Xu DL, Yang SL (2016) Distributed preference relations for multiple attribute decision analysis. J Oper Res Soc 67(3):457–473

    Google Scholar 

  • Fu C, Chang W, Xue M, Yang S (2019) Multiple criteria group decision making with belief distributions and distributed preference relations. Eur J Oper Res 273(2):623–633

    MathSciNet  Google Scholar 

  • Gao S, Deng Y (2019) An evidential evaluation of nuclear safeguards. Int J Distrib Sens Netw 15(12):550. https://doi.org/10.1177/1550147719894

    Article  Google Scholar 

  • Gao X, Deng Y (2020) Quantum model of mass function. Int J Intell Syst 35(2):267–282

    Google Scholar 

  • Gao X, Deng Y (2020) The pseudo-pascal triangle of maximum deng entropy. Int J Comput Commun Control 15(1):1006. https://doi.org/10.15837/3735/ijccc.2020.1.3735

    Article  Google Scholar 

  • Geng J, Ma X, Zhou X, Wang H (2019) Saliency-guided deep neural networks for sar image change detection. IEEE Trans Geosci Remote Sens. https://doi.org/10.1109/TGRS.2019.2913095

    Article  Google Scholar 

  • Gong Y, Su X, Qian H, Yang N (2018) Research on fault diagnosis methods for the reactor coolant system of nuclear power plant based on D–S evidence theory. Ann Nucl Energy 112:395–399

    Google Scholar 

  • Han Y, Deng Y, Cao Z, Lin CT (2019) An interval-valued pythagorean prioritized operator based game theoretical framework with its applications in multicriteria group decision making. Neural Comput Appl. https://doi.org/10.1007/s00521-019-04014-1

    Article  Google Scholar 

  • He Z, Jiang W (2018) An evidential dynamical model to predict the interference effect of categorization on decision making. Knowl Based Syst 150:139–149

    Google Scholar 

  • Hong DH, Choi CH (2000) Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 114(1):103–113

    MATH  Google Scholar 

  • Huang Z, Yang L, Jiang W (2019) Uncertainty measurement with belief entropy on the interference effect in the quantum-like Bayesian Networks. Appl Math Comput 347:417–428

    MathSciNet  MATH  Google Scholar 

  • Jiang W (2018) A correlation coefficient for belief functions. Int J Approx Reason 103:94–106

    MathSciNet  MATH  Google Scholar 

  • 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

    MathSciNet  MATH  Google Scholar 

  • Jiang W, Cao Y, Deng X (2019) A Novel Z-network model based on bayesian network and Z-number. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2019.2918999

    Article  Google Scholar 

  • Kang B, Deng Y (2019) The maximum Deng entropy. IEEE Access 7(1):120,758–120,765

    Google Scholar 

  • Kang B, Zhang P, Gao Z, Chhipi-Shrestha G, Hewage K, Sadiq R (2019) Environmental assessment under uncertainty using dempster-shafer theory and Z-numbers. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12,652-019-01,228-y

    Article  Google Scholar 

  • Li Y, Deng Y (2019) Intuitionistic evidence sets. IEEE Access 7(1):106,417–106,426

    Google Scholar 

  • Li Y, Qin K, He X (2013) Relations among similarity measure, subsethood measure and fuzzy entropy. Int J Comput Intell Syst 6(3):411–422

    Google Scholar 

  • Li Y, Qin K, He X (2014) Dissimilarity functions and divergence measures between fuzzy sets. Inf Sci 288:15–26

    MathSciNet  MATH  Google Scholar 

  • Li Y, Qin K, He X, Meng D (2015) Similarity measures of interval-valued fuzzy sets. J Intell Fuzzy Syst 28(5):2113–2125

    MathSciNet  MATH  Google Scholar 

  • Li Y, Qin K, He X, Meng D (2016) Robustness of fuzzy connectives and fuzzy reasoning with respect to general divergence measures. Fuzzy Sets Syst 294:63–78

    MathSciNet  MATH  Google Scholar 

  • Liu B, Deng Y (2019) Risk evaluation in failure mode and effects analysis based on D numbers theory. Int J Comput Commun Control 14(5):672–691

    Google Scholar 

  • Liu Y, Pal NR, Marathe AR, Lin C (2018) Weighted fuzzy dempster-shafer framework for multimodal information integration. IEEE Trans Fuzzy Syst 26(1):338–352. https://doi.org/10.1109/TFUZZ.2017.2659764

    Article  Google Scholar 

  • Liu Z, Pan Q, Dezert J, Martin A (2018) Combination of classifiers with optimal weight based on evidential reasoning. IEEE Trans Fuzzy Syst 26(3):1217–1230

    Google Scholar 

  • Liu F, Gao X, Zhao J, Deng Y (2019) Generalized belief entropy and its application in identifying conflict evidence. IEEE Access 7(1):126,625–126,633

    Google Scholar 

  • Luo Z, Deng Y (2020) A vector and geometry interpretation of basic probability assignment in Dempster–Shafer theory. Int J Intell Syst. https://doi.org/10.1002/int.22,231

    Article  Google Scholar 

  • Maji PK (2009) More on intuitionistic fuzzy soft sets. In: Hiroshi S, Kumar CM, Ella HA, Dominik S, William Z (eds) International workshop on rough sets, fuzzy sets, data mining, and granular-soft computing, pp 231–240. Springer

  • Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 9(3):589–602

    MathSciNet  MATH  Google Scholar 

  • Maji PK, Biswas R, Roy AR (2001) Intuitionistic fuzzy soft sets. J Fuzzy Math 9(3):677–692

    MathSciNet  MATH  Google Scholar 

  • Majumdar P, Samanta SK (2010) Generalised fuzzy soft sets. Comput Math Appl 59(4):1425–1432

    MathSciNet  MATH  Google Scholar 

  • Mo H, Deng Y (2019) Identifying node importance based on evidence theory in complex networks. Stat Mech Appl 529:121538

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Nguyen H (2016) A new interval-valued knowledge measure for interval-valued intuitionistic fuzzy sets and application in decision making. Expert Syst Appl 56:143–155

    Google Scholar 

  • Ozkan K (2018) Comparing shannon entropy with deng entropy and improved deng entropy for measuring biodiversity when a priori data is not clear. J Fac For Istanb Univ 68:136–140

    Google Scholar 

  • Pan L, Deng Y (2020) An association coefficient of belief function and its application in target recognition system. Int J Intell Syst 35:85–104

    Google Scholar 

  • Seiti H, Hafezalkotob A (2018) Developing pessimistic-optimistic risk-based methods for multi-sensor fusion: an interval-valued evidence theory approach. Appl Soft Comput 72:609–623

    Google Scholar 

  • Seiti H, Hafezalkotob A, Najafi S, Khalaj M (2018) A risk-based fuzzy evidential framework for FMEA analysis under uncertainty: an interval-valued DS approach. J Intell Fuzzy Syst 35(2):1419–1430

    Google Scholar 

  • Shafer G (1976) A mathematical theory of evidence. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Song Y, Deng Y (2019) A new soft likelihood function based on power ordered weighted average operator. Int J Intell Syst 34(11):2988–2999

    Google Scholar 

  • Song Y, Wang X, Lei L, Yue S (2016) Uncertainty measure for interval-valued belief structures. Measurement 80:241–250

    Google Scholar 

  • Song Y, Wang X, Zhu J, Lei L (2018) Sensor dynamic reliability evaluation based on evidence theory and intuitionistic fuzzy sets. Appl Intell 48(11):3950–3962

    Google Scholar 

  • Song Y, Wang X, Quan W, Huang W (2019) A new approach to construct similarity measure for intuitionistic fuzzy sets. Soft Comput 23(6):1985–1998

    MATH  Google Scholar 

  • Su X, Li L, Shi F, Qian H (2018) Research on the fusion of dependent evidence based on mutual information. IEEE Access 6:71839–71845

    Google Scholar 

  • Vijayabalaji S, Ramesh A (2019) Belief interval-valued soft set. Expert Syst Appl 119:262–271

    Google Scholar 

  • Wang Q, Li Y, Liu X (2018) Analysis of feature fatigue EEG signals based on wavelet entropy. Int J Pattern Recognit Artif Intell 32(08):1854,023

    Google Scholar 

  • Xiao F (2018) A hybrid fuzzy soft sets decision making method in medical diagnosis. IEEE Access 6:25300–25312

    Google Scholar 

  • Xiao F (2019) A distance measure for intuitionistic fuzzy sets and its application to pattern classification problems. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2019.2958635

    Article  Google Scholar 

  • Xiao F (2019) EFMCDM: evidential fuzzy multicriteria decision making based on belief entropy. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2019.2936368

    Article  Google Scholar 

  • Xiao F (2019) Generalization of Dempster–Shafer theory: a complex mass function. Appl Intell. https://doi.org/10.1007/s10,489-019-01,617-y

    Article  Google Scholar 

  • Xiao F (2020) A new divergence measure for belief functions in D–S evidence theory for multisensor data fusion. Inf Sci 514:462–483

    MathSciNet  Google Scholar 

  • Xiao F, Zhang Z, Abawajy J (2019) Workflow scheduling in distributed systems under fuzzy environment. J Intell Fuzzy Syst 37(4):5323–5333

    Google Scholar 

  • Xu W, Ma J, Wang S, Hao G (2010) Vague soft sets and their properties. Comput Math Appl 59(2):787–794

    MathSciNet  MATH  Google Scholar 

  • Xue Y, Deng Y (2020) Entailment for Intuitionistic fuzzy sets based on generalized belief structures. Int J Intell Syst. https://doi.org/10.1002/int.22,232

    Article  Google Scholar 

  • Yager RR (2015) Multicriteria decision making with ordinal/linguistic intuitionistic fuzzy sets for mobile apps. IEEE Trans Fuzzy Syst 24(3):590–599

    Google Scholar 

  • Ye Y, Hang XR, Koh JM, Miszczak JA, Cheong KH, Xie N (2020) Passive network evolution promotes group welfare in complex networks. Chaos Solitons Fractals 130:109,464

    MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  • Zavadskas EK, Antucheviciene J, Hajiagha SHR, Hashemi SS (2014) Extension of weighted aggregated sum product assessment with interval-valued intuitionistic fuzzy numbers (WASPAS-IVIF). Appl Soft Comput 24:1013–1021

    Google Scholar 

  • Zavadskas EK, Turskis Z, Vilutienė T, Lepkova N (2017) Integrated group fuzzy multi-criteria model: case of facilities management strategy selection. Expert Syst Appl 82:317–331

    Google Scholar 

  • Zhou D, Al-Durra A, Gao F, Ravey A, Matraji I, Simões MG (2017) Online energy management strategy of fuel cell hybrid electric vehicles based on data fusion approach. J Power Sour 366:278–291

    Google Scholar 

  • Zhou M, Liu X, Yang J (2017) Evidential reasoning approach for MADM based on incomplete interval value. J Intell Fuzzy Syst 33(6):3707–3721

    Google Scholar 

  • Zhou M, Liu XB, Chen YW, Yang JB (2018) Evidential reasoning rule for MADM with both weights and reliabilities in group decision making. Knowl Based Syst 143:142–161

    Google Scholar 

  • Zhou D, Al-Durra A, Zhang K, Ravey A, Gao F (2019) A robust prognostic indicator for renewable energy technologies: a novel error correction grey prediction model. IEEE Trans Ind Electron. https://doi.org/10.1109/TIE.2019.2893867

    Article  Google Scholar 

  • Zhou M, Liu XB, Yang JB, Chen YW, Wu J (2019) Evidential reasoning approach with multiple kinds of attributes and entropy-based weight assignment. Knowl Based Syst 163:358–375

    Google Scholar 

Download references

Funding

This study is partially supported by the Fundamental Research Funds for the Central Universities (No. XDJK2019C085) and Chongqing Overseas Scholars Innovation Program (No. cx2018077).

Author information

Authors and Affiliations

  1. School of Computer and Information Science, Southwest University, Chongqing, 400715, China

    Cuiping Cheng & Fuyuan Xiao

  2. The Discipline of ICT, School of Technology, Environments and Design, University of Tasmania, Hobart, TAS, Australia

    Zehong Cao

Authors
  1. Cuiping Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zehong Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fuyuan Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Zehong Cao or Fuyuan Xiao.

Ethics declarations

Conflict of interest

Author Cuiping Cheng declares that she has no conflict of interest. Author Zehong Cao declares that he has no conflict of interest. Author Fuyuan Xiao declares that she has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Communicated by A. Di Nola.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheng, C., Cao, Z. & Xiao, F. A generalized belief interval-valued soft set with applications in decision making. Soft Comput 24, 9339–9350 (2020). https://doi.org/10.1007/s00500-020-04949-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-020-04949-x

Keywords

Search

Navigation