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Weighted interval-valued dual-hesitant fuzzy sets and its application in teaching quality assessment

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Abstract

As a robust generalization to fuzzy set, the interval-valued dual-hesitant fuzzy set (IVDHFS) was put forward, which provided several possible membership and non-membership interval values to be associated with a specific substance. But IVDHFS does not couple the membership and non-membership values with their corresponding weights/importance degrees to assess a variable, which is irrational. To circumvent this issue, this study introduces the weighted interval-valued dual-hesitant fuzzy set (WIVDHFS) which describe the membership and non-membership values in the form of interval along with their weights. These assigned weights give more detail about the level of agreeness and disagreeness and thereby can help the decision makers (DMs) to obtain precise, rational, and consistent decision consequences. After introducing the pioneer notion of WIVDHFS, several related terms, viz. connected weighted interval-valued dual-hesitant element (WIVDHFE), score function, and accuracy function are defined. Using Archimedean t-norm and t-conorm, some basic operational laws for WIVDHFEs are constructed. Next, to aggregate WIVDHFEs, two types of aggregation operators based on Archimedean t-norm and t-conorm, namely the generalized weighted interval-valued dual-hesitant fuzzy-weighted averaging operator and the generalized weighted interval-valued dual-hesitant fuzzy-weighted geometric operator are designed along with their relevant properties. Meanwhile, some of their special cases and relationships are also explored. On the basis of special cases, a novel multi-criteria group decision-making approach under weighted interval-valued dual-hesitant fuzzy environment is then constructed. Finally, an application case about teaching quality assessment is presented, and some analyses and comparisons are provided to validate the proposed approach.

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References

  • Alcantud JCR, Giarlotta A (2019) Necessary and possible hesitant fuzzy sets: a novel model for group decision making. Inf Fusion 46:63–76

    Google Scholar 

  • Amin F, Fahmi A, Abdullah S (2019) Dealer using a new trapezoidal cubic hesitant fuzzy TOPSIS method and application to group decision-making program. Soft Comput 23:5353–5366

    MATH  Google Scholar 

  • Amin F, Fahmi A (2019) Human immunodeficiency virus (HIV) infection model based on triangular neutrosophic cubic hesitant fuzzy number. Int J Biomath 12:1950055

    Google Scholar 

  • Arqub OA, Al-Smadi M, Momani S, Hayat T (2017) Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems. Soft Comput 21:7191–7206

    MATH  Google Scholar 

  • Arqub OA, Al-Smadi M (2020) Fuzzy conformable fractional differential equations: Novel extended approach and new numerical solutions. Soft Comput 24:12501–1252

    Google Scholar 

  • Atanassov K, Gargov G (1989) Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31:343–349

    MathSciNet  MATH  Google Scholar 

  • Bagchi U (2010) Delivering student satisfaction in higher education: a QFD approach. In: 2010 7th international conference on service systems and service management, vol 10, pp 1049–1052

  • Bashir Z, Bashir Y, Rashid T, Ali J, Gao W (2019) A novel multi-attribute group decision-making approach in the framework of proportional dual hesitant fuzzy sets. Appl Sci 9:1232

    Google Scholar 

  • Bustince H, Burillo P (1995) Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 74:237–244

    MathSciNet  MATH  Google Scholar 

  • Chang TC, Wang H (2016) A multi criteria group decision-making model for teacher evaluation in higher education based on cloud model and decision tree. Eurasia J Math Sci Technol Educ 12:1243–1262

    MathSciNet  Google Scholar 

  • Chen JF, Hsieh HN, Do QH (2015) Evaluating teaching performance based on fuzzy AHP and comprehensive evaluation approach. Appl Soft Comput 28:100–108

    Google Scholar 

  • Chen N, Xu Z, **a M (2013) Interval-valued hesitant preference relations and their applications to group decision making. Knowl-Based Syst 37:528–540

    Google Scholar 

  • Chen N, Xu Z (2014) Properties of interval-valued hesitant fuzzy sets. J Intell Fuzzy Syst 27:143–158

    MathSciNet  MATH  Google Scholar 

  • Cheng SH (2018) Autocratic decision making using group recommendations based on hesitant fuzzy sets for green hotels selection and bidders selection. Inf Sci 467:604–617

    MathSciNet  MATH  Google Scholar 

  • Fahmi A, Abdullah S, Amin F, Ali A, Ahmed R, Shakeel M (2019) Trapezoidal cubic hesitant fuzzy aggregation operators and their application in group decision-making. J Intell Fuzzy Syst 36(4):3619–3635

    Google Scholar 

  • Farhadinia B (2013) Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inf Sci 240:129–144

    MathSciNet  MATH  Google Scholar 

  • Gao Y, **ao J, Yinglan S, Zhong Y, ** H (2010) Factor analysis in the teaching quality assessment. Educational Management and Evaluation

  • Gitinavard H, Mousavi SM, Vahdani B (2016) A new multi-criteria weighting and ranking model for group decision-making analysis based on interval-valued hesitant fuzzy sets to selection problems. Neural Comput Appl 27:1593–1605

    Google Scholar 

  • Gorzałczany MB (1987) A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 21:1–17

    MathSciNet  MATH  Google Scholar 

  • Hafezalkotob A, Hafezalkotob A, Liao H, Herrera F (2019) An overview of MULTIMOORA for multi-criteria decision-making: theory, developments, applications, and challenges. Inf Fusion 51:145–177

    Google Scholar 

  • Hamachar H (1978) Uber logische verknunpfungenn unssharfer Aussagen und deren Zugenhorige Bewertungsfunktione Trappl. In: Riccardi K (ed) Progress in cybernatics and systems research, vol 3. Hemisphere, Washington DC, pp 276–288

    Google Scholar 

  • Han Y (2001) On the evaluation criteria of teaching. Curriculum reform, Heilongjiang education 5

  • Hu BQ (2016) Three-way decision spaces based on partially ordered sets and three-way decisions based on hesitant fuzzy sets. Knowl-Based Syst 91:16–31

    Google Scholar 

  • Jiang C, Jiang S, Chen J (2019) Interval-valued dual hesitant fuzzy Hamacher aggregation operators for multiple attribute decision making. J Syst Sci Inf 7:227–256

    Google Scholar 

  • ** C, Wang H, Xu Z (2019) Uncertain probabilistic linguistic term sets in group decision making. Int J Fuzzy Syst 21:1241–1258

    MathSciNet  Google Scholar 

  • Ju Y, Liu X, Yang S (2014) Interval-valued dual hesitant fuzzy aggregation operators and their application to multiple attribute decision making. J Intell Fuzzy Syst 27:1203–1218

    MathSciNet  MATH  Google Scholar 

  • Khan MSA, Abdullah S, Ali A, Siddiqui N, Amin F (2017) Pythagorean hesitant fuzzy sets and their application to group decision making with incomplete weight information. J Intell Fuzzy Syst 33:3971–3985

    Google Scholar 

  • Klement EP, Mesiar R (2005) Logical, algebraic, analytic and probabilistic aspects of triangular norms. Elsevier, New York

    MATH  Google Scholar 

  • Krishankumar R, Ravichandran KS, Gandomi AH, Kar S (2020) Interval-valued probabilistic hesitant fuzzy set-based framework for group decision-making with unknown weight information. Neural Comput Appl. https://doi.org/10.1007/s00521-020-

    Article  Google Scholar 

  • Lan J, ** R, Zheng Z, Hu M (2017) Priority degrees for hesitant fuzzy sets: application to multiple attribute decision making. Oper Res Perspect 4:67–73

    MathSciNet  Google Scholar 

  • Li XG (2012) Computer-web-based multimedia college English teaching assessment model with uncertain linguistic information. Adv Inf Sci Serv Sci 4:178–183

    Google Scholar 

  • Li DF (2010) TOPSIS-based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets. IEEE Trans Fuzzy Syst 18:299–311

    Google Scholar 

  • Liu S, Liu C (2018) Scale-varying dynamic time war** based on hesitant fuzzy sets for multivariate time series classification. Measurement 130:290–297

    Google Scholar 

  • Meng F, Wang C, Chen X, Zhang Q (2016) Correlation coefficients of interval-valued hesitant fuzzy sets and their application based on the shapley function. Int J Intell Syst 31:17–43

    Google Scholar 

  • Morente-Molinera JA, Ríos-Aguilar S, González-Crespo R, Herrera-Viedma E (2019) Dealing with group decision-making environments that have a high amount of alternatives using card-sorting techniques. Expert Syst Appl 127:187–198

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Nawaz F, Asadabadi MR, Janjua NK, Hussain OK, Chang E, Saberi M (2018) An MCDM method for cloud service selection using a Markov chain and the best-worst method. Knowl-Based Syst 159:120–131

    Google Scholar 

  • Nayagam VLG, Muralikrishnan S, Sivaraman G (2011) Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets. Expert Syst Appl 38:1464–1467

    Google Scholar 

  • Peng X, Dai J, Liu L (2018) Interval-valued dual hesitant fuzzy information aggregation and its application in multiple attribute decision making. Int J Uncertain Quant 8:361–382

    MathSciNet  Google Scholar 

  • Peng X, Dai J (2019) Research on the assessment of classroom teaching quality with q-rung orthopair fuzzy information based on multiparametric similarity measure and combinative distance-based assessment. Int J Intell Syst 34:1588–1630

    Google Scholar 

  • Quirós P, Alonso P, Bustince H, Díaz I, Montes S (2015) An entropy measure definition for finite interval-valued hesitant fuzzy sets. Knowl-Based Syst 84:121–133

    Google Scholar 

  • Qu G, Qu W, Li C (2018) Some new interval-valued dual hesitant fuzzy Choquet integral aggregation operators and their applications. J Intell Fuzzy Syst 34:245–266

    Google Scholar 

  • Ranjbar M, Effati S, Kamyad AV (2018) T-operators in hesitant fuzzy sets and their applications to fuzzy rule-based classifier. Appl Soft Comput 62:423–440

    Google Scholar 

  • Ren Z, Xu Z, Wang H (2018) Normal wiggly hesitant fuzzy sets and their application to environmental quality evaluation. Knowl-Based Syst 159:286–297

    Google Scholar 

  • Roychowdhury S, Wang BH (1998) On generalized Hamacher families of triangular operators. Int J Approx Reason 19:419–439

    MathSciNet  MATH  Google Scholar 

  • Sarkar A, Biswas A (2020) Development of Archimedean t-norm and t-conorm-based interval-valued dual hesitant fuzzy aggregation operators with their application in multicriteria decision making. Eng Rep 2:e12106

    Google Scholar 

  • Sarkar A, Biswas A (2019) On develo** interval-valued dual hesitant fuzzy Bonferroni mean aggregation operator and their application to multicriteria decision making 27–46

  • Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25:529–539

    MATH  Google Scholar 

  • Wang L, Wang H, Xu Z, Ren Z (2019) The interval-valued hesitant Pythagorean fuzzy set and its applications with extended TOPSIS and Choquet integral-based method. Int J Intell Syst 34:1063–1085

    Google Scholar 

  • Wei CP, Wang P, Zhang YZ (2011) Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications. Inf Sci 181:4273–4286

    MathSciNet  MATH  Google Scholar 

  • Xu Y, Shang X, Wang J, Zhao H, Zhang R, Bai K (2019) Some interval-valued q-rung dual hesitant fuzzy Muirhead mean operators with their application to multi-attribute decision-making. IEEE Access 7:54724–54745

    Google Scholar 

  • Yang P (2004) AHP method in the evaluation of classroom teaching. Math Pract Theory 2:34

    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 58:521–527

    MathSciNet  MATH  Google Scholar 

  • Yingying F, Gan Y, Hongzhi Z (2013) Teaching quality evaluation model based on neural network and analytic hierarchy process. Comput Eng Appl 49:235–238

    Google Scholar 

  • Yongbiao L, Jun Y, **aowen M (2009) Multicriteria fuzzy decision-making method based on weighted correlation coefficients under interval-valued intuitionistic fuzzy environment. In: 2009 IEEE 10th international conference on computer-aided industrial design & conceptual design, pp 2057–2060

  • Zadeh LA (1975) The concept of a linguistic varible and its application to approximate reasoning-I. Inf Sci 8:199–249

    MATH  Google Scholar 

  • Zang Y, Zhao X, Li S (2018) Interval-valued dual hesitant fuzzy heronian mean aggregation operators and their application to multi-attribute decision making. Int J Comput Intell Appl 17:1850005

    Google Scholar 

  • Zeng W, Li D, Yin Q (2016) Distance and similarity measures between hesitant fuzzy sets and their application in pattern recognition. Pattern Recognit Lett 84:267–271

    Google Scholar 

  • Zeng W, Li D, Yin Q (2019) Weighted interval-valued hesitant fuzzy sets and its application in group decision making. Int J Fuzzy Syst 21:421–432

    Google Scholar 

  • Zhang C, Li D, Mu Y, Song D (2017) An interval-valued hesitant fuzzy multigranulation rough set over two universes model for steam turbine fault diagnosis. Appl Math Model 42:693–704

    MathSciNet  MATH  Google Scholar 

  • Zhang Z (2013) Interval-valued intuitionistic hesitant fuzzy aggregation operators and their application in group decision-making. J Appl Math 2013:33

    MATH  Google Scholar 

  • Zhiming Z, Chong W (2014) Some interval-valued hesitant fuzzy aggregation operators based on Archimedean t-norm and t-conorm with their application in multi-criteria decision making. J Intell Fuzzy Syst 27:2737–2748

    MathSciNet  MATH  Google Scholar 

  • Zhu B, Xu Z, **a M (2012) Dual hesitant fuzzy sets. J Appl Math. https://doi.org/10.1155/2012/879629

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors are grateful to the editor and anonymous reviewers for their valuable suggestions which helped us to improve the presentation of this manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan

    Jawad Ali & Zia Bashir

  2. Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, KPK, Pakistan

    Jawad Ali

  3. Department of Mathematics, University of Management and Technology, Lahore, 54770, Pakistan

    Tabasam Rashid

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  1. Jawad Ali
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Correspondence to Tabasam Rashid.

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Ali, J., Bashir, Z. & Rashid, T. Weighted interval-valued dual-hesitant fuzzy sets and its application in teaching quality assessment. Soft Comput 25, 3503–3530 (2021). https://doi.org/10.1007/s00500-020-05383-9

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