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Generalized trapezoidal hesitant fuzzy numbers and their applications to multi criteria decision-making problems

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Abstract

Generalized hesitant trapezoidal fuzzy number whose membership degrees are expressed by several possible trapezoidal fuzzy numbers, is more adequate or sufficient to solve real-life decision problem than real numbers. Therefore, in this paper, to model the some multi-criteria decision-making (MCDM) problems, we define concept of generalized trapezoidal hesitant fuzzy (GTHF) number, whose membership degrees of an element to a given set are expressed by several different generalized trapezoidal fuzzy numbers in the set of real numbers R. Then, we introduce some basic operational laws of GTHF-numbers and some properties of them. Also, we propose a decision-making method to solve the MCDM problems in which criteria values take the form of GTHF information. To use in proposed decision-making method, we first give definitions of some concepts such as score, standard deviation degree, deviation degree of GTHF-numbers. We second develop some GTHF aggregation operators called the GTHF-number weighted geometric operator, GTHF-number weighted arithmetic operator, GTHF-number weighted geometric operator, GTHF-number weighted arithmetic operator. Finally, we give a numerical example for proposed MCDM to validate the reasonable and applicable of the proposed method.

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References

  • Alcantud JCR, Calle RDA (2016) A segment based approach to the analysis of project evaluation problems by hesitant fuzzy sets. Int J Comput Int Syst 29:325–339

    Article  Google Scholar 

  • Alcantud JCR, Calle RDA, Torrecillas MJM (2016) Hesitant fuzzy worth: an innovative ranking methodology for hesitant fuzzy subsets. Appl Soft Comput 38:232–243

    Article  Google Scholar 

  • Amin F, Fahmi A (2019) Human immunodeficiency virus (HIV) infection model based on triangular neutrosophic cubic hesitant fuzzy number. Int J Biomath. https://doi.org/10.1142/S1793524519500554

    Article  Google Scholar 

  • Amin F, Fahmi A, Abdullah S, Ali A, Ahmed R, Ghani F (2017) Triangular cubic linguistic hesitant fuzzy aggregation operators and their application in group decision making. J Intell Fuzzy Syst 34:2401–2416

    Article  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

    Article  MATH  Google Scholar 

  • Bedregal B, Reiser R, Bustince H, Lopez MC, Torra V (2014) Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms. Inform Sci 255:82–99

    Article  MathSciNet  MATH  Google Scholar 

  • Carlos J, Alcantuda R, Torra V (2018) Decomposition theorems and extension principles for hesitant fuzzy sets. Inf Fusion 41:48–56

    Article  Google Scholar 

  • Chakraborty D, Guha D (2010) Addition two generalized fuzzy numbers. Int J Ind Math 2(1):9–20

    Google Scholar 

  • Chen N, Xu ZS, Xia MM (2013) Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Model 37:2197–2211

    Article  MathSciNet  MATH  Google Scholar 

  • Chen N, Xu ZS, Xia MM (2014) Hierarchical hesitant fuzzy k means clustering algorithm. Appl Math A J Chin Univ 29(1):1–17

    Article  MathSciNet  MATH  Google Scholar 

  • Chen N, Xu ZS, Xia MM (2015) The ELECTRE I multi criteria decision making method based on hesitant fuzzy sets. Int J Inf Technol Decis Mak 14(3):621–657

    Article  Google Scholar 

  • Deli I, Subas Y (2017) Some weighted geometric operators with SVTrN numbers and their application to multi criteria decision making problems. J Intell Fuzzy Syst 32(1):291–301

    Article  MATH  Google Scholar 

  • Deng W, Zhao H, Yang X, Xiong J, Sun M, Li B (2017a) Study on an improved adaptive PSO algorithm for solvingmulti objective gate assignment. Appl Soft Comput 59:288–302

    Article  Google Scholar 

  • Deng W, Zhao H, Zou L, Li G, Yang X, Wu D (2017b) A novel collaborative optimization algorithm in solving complex optimization problems. Soft Comput 21:4387–4398

    Article  Google Scholar 

  • Deng W, Zhang S, Zhao H, Yang X (2018) A novel fault diagnosis method based on integrating empirical wavelet transform and fuzzy entropy for motor bearing. IEEE Access 6:35042–35056

    Article  Google Scholar 

  • Deng W, Yao R, Zhao H, Yang X, Li G (2019) A novel intelligent diagnosis method using optimal LS SVM with improved PSO algorithm. Soft Comput 23:2445–2462

    Article  Google Scholar 

  • Diewald W (1989) Risk analysis in public works facilities planning, design, and construction. In: Haimes YY, Stakhiv EZ (eds) Risk analysis and management of natural and man made hazards. Proceedings of the 3rd conference sponsored by the Engineering Foundation in 1987. American Society of Civil Engineers, New York

  • Dubois D, Prade H (1983) Ranking fuzzy number in the setting of possibility theory. Inf Sci 30:183–224

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Fahmi A, Abdullah S, Amin F (2017a) Trapezoidal linguistic cubic hesitant fuzzy topsis method and application to group decision making program. J New Theory 19:27–47

    MATH  Google Scholar 

  • Fahmi A, Abdullah S, Amin F, Siddque N, Ali A (2017b) Aggregation operators on triangular cubic fuzzy numbers and its application to multi criteria decision making problems. J Intell Fuzzy Syst 33:3323–3337

    Article  Google Scholar 

  • Fahmi A, Abdullah S, Amin F, Ali A (2018a) Weighted average rating (War) method for solving group decision making problem using triangular cubic fuzzy hybrid aggregation (Tcfha). Punjab Univ J Math 50(1):23–34

    MathSciNet  Google Scholar 

  • Fahmi A, Abdullah S, Amin F, Ali A, Khan WA (2018b) Some geometric operators with triangular cubic linguistic hesitant fuzzy number and their application in group decision making. J Intell Fuzzy Syst 35(2):2485–2499

    Article  Google Scholar 

  • Fahmi A, Amin F, Abdullah S, Ali A (2018c) Cubic fuzzy Einstein aggregation operators and its application to decision making. Int J Syst Sci 49(11):2385–2397

    Article  MathSciNet  Google Scholar 

  • Fahmi A, Amin F, Smarandache F, Khan M, Hassan N (2018d) Triangular cubic hesitant fuzzy einstein hybrid weighted averaging operator and its application todecision making. Symmetry. https://doi.org/10.3390/sym10110658

    Article  MATH  Google Scholar 

  • Fahmi A, Abdullah S, Amin F, Ali A (2019a) Precursor selection for sol gel synthesis of titanium carbide nanopowders by a new cubic fuzzy multi attribute group decision-making model. J Intell Syst 28(5):699–720

    Article  Google Scholar 

  • Fahmi A, Abdullah S, Amin F, Khan MSA (2019b) Trapezoidal cubic fuzzy number einstein hybrid weighted averaging operators and its application to decision making. Soft Comput 23:5753–5783

    Article  MATH  Google Scholar 

  • Fahmi A, Abdullah S, Amin F (2019c) Cubic uncertain linguistic powered Einstein aggregation operators and their application to multi attribute group decision making. Math Sci 13:129–152

    Article  MathSciNet  MATH  Google Scholar 

  • Fahmi A, Amin F, Khan M, Smarandache F (2019d) Group decision making based on triangular neutrosophic cubic fuzzy einstein hybrid weighted averaging operators. Symmetry. https://doi.org/10.3390/sym11020180

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Fahmi A, Abdullah S, Amin F, Aslam M, Hussain S (2020) Trapezoidal linguistic cubic fuzzy TOPSIS method and application in a group decision making program. J Intell Syst 29(1):1283–1300

    Article  Google Scholar 

  • Kaufmann A, Gupta MM (1988) Fuzzy mathematical models in engineering and management science. Elsevier Science Publishers, Amsterdam

    MATH  Google Scholar 

  • Liao HC, Xu ZS (2014a) Satisfaction degree based interactive decision making method under hesitant fuzzy environment with incomplete weights. Int J Uncertain Fuzziness Knowl Based Syst 22(4):553–572

    Article  MATH  Google Scholar 

  • Liao HC, Xu ZS (2014b) Subtraction and division operations over hesitant fuzzy sets. J Intell Fuzzy Syst 27(1):65–72

    Article  MathSciNet  MATH  Google Scholar 

  • Liao HC, Xu ZS (2014c) Some new hybrid weighted aggregation operators under hesitant fuzzy multi criteria decision making environment. J Intell Fuzzy Syst 26(4):1601–1617

    Article  MathSciNet  MATH  Google Scholar 

  • Ngan SC (2017) A unified representation of intuitionistic fuzzy sets, hesitant fuzzy sets and generalized hesitant fuzzy sets based on their u maps. Expert Syst Appl 69(1):257–276

    Article  Google Scholar 

  • Pathinathan T, Johnson SS (2015) Trapezoidal hesitant fuzzy multi attribute decision making based on TOPSIS. Int Arch Appl Sci Technol 6(3):39–49

    Google Scholar 

  • Peng JJ, Wang JQ, Wang J, Yang LJ, Chen XH (2015) An extension of ELECTRE to multi criteria decision-making problems with multi hesitant fuzzy sets. Inf Sci 307:113–126

    Article  MathSciNet  MATH  Google Scholar 

  • Qian G, Wang H, Feng X (2013) Generalized of hesitant fuzzy sets and their application in decision support system. Knowl Based Syst 37:357–365

    Article  Google Scholar 

  • Rashid T, Husnine SM (2014) Multicriteria group decision making by using trapezoidal valued hesitant fuzzy sets. Sci World J. https://doi.org/10.1155/2014/304834

    Article  Google Scholar 

  • Rodriguez R, Martinez L, Torra V, Xu Z, Herrera F (2014) Hesitant fuzzy sets: state of the art and future directions. Int J Intell Syst 29:495–524

    Article  Google Scholar 

  • Rodriguez R, Bedregal B, Bustince H, Dong Y, Farhadinia B, Kahraman C, Martinez L, Torra V, Xu Y, Xu Z, Herrera F (2016) A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making towards high quality progress. Inf Fusion 29:89–97

    Article  Google Scholar 

  • Roseline SS, Amirtharaj S (2014) Generalized fuzzy Hungarian method for generalized trapezoidal fuzzy transportation problem with ranking of generalized fuzzy numbers. Int J Appl Math Stat Sci 3:5–12

    Google Scholar 

  • Roseline SS, Amirtharaj S (2015) Improved ranking of generalized trapezoidal fuzzy numbers. Int J Innov Res Sci Eng Technol 4:6106–6113

    Google Scholar 

  • Surapati P, Biswas P (2012) Multi-objective assignment problem with generalized trapezoidal fuzzy numbers. Int J App Inf Syst 2(6):13–20

    Google Scholar 

  • Torra V (2009) Hesitant fuzzy sets. Int J Intell Syst 25:529–539

    MATH  Google Scholar 

  • Torra V, Narukawa Y (2009) On hesitant fuzzy sets and decision. The 18th IEEE international conference on fuzzy systems. Jeju Island, Korea, pp 1378–1382

    Google Scholar 

  • Umamaheswari A, Kumari P (2014) Fuzzy topsis and fuzzy VIKOR methods using the triangular fuzzy hesitant sets. Int J Comput Sci Eng Inf Technol Res 4(3):15–24

    Google Scholar 

  • Vanclay F (2003) International principles for social impact assessment. Impact Assess Proj Apprais 21(1):5–11

    Article  Google Scholar 

  • Wei GW (2012) Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowl Based Syst 31:176–182

    Article  Google Scholar 

  • Wang JQ, Wu JT, Wang J, Zhang HY, Chen XH (2014) Interval valued hesitant fuzzy linguistic sets and their applications in multi criteria decision-making problems. Inf Sci 288(20):55–72

    Article  MathSciNet  MATH  Google Scholar 

  • Wang JQ, Wu JT, Wang J, Zhang HY, Chen XH (2016) Multi criteria decision making methods based on the Hausdorff distance of hesitant fuzzy linguistic numbers. Soft Comput 20(4):1621–1633

    Article  Google Scholar 

  • Wood C (2003) Environmental impact assessment: a comparative review. Pearson, London

    Google Scholar 

  • Xia MM, Xu ZS (2011a) Studies on the aggregation of intuitionistic fuzzy and hesitant fuzzy information. Technical report

  • Xia MM, Xu ZS (2011b) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52:395–407

    Article  MathSciNet  MATH  Google Scholar 

  • Xia MM, Xu ZS, Chen N (2013) Some hesitant fuzzy aggregation operators with their application in group decision making. Group Decis Negot 22:259–279

    Article  Google Scholar 

  • Xu ZS (2000) On consistency of the weighted geometric mean complex judgment matrix in AHP. Eur J Oper Res 126:683–687

    Article  MATH  Google Scholar 

  • Xu Z (2014) Hesitant fuzzy sets theory. Studies in fuzziness and soft computing, vol 314. Springer International Publishing, Berlin

  • Xu ZS, Xia MM (2011) Distance and similarity measures for hesitant fuzzy sets. Inf Sci 181:2128–2138

    Article  MathSciNet  MATH  Google Scholar 

  • Xu ZS, Xia MM (2012) Hesitant fuzzy entropy and cross entropy and their use in multi attribute decision making. Int J Intell Syst 27:799–822

    Article  Google Scholar 

  • Xu ZS, Xia MM (2013) On distance and correlation measures of hesitant fuzzy information. Int J Intell Syst 26:410–425

    Article  MATH  Google Scholar 

  • Xu ZS, Zhang XL (2013) Hesitant fuzzy multi attribute decision making based on TOPSIS with incomplete weight information. Knowl Based Syst 52:53–64

    Article  Google Scholar 

  • Ye J (2013) Multicriteria decision making method using expected values in trapezoidal hesitant fuzzy setting. J Converg Inf Technol 8(11):135. https://doi.org/10.4156/jcit.vol8.issue11.16

    Article  Google Scholar 

  • Yu D (2013) Triangular hesitant fuzzy set and its application to teaching quality evaluation. J Inf Comput Sci 10(7):1925–1934

    Article  Google Scholar 

  • Yu DJ, Wu YY, Zhou W (2011) Multi criteria decision making based on Choquet integral under hesitant fuzzy environment. J Comput Inf Syst 7:4506–4513

    Google Scholar 

  • Yu DJ, Wu YY, Zhou W (2012) Generalized hesitant fuzzy Bonferroni mean and its application in multi criteria group decision making. J Inf Comput Sci 9:267–274

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang XL, Xu ZS (2013) A MST clustering analysis method under hesitant fuzzy environment. Control Cybern 41:645–666

    MATH  Google Scholar 

  • Zhang XL, Xu ZS (2015) Hesitant fuzzy agglomerative hierarchical clustering algorithms. Int J Syst Sci 46(3):562–576

    Article  MATH  Google Scholar 

  • Zhang X, Yang T, Liang W, Xiong M (2018) Closeness degree based hesitant trapezoidal fuzzy multi criteria decision making method for evaluating green suppliers with qualitative information. Discrete Dyn Nat Soc. https://doi.org/10.1155/2018/3178039

    Article  MATH  Google Scholar 

  • Zhao X, Lin R, Wei G (2014) Hesitant triangular fuzzy information aggregation based on Einstein operations and their application to multiple attribute decision making. Expert Syst Appl 41:1086–1094

    Article  Google Scholar 

  • Zhao H, Sun M, Deng W, Yang X (2017) A new feature extraction method based on EEMD and multi scale fuzzy entropy for motor bearing. Entropy. https://doi.org/10.3390/e19010014

    Article  Google Scholar 

  • Zhao H, Yao R, Xu L, Yuan Y, Li G, Deng W (2018) Study on a novel fault damage degree identification method using high order differential mathematical morphology gradient spectrum entropy. Entropy. https://doi.org/10.3390/e20090682

    Article  Google Scholar 

  • Zhang X, Xu Z, Liu M (2016) Hesitant trapezoidal fuzzy QUALIFLEX method and its application in the evaluation of green supply chain initiatives. Sustainability 8:952. https://doi.org/10.3390/su8090952

    Article  Google Scholar 

  • Zhu B, Xu Z (2016) Extended hesitant fuzzy sets. Technol Econ Dev Econ 22(1):100–121

    Article  Google Scholar 

  • Zhu B, Xu ZS, Xia MM (2012) Dual hesitant fuzzy sets. J Appl Math. https://doi.org/10.1155/2012/879629

    Article  MathSciNet  MATH  Google Scholar 

  • Zimmermann HJ (1993) Fuzzy set theory and its applications. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

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Authors and Affiliations

  1. Muallim Rıfat Faculty of Education, 7 Aralık University, 79000, Kilis, Turkey

    Irfan Deli

  2. Department of Mathematics, Faculty and Sciences, Çankırı Karatekin University, 18100, Çankırı, Turkey

    Faruk Karaaslan

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  1. Irfan Deli
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  2. Faruk Karaaslan
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Correspondence to Irfan Deli.

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Deli, I., Karaaslan, F. Generalized trapezoidal hesitant fuzzy numbers and their applications to multi criteria decision-making problems. Soft Comput 25, 1017–1032 (2021). https://doi.org/10.1007/s00500-020-05201-2

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