Skip to main content
SpringerLink
Log in

Multiple-attribute decision making problems based on SVTNH methods

  • Original Research
  • Published:
Journal of Ambient Intelligence and Humanized Computing Aims and scope Submit manuscript

Abstract

The neutrosophic set (NS) is a leading tool in modeling of situations involving incomplete, indeterminate and inconsistent information. The single-valued neutrosophic sets (SVNs) is more useful tool than neutrosophic sets in some applications of engineering and scientific problems. In this paper, we study Hamacher operations and operations between single-valued trapezoidal neutrosophic numbers. Then we propose the single-valued trapezoidal neutrosophic Hamacher weighted arithmetic averaging (SVTNHWA) operator, single-valued trapezoidal neutrosophic Hamacher ordered weighted arithmetic averaging (SVTNHOWA) operator, single-valued trapezoidal neutrosophic Hamacher hybrid weighted averaging (SVTNHHWA) operator, single-valued trapezoidal neutrosophic Hamacher weighted geometric averaging (SVTNHWGA) operator and single-valued trapezoidal neutrosophic Hamacher ordered weighted geometric averaging (SVTNHOWGA) operator and single-valued trapezoidal neutrosophic Hamacher hybrid weighted geometric averaging (SVTNHHWGA) operator, and obtain some of their properties. Furthermore, we developed a multiple-attribute decision-making method in single-valued trapezoidal neutrosophic (SVTN) environment based on these operators. Finally, we proposed an application of MADM problem in assessment of potential of software system commercialization.

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

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

    MATH  Google Scholar 

  • Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners. Springer, Heidelberg

    MATH  Google Scholar 

  • Biswas P, Pramanik S, Giri BC (2014a) Cosine similarity measure base multi-attribute decision making with trapesoidal fuzzy neutrosophic numbers. Neutrosophic Sets Syst 8:46–56

    Google Scholar 

  • Biswas P, Pramanik S, Giri BC (2014b) A new methodology for neutrosophic multi-attribute decision-making with unknown weight information. Neutrosophic Sets Syst 3:42–50

    Google Scholar 

  • Broumi S, Smarandache F (2014) Single valued neutrosophic trapezoid linguistic aggregation operators based multi-attribute decision making. Bull Pure Appl Sci 33(2):135–155

    Google Scholar 

  • Deli I, Subaş Y (2014) Single valued neutrosophic numbers and their applications to multi-criteria decision making problem. Neutrosophic Sets Syst 2(1):1–3

    Google Scholar 

  • Deli I, Subaş Y (2015) Some weighted geometric operators with SVTrN-numbers and their application to multi-criteria decision making problems. J Intell Fuzzy Syst. https://doi.org/10.3233/jifs-151677

    Article  MATH  Google Scholar 

  • Deschrijver G, Kerre EE (2002) Ageneralization of operators on intuitionistic fuzzy sets using triangular norms and conorms. Notes on Intuitionistic Fuzzy Sets 8:19–27

    MATH  Google Scholar 

  • Deschrijver G, Cornelis C, Kerre EE (2004) On the representation of intuitionistic fuzzy \(t\)-norms and \(t\)-conorms. IEEE Trans Fuzzy Syst 12:45–61

    MATH  Google Scholar 

  • Fan C, Ye J, Hu K, Fan E (2017) Bonferroni mean operators of linguistic neutrosophic numbers and their multiple attribute group decision-making methods. Information 8:107. https://doi.org/10.3390/info8030107

    Article  Google Scholar 

  • Gao H, Wei GW, Huang YH (2018) Dual hesitant bipolar fuzzy Hamacher prioritized aggregation operators in multiple attribute decision making. IEEE Access 6(1):11508–11522

    Google Scholar 

  • Garg H, Kumar K (2018) A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory. Artif Intell Rev. https://doi.org/10.1007/s10462-018-9668-5

    Article  Google Scholar 

  • Gupta A, Kohli S (2016) An MCDM approach towards handling outliers in web data: a case study using OWA operators. Artif Intell Rev 46(1):59–82

    Google Scholar 

  • Hamachar H (1978) Uber logische verknunpfungenn unssharfer Aussagen undderen Zugenhorige Bewertungsfunktione. In: Trappl R, Klir GJ, Riccardi L (eds) Progress in cybernetics and systems research, vol 3. Hemisphere, Washington DC, pp 276–288

  • He YD, Chen HY, Zhou LG (2013) Generalized interval-valued Atanassovs intuitionistic fuzzy power operators and their application to group decision making. Int J Fuzzy Syst 15(4):401–411

    MathSciNet  Google Scholar 

  • Hu BQ, Wong H (2013) Generalized interval-valued fuzzy rough sets based on interval- valued fuzzy logical operators. Int J Fuzzy Syst 15(4):381–391

    MathSciNet  Google Scholar 

  • Jana C, Pal M (2019a) Assessment of enterprise performance based on picture fuzzy Hamacher aggregation operators. Symmetry 11(1):75. https://doi.org/10.3390/sym11010075

    Article  MATH  Google Scholar 

  • Jana C, Pal M (2019b) A robust single-valued neutrosophic soft aggregation operators in multi-criteria decision making. Symmetry 11(1):110. https://doi.org/10.3390/sym11010110

    Article  Google Scholar 

  • Jana C, Pal M, Wang JQ (2018) Bipolar fuzzy Dombi aggregation operators and its application in multiple attribute decision making process. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-018-1076-9

    Article  Google Scholar 

  • Jana C, Senapati T, Pal M, Yager RR (2019a) Picture fuzzy Dombi aggregation operators: application to MADM process. Appl Soft Comput 74(1):99–109. https://doi.org/10.1016/j.asoc.2018.10.021

    Article  Google Scholar 

  • Jana C, Pal M, Wang JQ (2019b) Bipolar fuzzy Dombi prioritized aggregation operators in multiple attribute decision making. J Soft Comput. https://doi.org/10.1007/s00500-019-04130-z

    Article  MATH  Google Scholar 

  • Jana C, Senapati T, Pal M (2019c) Pythagorean fuzzy Dombi aggregation operators and its applications in multiple attribute decision-making. Int J Intell Syst. https://doi.org/10.1002/int.22125

    Article  Google Scholar 

  • Ji P, Zhang HY, Wang JQ (2018a) A projection-based outranking method with multi-hesitant fuzzy linguistic term sets for hotel location selection. Cogn Comput. https://doi.org/10.1007/s12559-018-9552-2

    Article  Google Scholar 

  • Ji P, Wang JQ, Zhang HY (2018a) Frank prioritized Bonferroni mean operator with single-valued neutrosophic sets and its application in selecting third-party logistics providers. Neural Comput Appl 30(3):799–823

    Google Scholar 

  • Levy R, Brodsky A, Luo J (2016) Decision guidance framework to support operations and analysis of a hybrid renewable energy system. J Manag Anal 3(4):285–304. https://doi.org/10.1080/23270012.2016.1229140

    Article  Google Scholar 

  • Li J, Wang JQ (2017) Multi-criteria outranking methods with hesitant probabilistic fuzzy sets. Cogn Comput 9:611–625

    Google Scholar 

  • Liang RX, Wang JQ, Zhang HY (2017) A multi-criteria decision-making method based on single-valued trapezoidal neutrosophic preference relations with complete weight information. Neural Comput Appl. https://doi.org/10.1007/s00521-017-2925-8

    Article  Google Scholar 

  • Liu P (2013) Some generalized dependent aggregation operators with intuitionistic linguistic numbers and their application to group decision making. J Comput Syst Sci 79(1):131–143

    MathSciNet  MATH  Google Scholar 

  • Liu P (2016) The aggregation operators based on Archimedean t-conorm and t-norm for single-valued neutrosophic numbers and their application to decision making. Int J Fuzzy Syst 18(5):849–863

    Google Scholar 

  • Liu P, Liu Y (2014) An approach to multiple attribute group decision making based on intuitionistic trapezoidal fuzzy power generalized aggregation operator. Int J Comput Intell Syst 7(2):291–304

    Google Scholar 

  • Liu P, Wang Y (2014a) Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean. Neural Comput Appl 25:2001–2010

    Google Scholar 

  • Liu P, Wang YM (2014b) Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operators. Appl Soft Comput 17(1):90–104

    Google Scholar 

  • Liu P, Yu XC (2014) 2-dimension uncertain linguistic power generalized weighted aggregation operator and its application for multiple attribute group decision making. Knowl Based Syst 57(1):69–80

    Google Scholar 

  • Liu P, Liu Z, Zhang X (2014a) Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making. Appl Math Comput 230:570–586

    MathSciNet  MATH  Google Scholar 

  • Liu P, Li Y, Chen Y (2014b) Some generalized neutrosophic number Hamacher aggregation operators ad their application to group decision making. Int J Fuzzy Syst 16(2):212–255

    MathSciNet  Google Scholar 

  • Liu P, Zhang L, Liu X, Wang P (2016) Multi-valued neutrosophic number Bonferroni mean operators with their applications in multiple attribute group decision making. Int J Inf Technol Decis Mak 15:1–28

    Google Scholar 

  • Lu Z, Ye J (2017) Single-valued neutrosophic hybrid arithmetic and geometric aggregation operators and their decision-making method. Information. https://doi.org/10.3390/info8030084

    Article  Google Scholar 

  • Lu J, Tang X, Wei GW, Wei C, Wei Y (2019) Bidirectional project method for dual hesitant Pythagorean fuzzy multiple attribute decision-making and their application to performance assessment of new rural construction. Int J Intell Syst 34(8):1920–1934

    Google Scholar 

  • Nancy GH (2016) Novel single-valued neutrosophic aggregated operators under frank norm operation and its application to decision-making process. Int J Uncertain Quantif 6(4):361–375

    Google Scholar 

  • Peng J, Wang JQ, Chen H (2016) Simplified neutrosophic sets and their applications in multi-citeria group decision making problems. Int J Syst Sci 47(10):2342–2358

    MATH  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 

  • Smarandache F (1999) A unifying field in logics. Neutrosophy: neutrosophic probability, set and logic. American Research Press, Rehoboth

    MATH  Google Scholar 

  • Smarandache F (2005) Neutrosophic set—a generalization of the intuitionistic fuzzy set. Int J Pure Appl Math 24(3):287–297

    MathSciNet  MATH  Google Scholar 

  • Tan R, Zhang W, Chen S (2017) Some generalized single valued neutrosophic linguistic operators and their application to multiple attribute group decision making. J Syst Sci Inf 5(2):148–162

    Google Scholar 

  • Tang X, Wei GW (2019) Multiple attribute decision-making with dual hesitant Pythagorean fuzzy information. Cogn Comput 11(2):193–211

    MathSciNet  Google Scholar 

  • Teixeira C, Lopes I, Figueiredo M (2018) Classification methodology for spare parts management combining maintenance and logistics perspectives. J Manag Anal 5(2):116–135. https://doi.org/10.1080/23270012.2018.1436989

    Article  Google Scholar 

  • Thamaraiselvi A, Santhi R (2016) A new approach for optimization of real life transportation problem in neutrosophic environment. Math Probl Eng. https://doi.org/10.1155/2016/5950747

    Article  Google Scholar 

  • Wang WZ, Liu XW (2011) Intuitionistic fuzzy geometric aggregation operators based on Einstein operations. Int J Intell Syst 26(11):1049–1075

    Google Scholar 

  • Wang JQ, Zhang Z (2009) Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems. Syst Eng Electron 20(2):321–326

    Google Scholar 

  • Wang H, Smarandache F, Zhang YQ, Sunderraman R (2010) Single valued neutrosophic sets. Multispace Multistruct 4:410–413

    MATH  Google Scholar 

  • Wei GW, Alsaadi FE, Tasawar H, Alsaedi A (2018) Bipolar fuzzy Hamacher aggregation operators in multiple attribute decision making. Int J Fuzzy Syst 20(1):1–12

    MathSciNet  MATH  Google Scholar 

  • Wu Q, Wu P, Zhou L, Chen H, Guan X (2018) Some new Hamacher aggregation operators under single-valued neutrosophic 2-tuple linguistic environment and their applications to multiattribute group decision making. Comput Ind Eng 116:144–162

    Google Scholar 

  • Wu L, Wang J, Gao H (2019) Models for competiveness evaluation of tourist destination with some interval-valued intuitionistic fuzzy Hamy mean operators. J Intell Fuzzy Syst 36(6):5693–5709

    Google Scholar 

  • Xia MM, Xu ZS, Zhu B (2012) Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm. Knowl Based Syst 31(1):78–88

    Google Scholar 

  • Xu DL (1987) Toward escape from the limitations of economic systems analysis: introduction of dimensionality. Syst Res 4(4):243–250. https://doi.org/10.1002/sres.3850040404

    Article  Google Scholar 

  • Xu DL (1988) A fuzzy multiobjective programming algorithm in decision support systems. Ann Oper Res 12(1):315–320

    MathSciNet  Google Scholar 

  • Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(6):1179–1187

    Google Scholar 

  • Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35(4):417–433

    MathSciNet  MATH  Google Scholar 

  • Yager R (1988) On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans Syst Man Cybern 18(1):183–190

    MATH  Google Scholar 

  • Ye J (2013) Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment. Int J Gen Syst 42(4):386–394

    MathSciNet  MATH  Google Scholar 

  • Ye J (2014a) Prioritized aggregation operators of trapezoidal intuitionistic fuzzy sets and their application to multicriteria decision making. Neural Comput Appl 25(6):1447–1454

    Google Scholar 

  • Ye J (2014b) Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making. J Int Fuzzy Syst 26:165–172

    MATH  Google Scholar 

  • Ye J (2014c) A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. J Intell Fuzzy Syst 26:2459–2466

    MathSciNet  MATH  Google Scholar 

  • Ye JJ (2014d) Some aggregation operators of interval neutrosophic linguistic numbers for multiple attribute decision making. J Intell Fuzzy Syst 27:2231–2241

    MathSciNet  MATH  Google Scholar 

  • Ye J (2015) Trapezoidal fuzzy neutrosophic set and its application to multiple attribute decision making. Neural Comput Appl 26(5):1157–1166

    Google Scholar 

  • Ye J (2016) Aggregation operators of neutrosophic linguistic numbers for multiple attribute group decision making. SpringerPlus 5:1–11

    Google Scholar 

  • Ye J (2017) Some weighted aggregation operators of trapezoidal neutrosophic numbers and their multiple attribute decision making method. Informatica 28(2):387–402

    MathSciNet  Google Scholar 

  • Yu DJ (2012) Group decision making based on generalized intuitionistic fuzzy prioritized geometric operator. Int J Intell Syst 27(7):635–661

    Google Scholar 

  • Yu DJ (2013a) Multi-criteria decision making based on generalized prioritized aggregation operators under intuitionistic fuzzy environment. Int J Fuzzy Syst 15(1):47–54

    MathSciNet  Google Scholar 

  • Yu DJ (2013b) Intuitionistic fuzzy Choquet aggregation operator based on Einstein operation laws. Sci Iran (Trans Ind Eng) 20(6):2109–2122

    Google Scholar 

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

    MATH  Google Scholar 

  • Zhang Z (2017) Interval-valued intuitionistic fuzzy Frank aggregation operators and their applications to multiple attribute group decision making. Neural Comput Appl 28(6):1471–1501

    Google Scholar 

  • Zhang HY, Wang JQ, Chen XH (2014) Interval neutrosophic sets and their application in multicriteria decision making problems. Sci World J, Article ID 645953, p 15

  • Zhang HY, Ji P, Wang JQ, Chen XH (2016) A neutrosophic normal cloud and its application in decision-making. Cogn Comput 8(4):649–669

    Google Scholar 

  • Zhang C, Wang C, Zhang Z, Tian D (2019) A novel technique for multiple attribute group decision making in interval-valued hesitant fuzzy environments with incomplete weight information. J Ambient Intell Humaniz Comput 10(6):2417–2437

    Google Scholar 

  • Zhao XF, Wei GW (2013) Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making. Knowl Based Syst 37:472–479

    Google Scholar 

  • Zhao H, Xu ZS, Ni MF, Liu SS (2010) Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intell Syst 25(1):1–30

    MATH  Google Scholar 

Download references

Acknowledgements

The authors wish to thank the anonymous reviewers for their valuable comments and helpful suggestions which greatly improved the quality of this paper. The second author was supported by the research grant S-0064-1439, Deanship of Scientific Research, University of Tabuk, Tabuk-71491, Saudi Arabia

Author information

Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India

    Chiranjibe Jana & Madhumangal Pal

  2. Department of Mathematics, University of Tabuk, Tabuk, 71491, Saudi Arabia

    G. Muhiuddin

Authors
  1. Chiranjibe Jana
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Muhiuddin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Madhumangal Pal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chiranjibe Jana.

Ethics declarations

Conflict of interest

There is no conflict of interest between the authors and the institute where the work has been carried out.

Ethical approval

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

Additional information

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

Jana, C., Muhiuddin, G. & Pal, M. Multiple-attribute decision making problems based on SVTNH methods. J Ambient Intell Human Comput 11, 3717–3733 (2020). https://doi.org/10.1007/s12652-019-01568-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12652-019-01568-9

Keywords

Search

Navigation