Skip to main content
SpringerLink
Log in

Interval neutrosophic preference relations and their application in virtual enterprise partner selection

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

Abstract

How to select satisfactory partners is essential to virtual enterprise and has attracted lots of attention from practitioners and researchers. In many real situations, preference relation is an important structure in representing decision makers’ preference information during the partner selection process. As a special case of neutrosophic sets, interval neutrosophic set (INS) can be used to handle uncertain and inconsistent information in decision making. To show the application, this paper introduces the concept of interval neutrosophic preference relations (INPRs) using interval neutrosophic numbers to denote the true, indeterminacy and false judgments independently. Then, a multiplicative consistency concept for INPRs is proposed to guarantee the ranking accurately. After that, several multiplicative consistency-based nonlinear programming models to derive multiplicatively consistent INPRs and to determine missing values in incomplete INPRs are constructed, respectively. To broaden the application of INPRs, a consensus index based on the distance measure is defined. Meanwhile, an algorithm to group decision making based on INPRs is developed, which can be applied to address incomplete and inconsistent INPRs. Finally, the feasibility and practicability of the developed approach is manifested through an illustrative example, and comparison analysis is performed with several related previous methods about decision making with INSs.

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

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Ansari AQ, Biswas R, Aggarwal S (2011) Proposal for applicability of neutrosophic set theory in medical AI. Int J Comput Appl 27(5):5–11

    Google Scholar 

  • Arora M, Biswas R, Pandey US (2011) Neutrosophic relational database decomposition. Int J Adv Comput Sci Appl 2(8):121–125

    Google Scholar 

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

    MATH  Google Scholar 

  • Atanassov KT, Gargov G (1989) Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31(3):343–349

    MathSciNet  MATH  Google Scholar 

  • Bausys R, Zavadskas EK (2017) Multicriteria decision making approach by VIKOR under interval neutrosophic set environment. Econ Comput Econ Cybern Stud Res 49(4):33–48

    Google Scholar 

  • Chen JQ, Ye J, Du SG (2017) Vector similarity measures between refined simplified neutrosophic sets and their multiple attribute decision-making method. Symmetry 9(153):1–13

    Google Scholar 

  • Chi PP, Liu PD (2013) An extended TOPSIS method for the multiple attribute decision making problems based on interval neutrosophic set. Neutrosophic Sets Syst 1:63–70

    Google Scholar 

  • Dey PP, Pramanik S, Giri BC (2015) An extended grey relational analysis based interval neutrosophic multi attribute decision making for weaver selection. J N Theory 9:82–93

    Google Scholar 

  • Dong JY, Wan SP (2016) Virtual enterprise partner selection integrating LINMAP and TOPSIS. J Oper Res Soc 67(10):1288–1308

    Google Scholar 

  • Guo YH, Şengur A (2014) A novel image edge detection algorithm based on neutrosophic set. Comput Electr Eng 40(8):3–25

    Google Scholar 

  • Guo YH, Cheng HD, Zhang Y (2009) A new neutrosophic approach to image denoising. N Math Nat Comput 5(3):653–662

    MATH  Google Scholar 

  • Ip WH, Huang M, Yung KL, Wang DW (2003) Genetic algorithm solution for a risk-based partner selection problem in a virtual enterprise. Comput Oper Res 30(2):213–231

    MATH  Google Scholar 

  • Li YY, Wang JQ, Wang TL (2018) A linguistic neutrosophic multi-criteria group decision-making approach with EDAS method. Arab J Sci Eng. https://doi.org/10.1007/s13369-018-3487-5

    Article  Google Scholar 

  • Liang RX, Wang JQ, Zhang HY (2018) A multi-criteria decision-making method based on single-valued trapezoidal neutrosophic preference relations with complete weight information. Neural Comput Appl 30(11):3383–3398

    Google Scholar 

  • Liu PD, Li HG (2017) Interval-valued intuitionistic fuzzy power Bonferroni aggregation operators and their application to group decision making. Cogn Comput 9(4):494–512

    Google Scholar 

  • Liu PD, Chu YC, Li YW, Chen YB (2014) Some generalized neutrosophic number Hamacher aggregation operators and their application to group decision making. Int J Fuzzy Syst 16(2):242–255

    Google Scholar 

  • Luo SZ, Zhang HY, Wang JQ, Li L (2018) Group decision-making approach for evaluating the sustainability of constructed wetlands with probabilistic linguistic preference relations. J Oper Res Soc. https://doi.org/10.1080/01605682.2018.1510806

    Article  Google Scholar 

  • Meng FY, Chen XH, Tan CQ (2016) Cooperative fuzzy games with interval characteristic functions. Oper Res 16(1):1–24

    Google Scholar 

  • Meng FY, An QX, Tan CQ, Chen XH (2017a) An approach for group decision making with interval fuzzy preference relations based on additive consistency and consensus analysis. IEEE Trans Syst Man Cybern Syst 47(8):2069–2082

    Google Scholar 

  • Meng FY, Tan CQ, Chen XH (2017b) Multiplicative consistency analysis for interval fuzzy preference relations: a comparative study. Omega 68:17–38

    Google Scholar 

  • Meng FY, Tang J, An QX, Chen XH (2018a) Decision making with intuitionistic linguistic preference relations. Int Trans Oper Res. https://doi.org/10.1111/itor.12383

    Article  Google Scholar 

  • Meng FY, Tang J, Xu ZS (2018b) Exploiting the priority weights from interval linguistic fuzzy preference relations. Soft Comput. https://doi.org/10.1007/s00500-017-2878-y

    Article  MATH  Google Scholar 

  • Moore RE (1996) Interval analysis. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Orlovsky SA (1978) Decision-making with a fuzzy preference relation. Fuzzy Sets Syst 1(3):155–167

    MathSciNet  MATH  Google Scholar 

  • Peng JJ, Wang JQ, Wang J, Zhang HY, Chen XH (2015) Multi-valued neutrosophic sets and power aggregation operators with their applications in multi-criteria group decision-making problems. Int J Comput Intell Syst 8(2):345–363

    Google Scholar 

  • Pramanik S, Mondal K (2015) Interval neutrosophic multi-attribute decision making based on grey relational analysis. Neutrosophic Sets Syst 9:13–22

    Google Scholar 

  • Pramanik S, Biswas P, Giri BC (2017) Hybrid vector similarity measures and their applications to multi-attribute decision making under neutrosophic environment. Neural Comput Appl 28(5):1163–1176

    Google Scholar 

  • Saaty TL (1980) The analytic hierarchy process. McGraw-Hall, New York

    MATH  Google Scholar 

  • Şahin R (2017) Cross-entropy measure on interval neutrosophic sets and its applications in multicriteria decision making. Neural Comput Appl 28(5):1177–1187

    Google Scholar 

  • Şahin R, Karabacak M (2014) A multi attribute decision making method based on inclusion measure for interval neutrosophic sets. Int J Adv Eng Sci Appl Math 2(2):13–15

    Google Scholar 

  • Şahin R, Liu P (2016) Maximizing deviation method for neutrosophic multiple attribute decision making with incomplete weight information. Neural Comput Appl 27(7):2017–2029

    Google Scholar 

  • Salama AA, Smarandache F, Kroumov V (2014) Neutrosophic crisp sets and neutrosophic crisp topological spaces. Neutrosophic Sets Syst 32:24–30

    Google Scholar 

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

    MATH  Google Scholar 

  • Sun HX, Yang HX, Wu JZ, Yao OY (2015) Interval neutrosophic numbers choquet integral operator for multi-criteria decision making. J Intell Fuzzy Syst 28(6):2443–2455

    MathSciNet  MATH  Google Scholar 

  • Tang J, Meng FY (2018a) Decision making with multiplicative hesitant fuzzy linguistic preference relations. Neural Comput Appl. https://doi.org/10.1007/s00521-017-3227-x

    Article  Google Scholar 

  • Tang J, Meng FY (2018b) Ranking objects from group decision making with interval-valued hesitant fuzzy preference relations in view of additive consistency and consensus. Knowl Based Syst. https://doi.org/10.1016/j.knosys.2018.09.017

    Article  Google Scholar 

  • Tian ZP, Zhang HY, Wang JQ, Chen XH (2015) Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets. Int J Syst Sci 47(15):3598–3608

    MATH  Google Scholar 

  • Tian ZP, Nie RX, Wang JQ, Zhang HY (2018a) Signed distance-based ORESTE for multi-criteria group decision-making with multi-granular unbalanced hesitant fuzzy linguistic information. Expert Syst. https://doi.org/10.1111/exsy.12350

    Article  Google Scholar 

  • Tian ZP, Nie RX, Wang JQ, Zhang HY (2018b) A two-fold feedback mechanism to support consensus-reaching in social network group decision-making. Knowl Based Syst. https://doi.org/10.1016/j.knosys.2018.09.030

    Article  Google Scholar 

  • Turksen I (1986) Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst 20(2):191–210

    MathSciNet  MATH  Google Scholar 

  • Wang YM, Chin KS (2008) A linear goal programming priority method for fuzzy analytic hierarchy process and its applications in new product screening. Int J Approx Reason 49(2):451–465

    MATH  Google Scholar 

  • Wang HB, Smarandache F, Zhang YQ, Sunderraman R (2005) Interval neutrosophic sets and logic: theory and applications in computing. Hexis, Phoenix

    MATH  Google Scholar 

  • Wang YM, Elhag TMS, Hua ZS (2006) A modified fuzzy logarithmic least squares method for fuzzy analytic hierarchy process. Fuzzy Sets Syst 157(23):3055–3071

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Wang N, Meng FY, Xu YW (2018) Deriving the priority weights from multiplicative consistent single-valued neutrosophic preference relations. Neural Comput Appl. https://doi.org/10.1007/s00521-018-3493-2

    Article  Google Scholar 

  • Xu ZS (2001) A practical method for priority of interval number complementary judgment matrix. Oper Res Manag Sci 10(1):16–19

    Google Scholar 

  • Xu ZS (2004) Uncertain multiple attribute decision making: methods and applications. Tsinghua University Press, Beijing

    Google Scholar 

  • Xu ZS (2005) On method for uncertain multiple attribute decision making problems with uncertain multiplicative preference information on alternatives. Fuzzy Optim Decis Mak 4(2):131–139

    MathSciNet  MATH  Google Scholar 

  • Xu ZS (2007a) Intuitionistic preference relations and their application in group decision making. Inf Sci 177(11):2363–2379

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Xu ZS, Cai XQ (2009) Incomplete interval-valued intuitionistic fuzzy preference relations. Int J Gen Syst 38(8):871–886

    MathSciNet  MATH  Google Scholar 

  • Xu ZS, Chen J (2007) On geometric aggregation over interval-valued intuitionistic fuzzy information. Int conf Fuzzy Syst Knowl Dis 2:466–471

    Google Scholar 

  • Xu ZS, Liao HC (2015) A survey of approaches to decision making with intuitionistic fuzzy preference relations. Knowl Based Syst 80(5):131–142

    Google Scholar 

  • Xu ZS, Yager RR (2009) Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim Decis Mak 8(2):123–139

    MathSciNet  MATH  Google Scholar 

  • Yao LH, Shen GQ, Wang M, Zhang GX (2008) An improved method for virtual enterprise partner selection. Inf Comput Autom 3:1177–1180

    Google Scholar 

  • Ye F, Li YN (2009) Group multi-attribute decision model to partner selection in the formation of virtual enterprise under incomplete information. Expert Syst Appl 36(5):9350–9357

    Google Scholar 

  • Ye F, Lin Q (2013) Partner selection in a virtual enterprise: a group multiattribute decision model with weighted possibilistic mean values. Math Probl Eng. https://doi.org/10.1155/2013/519629

    Article  MathSciNet  MATH  Google Scholar 

  • Yuan RP, Meng FY, Tang J (2018) Linguistic intuitionistic fuzzy group decision making based on aggregation operators. Int J Fuzzy Syst. https://doi.org/10.1007/s40815-018-0582-4

    Article  Google Scholar 

  • Yuen KKF, Lau HCW (2011) A fuzzy group analytical hierarchy process approach for software quality assurance management: Fuzzy logarithmic least squares method. Expert Syst Appl 38(8):10292–10302

    Google Scholar 

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

    MATH  Google Scholar 

  • Zhang M, Zhang L, Cheng HD (2010) A neutrosophic approach to image segmentation based on watershed method. Signal Process 90(5):1510–1517

    MATH  Google Scholar 

  • Zhang HY, Wang JQ, Chen XH (2014) Interval neutrosophic sets and their application in multicriteria decision making problems. Sci World J. https://doi.org/10.1155/2014/645953

    Article  Google Scholar 

  • Zhang HY, Ji P, Wang JQ, Chen XH (2015) An improved weighted correlation coefficient based on integrated weight for interval neutrosophic sets and its application in multi-criteria decision-making. Int J Comput Intell Syst 8(6):1027–1043

    Google Scholar 

  • Zhang HY, Wang JQ, Chen XH (2016) An outranking approach for multi-criteria decision-making problems with interval-valued neutrosophic sets. Neural Comput Appl 27(3):615–627

    Google Scholar 

  • Zhang YN, Tang J, Meng FY (2018a) Programming model-based method for ranking objects from decision making with interval-valued hesitant fuzzy preference relations. Appl Intell. https://doi.org/10.1007/s10489-018-1292-1

    Article  Google Scholar 

  • Zhang XY, Wang XK, Yu SM, Wang JQ, Wang TL (2018b) Location selection of offshore wind power station by consensus decision framework using picture fuzzy modeling. J Clean Prod 202:980–992

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (nos. 71571192, 71601049, 71874112, and 71671188), the Innovation-Driven Project of Central South University (no. 2018CX039), the Fundamental Research Funds for the Central Universities of Central South University (no. 2018zzts094), the Major Project for National Natural Science Foundation of China (no. 71790615), and the State Key Program of National Natural Science of China (no. 71431006).

Author information

Authors and Affiliations

  1. School of Business, Central South University, Changsha, 410083, China

    Fanyong Meng, Na Wang & Yanwei Xu

  2. Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Fanyong Meng

Authors
  1. Fanyong Meng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Na Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yanwei Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Na Wang.

Ethics declarations

Conflict of interest

We declare that we 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

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Meng, F., Wang, N. & Xu, Y. Interval neutrosophic preference relations and their application in virtual enterprise partner selection. J Ambient Intell Human Comput 10, 5007–5036 (2019). https://doi.org/10.1007/s12652-019-01178-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12652-019-01178-5

Keywords

Search

Navigation