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Published in: Neural Processing Letters 5/2021

11-06-2021

Interval Neutrosophic Einstein Prioritized Normalized Weighted Geometric Bonferroni Mean Operator and its Application to Multicriteria Decision making

Author: Pankaj Kakati

Published in: Neural Processing Letters | Issue 5/2021

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Abstract

In a real or practical situation, there often exist different priority levels and interactions among the criteria of the MCDM problems. This paper combines the prioritized average operator with the normalized weighted geometric Bonferroni mean operator under the Einstein operational law of interval neutrosophic numbers (INNs) to propose the interval neutrosophic Einstein prioritized normalized weighted geometric Bonferroni mean (INEPNWGBM) operator to deal with the prioritization and correlation among the criteria in the real-life decision making problems. Then, some desired properties of the proposed aggregation operator are discussed. Furthermore, an approach to multicriteria decision making based on the Einstein prioritized normalized weighted geometric Bonferroni mean is developed. Finally, a numerical example is provided to illustrate the proposed approach.
Literature
2.
go back to reference Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96 CrossRef Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96 CrossRef
5.
go back to reference Torra V, Narukawa Y (2009). On hesitant fuzzy sets and decision. In: Fuzzy systems, FUZZ-IEEE 2009. IEEE international conference on. pp. 1378-1382 Torra V, Narukawa Y (2009). On hesitant fuzzy sets and decision. In: Fuzzy systems, FUZZ-IEEE 2009. IEEE international conference on. pp. 1378-1382
6.
go back to reference Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539 MATH Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539 MATH
7.
go back to reference Chen N, Xu Z, Xia M (2013) Interval-valued hesitant preference relations and their applications to group decision making. Knowl-Based Syst 37:528–540 CrossRef Chen N, Xu Z, Xia M (2013) Interval-valued hesitant preference relations and their applications to group decision making. Knowl-Based Syst 37:528–540 CrossRef
8.
go back to reference Zhang Z (2013) Interval-valued intuitionistic hesitant fuzzy aggregation operators and their application in group decision-making. J Appl Math 1–33 Zhang Z (2013) Interval-valued intuitionistic hesitant fuzzy aggregation operators and their application in group decision-making. J Appl Math 1–33
9.
go back to reference Smarandache F (1999) A unifying field in logics: neutrosophic logic. Philosophy. American Research Press, New Mexico, pp 1–141 Smarandache F (1999) A unifying field in logics: neutrosophic logic. Philosophy. American Research Press, New Mexico, pp 1–141
10.
go back to reference Wang H, Smarandache F, Zhang Y, Sunderraman R (2010) Single valued neutrosophic sets. Infinite Study Wang H, Smarandache F, Zhang Y, Sunderraman R (2010) Single valued neutrosophic sets. Infinite Study
11.
go back to reference Wang H, Smarandache F, Sunderraman R, Zhang YQ (2005) Interval neutrosophic sets and logic: Theory and applications in computing: Theory and applications in computing . Inf Stud, 5 Wang H, Smarandache F, Sunderraman R, Zhang YQ (2005) Interval neutrosophic sets and logic: Theory and applications in computing: Theory and applications in computing . Inf Stud, 5
12.
go back to reference Ye J (2014) Single valued neutrosophic cross-entropy for multicriteria decision making problems. Appl Math Model 38(3):1170–1175 MathSciNetCrossRef Ye J (2014) Single valued neutrosophic cross-entropy for multicriteria decision making problems. Appl Math Model 38(3):1170–1175 MathSciNetCrossRef
13.
go back to reference Ye J (2015) Multiple-attribute decision-making method under a single-valued neutrosophic hesitant fuzzy environment. J Intell Syst 24(1):23–36 CrossRef Ye J (2015) Multiple-attribute decision-making method under a single-valued neutrosophic hesitant fuzzy environment. J Intell Syst 24(1):23–36 CrossRef
14.
go back to reference Şahin R, Liu P (2017) Correlation coefficient of single-valued neutrosophic hesitant fuzzy sets and its applications in decision making. Neural Comput Appl 28(6):1387–1395 CrossRef Şahin R, Liu P (2017) Correlation coefficient of single-valued neutrosophic hesitant fuzzy sets and its applications in decision making. Neural Comput Appl 28(6):1387–1395 CrossRef
15.
go back to reference Biswas P, Pramanik S, Giri BC (2016) Some distance measures of single valued neutrosophic hesitant fuzzy sets and their applications to multiple attribute decision making. New Trends Neutrosophic Theory Appl 2:55–63 Biswas P, Pramanik S, Giri BC (2016) Some distance measures of single valued neutrosophic hesitant fuzzy sets and their applications to multiple attribute decision making. New Trends Neutrosophic Theory Appl 2:55–63
16.
go back to reference Liu CF, Luo YS (2017) New aggregation operators of single-valued neutrosophic hesitant fuzzy set and their application in multi-attribute decision making. Pattern Anal Appl 1–11 Liu CF, Luo YS (2017) New aggregation operators of single-valued neutrosophic hesitant fuzzy set and their application in multi-attribute decision making. Pattern Anal Appl 1–11
17.
go back to reference Liu P, Zhang L (2017) Multiple criteria decision making method based on neutrosophic hesitant fuzzy Heronian mean aggregation operators. J Intell Fuzzy Syst 32(1):303–319 CrossRef Liu P, Zhang L (2017) Multiple criteria decision making method based on neutrosophic hesitant fuzzy Heronian mean aggregation operators. J Intell Fuzzy Syst 32(1):303–319 CrossRef
19.
go back to reference Bonferroni C (1950) Sulle medie multiple di potenze. Bollettino dell’Unione Matematica Italiana 5(3–4):267–270 MathSciNetMATH Bonferroni C (1950) Sulle medie multiple di potenze. Bollettino dell’Unione Matematica Italiana 5(3–4):267–270 MathSciNetMATH
20.
go back to reference Sugeno M (1974) Theory of fuzzy integrals and its applications. Doct. Thesis, Tokyo Institute of technology Sugeno M (1974) Theory of fuzzy integrals and its applications. Doct. Thesis, Tokyo Institute of technology
21.
go back to reference Kakati P, Borkotokey S, Mesiar R, Rahman S (2018) Interval neutrosophic hesitant fuzzy choquet integral in multicriteria decision making. J Intell Fuzzy Syst 35(3):3213–3231 CrossRef Kakati P, Borkotokey S, Mesiar R, Rahman S (2018) Interval neutrosophic hesitant fuzzy choquet integral in multicriteria decision making. J Intell Fuzzy Syst 35(3):3213–3231 CrossRef
22.
go back to reference Kakati P, Borkotokey S, Rahman S, Davvaz B (2020) Interval neutrosophic hesitant fuzzy Einstein Choquet integral operator for multicriteria decision making. Artif Intell Rev 53(3):2171–2206 CrossRef Kakati P, Borkotokey S, Rahman S, Davvaz B (2020) Interval neutrosophic hesitant fuzzy Einstein Choquet integral operator for multicriteria decision making. Artif Intell Rev 53(3):2171–2206 CrossRef
23.
go back to reference Yager RR (2009) On generalized Bonferroni mean operators for multi-criteria aggregation. Int J Approx Reason 50(8):1279–1286 MathSciNetCrossRef Yager RR (2009) On generalized Bonferroni mean operators for multi-criteria aggregation. Int J Approx Reason 50(8):1279–1286 MathSciNetCrossRef
24.
go back to reference Beliakov G, James S, Mordelová J, Rückschlossová T, Yager RR (2010) Generalized Bonferroni mean operators in multi-criteria aggregation. Fuzzy Sets Syst 161(17):2227–2242 MathSciNetCrossRef Beliakov G, James S, Mordelová J, Rückschlossová T, Yager RR (2010) Generalized Bonferroni mean operators in multi-criteria aggregation. Fuzzy Sets Syst 161(17):2227–2242 MathSciNetCrossRef
25.
go back to reference Li B L, Wang JR, Yang L H, Li XT (2018) Multiple criteria decision making approach with multivalued neutrosophic linguistic normalized weighted Bonferroni mean Hamacher operator. Math Problems Eng, 2018 Li B L, Wang JR, Yang L H, Li XT (2018) Multiple criteria decision making approach with multivalued neutrosophic linguistic normalized weighted Bonferroni mean Hamacher operator. Math Problems Eng, 2018
26.
go back to reference Garg H, Arora R (2018) Bonferroni mean aggregation operators under intuitionistic fuzzy soft set environment and their applications to decision-making. J Oper Res Soc 69(11):1711–1724 CrossRef Garg H, Arora R (2018) Bonferroni mean aggregation operators under intuitionistic fuzzy soft set environment and their applications to decision-making. J Oper Res Soc 69(11):1711–1724 CrossRef
27.
go back to reference Khan Q, Liu P, Mahmood T, Smarandache F, Ullah K (2018) Some interval neutrosophic dombi power bonferroni mean operators and their application in multi-attribute decision-making. Symmetry 10(10):459 CrossRef Khan Q, Liu P, Mahmood T, Smarandache F, Ullah K (2018) Some interval neutrosophic dombi power bonferroni mean operators and their application in multi-attribute decision-making. Symmetry 10(10):459 CrossRef
28.
go back to reference 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(3):107 CrossRef 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(3):107 CrossRef
29.
go back to reference Xia M, Xu Z, Zhu B (2013) Geometric Bonferroni means with their application in multi-criteria decision making. Knowl-Based Syst 40:88–100 CrossRef Xia M, Xu Z, Zhu B (2013) Geometric Bonferroni means with their application in multi-criteria decision making. Knowl-Based Syst 40:88–100 CrossRef
30.
go back to reference Xia M, Xu Z, Zhu B (2012) Generalized intuitionistic fuzzy Bonferroni means. Int J Intell Syst 27(1):23–47 CrossRef Xia M, Xu Z, Zhu B (2012) Generalized intuitionistic fuzzy Bonferroni means. Int J Intell Syst 27(1):23–47 CrossRef
31.
go back to reference Liu P, Wang Y (2014) Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean. Neural Comput Appl 25(7–8):2001–2010 CrossRef Liu P, Wang Y (2014) Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean. Neural Comput Appl 25(7–8):2001–2010 CrossRef
32.
go back to reference Wei G, Wang R, Wang J, Wei C, Zhang Y (2019) Methods for evaluating the technological innovation capability for the high-tech enterprises with generalized interval neutrosophic number Bonferroni mean operators. IEEE Access 7:86473–86492 CrossRef Wei G, Wang R, Wang J, Wei C, Zhang Y (2019) Methods for evaluating the technological innovation capability for the high-tech enterprises with generalized interval neutrosophic number Bonferroni mean operators. IEEE Access 7:86473–86492 CrossRef
33.
go back to reference Pamučar D, Božanić D, Lukovac V, Komazec N (2018) Normalized weighted geometric bonferroni mean operator of interval rough numbers-application in interval rough dematel-copras model. Facta Universitatis, Ser: Mech Eng 16(2):171–191 CrossRef Pamučar D, Božanić D, Lukovac V, Komazec N (2018) Normalized weighted geometric bonferroni mean operator of interval rough numbers-application in interval rough dematel-copras model. Facta Universitatis, Ser: Mech Eng 16(2):171–191 CrossRef
36.
go back to reference Yu D (2013) Intuitionistic fuzzy prioritized operators and their application in multi-criteria group decision making. Technol Econ Develop Econ 19(1):1–21 CrossRef Yu D (2013) Intuitionistic fuzzy prioritized operators and their application in multi-criteria group decision making. Technol Econ Develop Econ 19(1):1–21 CrossRef
37.
go back to reference Yu D, Wu Y, Lu T (2012) Interval-valued intuitionistic fuzzy prioritized operators and their application in group decision making. Knowl-Based Syst 30:57–66 CrossRef Yu D, Wu Y, Lu T (2012) Interval-valued intuitionistic fuzzy prioritized operators and their application in group decision making. Knowl-Based Syst 30:57–66 CrossRef
38.
go back to reference Wei G (2012) Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowl-Based Syst 31:176–182 CrossRef Wei G (2012) Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowl-Based Syst 31:176–182 CrossRef
39.
go back to reference Wang R, Li Y (2018) Generalized single-valued neutrosophic hesitant fuzzy prioritized aggregation operators and their applications to multiple criteria decision-making. Information 9(1):10 CrossRef Wang R, Li Y (2018) Generalized single-valued neutrosophic hesitant fuzzy prioritized aggregation operators and their applications to multiple criteria decision-making. Information 9(1):10 CrossRef
40.
go back to reference Jin F, Ni Z, Chen H (2016) Interval-valued hesitant fuzzy Einstein prioritized aggregation operators and their applications to multi-attribute group decision making. Soft Comput 20(5):1863–1878 CrossRef Jin F, Ni Z, Chen H (2016) Interval-valued hesitant fuzzy Einstein prioritized aggregation operators and their applications to multi-attribute group decision making. Soft Comput 20(5):1863–1878 CrossRef
41.
go back to reference Liu P, Wang Y (2016) Interval neutrosophic prioritized OWA operator and its application to multiple attribute decision making. J Syst Sci Complexity 29(3):681–697 CrossRef Liu P, Wang Y (2016) Interval neutrosophic prioritized OWA operator and its application to multiple attribute decision making. J Syst Sci Complexity 29(3):681–697 CrossRef
42.
go back to reference Ji P, Wang JQ, Zhang HY (2018) 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 CrossRef Ji P, Wang JQ, Zhang HY (2018) 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 CrossRef
43.
go back to reference Fan J, Jia X, Wu M (2019) Green supplier selection based on dombi prioritized bonferroni mean operator with single-valued triangular neutrosophic sets. Int J Comput Intell Syst 12(2):1091–1101 CrossRef Fan J, Jia X, Wu M (2019) Green supplier selection based on dombi prioritized bonferroni mean operator with single-valued triangular neutrosophic sets. Int J Comput Intell Syst 12(2):1091–1101 CrossRef
44.
go back to reference Xia M, Xu Z, Zhu B (2012) Some issues on intuitionistic fuzzy aggregation operators based on Archimedean \(t\)-conorm and \(t\)-norm. Knowl-Based Syst 31:78–88 CrossRef Xia M, Xu Z, Zhu B (2012) Some issues on intuitionistic fuzzy aggregation operators based on Archimedean \(t\)-conorm and \(t\)-norm. Knowl-Based Syst 31:78–88 CrossRef
45.
go back to reference Klement E, Mesiar R, Pap E (2000) Triangular Norms. Kluwer Academic Publishers, Dordrecht CrossRef Klement E, Mesiar R, Pap E (2000) Triangular Norms. Kluwer Academic Publishers, Dordrecht CrossRef
46.
go back to reference Şahin R (2014) Multi-criteria neutrosophic decision making method based on score and accuracy functions under neutrosophic environment. arXiv preprint arXiv:​1412.​5202 Şahin R (2014) Multi-criteria neutrosophic decision making method based on score and accuracy functions under neutrosophic environment. arXiv preprint arXiv:​1412.​5202
47.
go back to reference Wang W, Liu X (2011) Intuitionistic fuzzy geometric aggregation operators based on Einstein operations. Int J Intell Syst 26(11):1049–1075 CrossRef Wang W, Liu X (2011) Intuitionistic fuzzy geometric aggregation operators based on Einstein operations. Int J Intell Syst 26(11):1049–1075 CrossRef
48.
go back to reference Wang W, Liu X (2012a) Intuitionistic fuzzy information aggregation using Einstein operations. IEEE Trans Fuzzy Syst 20(5):923–938 CrossRef Wang W, Liu X (2012a) Intuitionistic fuzzy information aggregation using Einstein operations. IEEE Trans Fuzzy Syst 20(5):923–938 CrossRef
49.
go back to reference Wang W, Liu X (2012b). Some interval-valued intuitionistic fuzzy geometric aggregation operators based on einstein operations. In: 9th International conference on fuzzy systems and knowledge discovery, pp. 604-608 Wang W, Liu X (2012b). Some interval-valued intuitionistic fuzzy geometric aggregation operators based on einstein operations. In: 9th International conference on fuzzy systems and knowledge discovery, pp. 604-608
50.
go back to reference Xu Z, Yager RR (2010) Intuitionistic fuzzy Bonferroni means. IEEE Trans Syst, Man, Cybern, Part B (Cybernetics) 41(2):568–578 Xu Z, Yager RR (2010) Intuitionistic fuzzy Bonferroni means. IEEE Trans Syst, Man, Cybern, Part B (Cybernetics) 41(2):568–578
51.
go back to reference Zhou W, He JM (2012) Intuitionistic fuzzy normalized weighted Bonferroni mean and its application in multicriteria decision making. J Appl Math, 2012 Zhou W, He JM (2012) Intuitionistic fuzzy normalized weighted Bonferroni mean and its application in multicriteria decision making. J Appl Math, 2012
52.
go back to reference Zhang H Y, Wang J Q, Chen X H (2014). Interval neutrosophic sets and their application in multicriteria decision making problems. Sci World J, 2014 Zhang H Y, Wang J Q, Chen X H (2014). Interval neutrosophic sets and their application in multicriteria decision making problems. Sci World J, 2014
53.
go back to reference Awang A, Aizam NAH, Ab Ghani AT, Othman M, Abdullah L (2020) A Normalized Weighted Bonferroni Mean Aggregation Operator Considering Shapley Fuzzy Measure Under Interval-valued Neutrosophic Environment for Decision-Making. Int J Fuzzy Syst 22(1):321–336 CrossRef Awang A, Aizam NAH, Ab Ghani AT, Othman M, Abdullah L (2020) A Normalized Weighted Bonferroni Mean Aggregation Operator Considering Shapley Fuzzy Measure Under Interval-valued Neutrosophic Environment for Decision-Making. Int J Fuzzy Syst 22(1):321–336 CrossRef
Metadata
Title
Interval Neutrosophic Einstein Prioritized Normalized Weighted Geometric Bonferroni Mean Operator and its Application to Multicriteria Decision making
Author
Pankaj Kakati
Publication date
11-06-2021
Publisher
Springer US
Published in
Neural Processing Letters / Issue 5/2021
Print ISSN: 1370-4621
Electronic ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-021-10553-3

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