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Published in: Neural Computing and Applications 3/2018

20-07-2016 | Original Article

Similarity measures of bipolar neutrosophic sets and their application to multiple criteria decision making

Authors: Vakkas Uluçay, Irfan Deli, Mehmet Şahin

Published in: Neural Computing and Applications | Issue 3/2018

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Abstract

In this paper, we introduced some similarity measures for bipolar neutrosophic sets such as; Dice similarity measure, weighted Dice similarity measure, Hybrid vector similarity measure and weighted Hybrid vector similarity measure. Also we examine the propositions of the similarity measures. Furthermore, a multi-criteria decision-making method for bipolar neutrosophic set is developed based on these given similarity measures. Then, a practical example is shown to verify the feasibility of the new method. Finally, we compare the proposed method with the existing methods in order to demonstrate the practicality and effectiveness of the developed method in this paper.

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Literature
1.
go back to reference Ali M, Smarandache F (2016) Complex neutrosophic set. Neural Comput Appl 25:1–18 Ali M, Smarandache F (2016) Complex neutrosophic set. Neural Comput Appl 25:1–18
2.
go back to reference Ali M, Deli I, Smarandache F (2016) The theory of neutrosophic cubic sets and their applications in pattern recognition. J Intell Fuzzy Syst 30(4):1957–1963CrossRefMATH Ali M, Deli I, Smarandache F (2016) The theory of neutrosophic cubic sets and their applications in pattern recognition. J Intell Fuzzy Syst 30(4):1957–1963CrossRefMATH
5.
go back to reference Aydoğdu A (2015) On similarity and entropy of single valued neutrosophic sets. Gen Math Notes 29(1):67–74 Aydoğdu A (2015) On similarity and entropy of single valued neutrosophic sets. Gen Math Notes 29(1):67–74
6.
go back to reference Broumi S, Smarandache F (2013) Several similarity measures of neutrosophic sets. Neutro Sophic Sets Syst 1(1):54–62 Broumi S, Smarandache F (2013) Several similarity measures of neutrosophic sets. Neutro Sophic Sets Syst 1(1):54–62
7.
go back to reference Broumi S (2013) Generalized neutrosophic soft set. Int J Comput Scie Eng Inf Technol(IJCSEIT) 3/2:17–30 Broumi S (2013) Generalized neutrosophic soft set. Int J Comput Scie Eng Inf Technol(IJCSEIT) 3/2:17–30
8.
go back to reference Broumi S, Talea M, Bakali A, Smarandache F (2016) Single valued neutrosophic graphs. J New Theory 10:86–101 Broumi S, Talea M, Bakali A, Smarandache F (2016) Single valued neutrosophic graphs. J New Theory 10:86–101
9.
go back to reference Broumi S, Talea M, Bakali A, Smarandache F (2016) On bipolar single valued neutrosophic graphs. J New Theory 11:84–102 Broumi S, Talea M, Bakali A, Smarandache F (2016) On bipolar single valued neutrosophic graphs. J New Theory 11:84–102
10.
go back to reference Broumi S, Smarandache F, Talea M, Bakali A (2016) An introduction to bipolar single valued neutrosophic graph theory. Appl Mech Mater 841:184–191CrossRef Broumi S, Smarandache F, Talea M, Bakali A (2016) An introduction to bipolar single valued neutrosophic graph theory. Appl Mech Mater 841:184–191CrossRef
11.
go back to reference Broumi S, Bakali A, Talea M, Smarandache F (2016) Isolated single valued neutrosophic graphs. neutrosophic Sets Syst 11:74–78 Broumi S, Bakali A, Talea M, Smarandache F (2016) Isolated single valued neutrosophic graphs. neutrosophic Sets Syst 11:74–78
12.
go back to reference Balasubramanian A, Prasad KM, Arjunan K (2015) Bipolar interval valued fuzzy subgroups of a group. Bull Math stat Res 3(3):234–239 Balasubramanian A, Prasad KM, Arjunan K (2015) Bipolar interval valued fuzzy subgroups of a group. Bull Math stat Res 3(3):234–239
13.
go back to reference Broumi S, Smarandache F (2013) Several similarity measures of neutrosophic sets. Neutrosophic Sets Syst 1(1):54–62 Broumi S, Smarandache F (2013) Several similarity measures of neutrosophic sets. Neutrosophic Sets Syst 1(1):54–62
14.
go back to reference Broumi S, Deli I, Smarandache F (2014) Distance and similarity measures of interval neutrosophic soft sets. In: Critical review, center for mathematics of uncertainty, Creighton University, USA, vol 8, pp 14–31 Broumi S, Deli I, Smarandache F (2014) Distance and similarity measures of interval neutrosophic soft sets. In: Critical review, center for mathematics of uncertainty, Creighton University, USA, vol 8, pp 14–31
15.
go back to reference Broumi S, Deli I (2016) Correlation measure for neutrosophic refined sets and its application in medical diagnosis. Palest J Math 5(1):135–143MathSciNetMATH Broumi S, Deli I (2016) Correlation measure for neutrosophic refined sets and its application in medical diagnosis. Palest J Math 5(1):135–143MathSciNetMATH
16.
go back to reference Deli I, Subas YA (2016) Multiple criteria decision making method on single valued bipolar neutrosophic set based on correlation coefficient similarity measure. In: International conference on mathematics and mathematics education (ICMME-2016), Frat University, May 12–14, Elazg, Turkey Deli I, Subas YA (2016) Multiple criteria decision making method on single valued bipolar neutrosophic set based on correlation coefficient similarity measure. In: International conference on mathematics and mathematics education (ICMME-2016), Frat University, May 12–14, Elazg, Turkey
18.
go back to reference Deli I, Ali M, Smarandache F (2015) Bipolar neutrosophic sets and their application based on multi-criteria decision making problems. In: 2015 International conference on advanced mechatronic systems (ICAMechS). IEEE.(2015, August), pp 249–254 Deli I, Ali M, Smarandache F (2015) Bipolar neutrosophic sets and their application based on multi-criteria decision making problems. In: 2015 International conference on advanced mechatronic systems (ICAMechS). IEEE.(2015, August), pp 249–254
19.
20.
21.
go back to reference Lee KM (2000) Bipolar-valued fuzzy sets and their operations. In: Proceedings of international conference on intelligent technologies, Bangkok, Thailand, pp 307–312 Lee KM (2000) Bipolar-valued fuzzy sets and their operations. In: Proceedings of international conference on intelligent technologies, Bangkok, Thailand, pp 307–312
22.
go back to reference Lee KJ (2009) Bipolar fuzzy subalgebras and bipolar fuzzy ideals of BCK/BCI-algebras. Bull Malays Math Sci Soc 32(3):361–373MathSciNetMATH Lee KJ (2009) Bipolar fuzzy subalgebras and bipolar fuzzy ideals of BCK/BCI-algebras. Bull Malays Math Sci Soc 32(3):361–373MathSciNetMATH
23.
go back to reference Ma YX, Wang JQ, Wang J, Wu XH (2016) An interval neutrosophic linguistic multi-criteria group decision–making method and its application in selecting medical treatment options. Neural Comput Appl. doi:10.1007/s00521-016-2203-1 Ma YX, Wang JQ, Wang J, Wu XH (2016) An interval neutrosophic linguistic multi-criteria group decision–making method and its application in selecting medical treatment options. Neural Comput Appl. doi:10.​1007/​s00521-016-2203-1
25.
26.
go back to reference Majumdar P, Smanata SK (2014) On similarity and entropy of neutrosophic sets. J Intell Fuzzy Syst 26(3):1245–1252MathSciNetMATH Majumdar P, Smanata SK (2014) On similarity and entropy of neutrosophic sets. J Intell Fuzzy Syst 26(3):1245–1252MathSciNetMATH
27.
go back to reference Mondal K, Pramanik S (2015) Neutrosophic tangent similarity measure and its application to multiple attribute decision making. Neutrosophic Sets Syst 9:85–92 Mondal K, Pramanik S (2015) Neutrosophic tangent similarity measure and its application to multiple attribute decision making. Neutrosophic Sets Syst 9:85–92
28.
go back to reference Mukherjee A, Sarkar S (2014) Several similarity measures of neutrosophic soft sets and its application in real life problems. Ann Pure Appl Math 7(1):1–6 Mukherjee A, Sarkar S (2014) Several similarity measures of neutrosophic soft sets and its application in real life problems. Ann Pure Appl Math 7(1):1–6
29.
go back to reference Pramanik S, Biswas P, Giri BC (2015) Hybrid vector similarity measures and their applications to multi-attribute decision making under neutrosophic environment. Neural Comput Appl 1–14. doi:10.1007/s00521-015-2125-3 Pramanik S, Biswas P, Giri BC (2015) Hybrid vector similarity measures and their applications to multi-attribute decision making under neutrosophic environment. Neural Comput Appl 1–14. doi:10.​1007/​s00521-015-2125-3
30.
go back to reference Pramanik S, Mondal K (2015) Cosine similarity measure of rough neutrosophic sets and its application in medical diagnosis. Global J Adv Res 2(1):212–220 Pramanik S, Mondal K (2015) Cosine similarity measure of rough neutrosophic sets and its application in medical diagnosis. Global J Adv Res 2(1):212–220
31.
go back to reference Peng JJ, Wang JQ, Zhang HY, Chen XH (2014) An outranking approach for multi-criteria decision–making problems with simplified neutrosophic sets. Appl Soft Comput 25:336–346CrossRef Peng JJ, Wang JQ, Zhang HY, Chen XH (2014) An outranking approach for multi-criteria decision–making problems with simplified neutrosophic sets. Appl Soft Comput 25:336–346CrossRef
32.
go back to reference Smarandache F (1998) A unifying field in logics neutrosophy: neutrosophic probability, set and logic. American Research Press, RehobothMATH Smarandache F (1998) A unifying field in logics neutrosophy: neutrosophic probability, set and logic. American Research Press, RehobothMATH
33.
go back to reference Smarandache F (2005) Neutrosophic set, a generalisation of the intuitionistic fuzzy sets. Int J Pure Appl Math 24:287–297MathSciNetMATH Smarandache F (2005) Neutrosophic set, a generalisation of the intuitionistic fuzzy sets. Int J Pure Appl Math 24:287–297MathSciNetMATH
34.
go back to reference Santhi V, Shyamala G (2015) Notes On Bipolar-Valued Multi Fuzzy Subgroups Of A Group. Int J Math Arch (IJMA). 6(6). ISSN 2229–5046 Santhi V, Shyamala G (2015) Notes On Bipolar-Valued Multi Fuzzy Subgroups Of A Group. Int J Math Arch (IJMA). 6(6). ISSN 2229–5046
35.
go back to reference Saeid AB (2009) Bipolar-valued fuzzy BCK/BCI-algebras. World Appl Sci J 7(11):1404–1411 Saeid AB (2009) Bipolar-valued fuzzy BCK/BCI-algebras. World Appl Sci J 7(11):1404–1411
36.
go back to reference Şahin M, Deli I, and Ulucay V (2016) Jaccard vector similarity measure of bipolar neutrosophic set based on multi-criteria decision making. In: International conference on natural science and engineering (ICNASE’16), March 19–20, Kilis Şahin M, Deli I, and Ulucay V (2016) Jaccard vector similarity measure of bipolar neutrosophic set based on multi-criteria decision making. In: International conference on natural science and engineering (ICNASE’16), March 19–20, Kilis
37.
go back to reference Tian ZP, Wang J, Wang JQ, Zhang HY (2016) Simplified neutrosophic linguistic multi-criteria group decision–making approach to green product development. Group Decis Negot 1–31. doi:10.1007/s10726-016-9479-5 Tian ZP, Wang J, Wang JQ, Zhang HY (2016) Simplified neutrosophic linguistic multi-criteria group decision–making approach to green product development. Group Decis Negot 1–31. doi:10.​1007/​s10726-016-9479-5
38.
go back to reference Tian ZP, Wang J, Wang JQ, Zhang HY (2016) An improved MULTIMOORA approach for multi-criteria decision–making based on interdependent inputs of simplified neutrosophic linguistic information. Neural Comput Appl. doi:10.1007/s00521-016-2378-5 Tian ZP, Wang J, Wang JQ, Zhang HY (2016) An improved MULTIMOORA approach for multi-criteria decision–making based on interdependent inputs of simplified neutrosophic linguistic information. Neural Comput Appl. doi:10.​1007/​s00521-016-2378-5
39.
go back to reference Tian ZP, Zhang HY, Wang J, Wang JQ, Chen XH (2015) Multi-criteria decision–making method based on a cross-entropy with interval neutrosophic sets. Int J Syst Sci. doi:10.1080/00207721.1102359 Tian ZP, Zhang HY, Wang J, Wang JQ, Chen XH (2015) Multi-criteria decision–making method based on a cross-entropy with interval neutrosophic sets. Int J Syst Sci. doi:10.​1080/​00207721.​1102359
40.
go back to reference Wang H, Smarandache FYQ, Zhang Q, Sunderraman R (2010) Single valued neutrosophic sets. Multispace Multistructure 4:410–413MATH Wang H, Smarandache FYQ, Zhang Q, Sunderraman R (2010) Single valued neutrosophic sets. Multispace Multistructure 4:410–413MATH
41.
go back to reference Wu J, Cao QW (2013) Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers. Appl Math Model 37:318–327MathSciNetCrossRefMATH Wu J, Cao QW (2013) Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers. Appl Math Model 37:318–327MathSciNetCrossRefMATH
42.
go back to reference Wu XH, Wang JQ, Peng JJ, Chen XH (2016) Cross-entropy and prioritized aggregation operator with simplified neutrosophic sets and their application in multi-criteria decision–making problems. Int J Fuzzy Syst. doi:10.1007/s40815-016-0180-2 Wu XH, Wang JQ, Peng JJ, Chen XH (2016) Cross-entropy and prioritized aggregation operator with simplified neutrosophic sets and their application in multi-criteria decision–making problems. Int J Fuzzy Syst. doi:10.​1007/​s40815-016-0180-2
43.
go back to reference Xu X, Zhang L, Wan Q (2012) A variation coefficient similarity measure and its application in emergency group decision making. Syst Eng Proc 5:119–124CrossRef Xu X, Zhang L, Wan Q (2012) A variation coefficient similarity measure and its application in emergency group decision making. Syst Eng Proc 5:119–124CrossRef
44.
go back to reference Ye J (2014) Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making. Int J Fuzzy Syst 16(2):204–215 Ye J (2014) Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making. Int J Fuzzy Syst 16(2):204–215
45.
go back to reference Ye J (2014) Improved correlation coefficients of single valued neutrosophic sets and interval neutrosophic sets for multiple attribute decision making. J Intell Fuzzy Syst 27:24532462MATH Ye J (2014) Improved correlation coefficients of single valued neutrosophic sets and interval neutrosophic sets for multiple attribute decision making. J Intell Fuzzy Syst 27:24532462MATH
46.
go back to reference Ye J, Zhang QS (2014) Single valued neutrosophic similarity measures for multiple attribute decision making. Neutrosophic Sets Syst 2:48–54 Ye J, Zhang QS (2014) Single valued neutrosophic similarity measures for multiple attribute decision making. Neutrosophic Sets Syst 2:48–54
47.
go back to reference Ye S, Ye J (2014) Dice similarity measure between single valued neutrosophic multisets and its application in medical diagnosis. Neutrosophic Sets Syst 6:48–52 Ye S, Ye J (2014) Dice similarity measure between single valued neutrosophic multisets and its application in medical diagnosis. Neutrosophic Sets Syst 6:48–52
48.
go back to reference Ye J, Fu J (2016) Multi-period medical diagnosis method using a single valued neutrosophic similarity measure based on tangent function. Comput Methods Program Biomed 123:142–149CrossRef Ye J, Fu J (2016) Multi-period medical diagnosis method using a single valued neutrosophic similarity measure based on tangent function. Comput Methods Program Biomed 123:142–149CrossRef
49.
go back to reference Ye J (2015) Single-valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine. Soft Comput 1–9. doi:10.1007/s00500-015-1818-y Ye J (2015) Single-valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine. Soft Comput 1–9. doi:10.​1007/​s00500-015-1818-y
50.
go back to reference Jun YB, Kang MS, Kim HS (2009) Bipolar fuzzy structures of some types of ideals in hyper BCK-algebras. Sci Math Jpn 70:109–121MathSciNetMATH Jun YB, Kang MS, Kim HS (2009) Bipolar fuzzy structures of some types of ideals in hyper BCK-algebras. Sci Math Jpn 70:109–121MathSciNetMATH
Metadata
Title
Similarity measures of bipolar neutrosophic sets and their application to multiple criteria decision making
Authors
Vakkas Uluçay
Irfan Deli
Mehmet Şahin
Publication date
20-07-2016
Publisher
Springer London
Published in
Neural Computing and Applications / Issue 3/2018
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-016-2479-1

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