Cross-entropy measure on interval neutrosophic sets and its applications in multicriteria decision making

Neural Computing and Applications

Volumn 28, Issue 5, 2017, Pages 1177-1187

  Şahin, Rıdvan ^a  

^a BAYBURT UNIVERSITY   (Turkey)

Author keywords

Cross entropy; Interval neutrosophic sets; Multicriteria decision making; Neutrosophic sets; Single valued neutrosophic sets

Indexed keywords

ENTROPY;

CROSS ENTROPY; INCOMPLETE INFORMATION; INCONSISTENT INFORMATION; INTERVAL NEUTROSOPHIC SETS; MULTI CRITERIA DECISION MAKING; MULTI-CRITERIA DECISION MAKING METHODS; NEUTROSOPHIC SETS; SCIENTIFIC AND ENGINEERING APPLICATIONS;

DECISION MAKING;

EID: 84949523810     PISSN: 09410643     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00521-015-2131-5     Document Type: Article

References (42)

1. Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96
2. Atanassov K, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31(3):343–349
3. Broumi S, Smarandache F (2013) Correlation coefficient of interval neutrosophic set. Appl Mech Mater 436:511–517
4. Burillo P, Bustince H (1996) Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst 78:305–316
5. Bhandari D, Pal NR (1993) Some new information measures for fuzzy sets. Inf Sci 67:209–228
6. Cheng HD, Guo Y (2008) A new neutrosophic approach to image thresholding. New Math Nat Comput 4(3):291–308
7. DeLuca A, Termini S (1972) A definition of nonprobabilistic entropy in the setting of fuzzy sets theory. Inf Control 20:301–312
8. Guo Y, Cheng HD (2009) New neutrosophic approach to image segmentation. Pattern Recognit 42:587–595
9. Kullback S (1968) Information theory and statistics. Dover Publications, New York
10. Liu PD (2013) Some generalized dependent aggregation operators with intuitionistic linguistic numbers and their application to group decision making. J Comput Syst Sci 79:131–143
11. Liu PD, Jin F (2012) The trapezoid fuzzy linguistic Bonferroni mean operators and their application to multiple attribute decision making. Sci Iran Trans E Ind Eng 19(6):1947–1959
12. Liu PD, Liu ZM, Zhang X (2014) Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making. Appl Math Comput 230:570–586
13. Liu PD, Wang YM (2014) Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operators. Appl Soft Comput 17:90–104
14. Liu PD, Xiaocun Yu (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
15. Liu PD, 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
16. Liu PD, Shi L (2015) The generalized hybrid weighted average operator based on interval neutrosophic hesitant set and its application to multiple attribute decision making. Neural Comput Appl 26(2):457–471
17. Majumdar P, Samanta SK (2014) On similarity and entropy of neutrosophic sets. J Intell Fuzzy Syst 26(3):1245–1252
18. Martínez L, Ruan D, Herrera F, Herrera-Viedma E, Wang PP (2009) Linguistic decision making: tools and applications. Inf Sci 179:2297–2298
19. Peng JJ, Wang JQ, Wang J, Zhang HY, Chen XH (2015) Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems. Int J Syst Sci. doi:10.1080/00207721.2014.994050
20. Peng JJ, Wang JQ, Wu XH, Wang J, 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
21. Shang XG, Jiang WS (1997) A note on fuzzy information measures. Pattern Recognit Lett 18:425–432
22. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423
23. Şahin R, Küçük A (2014) Subsethood measure for single valued neutrosophic sets. J Intell Fuzzy Syst. doi:10.3233/IFS-141304
24. Şahin R, Karabacak M (2015) A multi attribute decision making method based on inclusion measure for interval neutrosophic sets. Int J Eng Appl Sci 2(2):13–15
25. Smarandache F (1999) A unifying field in logics. Neutrosophy: neutrosophic probability, set and logic. American Research Press, Rehoboth
26. Smarandache F (1998) Neutrosophy. Neutrosophic probability, set, and logic. American Research Press, Rehoboth
27. Szmidt E, Kacprzyk J (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst 118:467–477
28. Turksen B (1986) Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst 20:191–210
29. Verma R (2014) On generalized fuzzy divergence measure and their application to multicriteria decision-making. J Comb Inf Syst Sci 39(1–4):191–213
30. Verma R, Sharma BD (2012) On generalized intuitionistic fuzzy relative information and their properties. J Uncertain Syst 6(4):308–320
31. Vlachos IK, Sergiadis GD (2007) Intuitionistic fuzzy information-applications to pattern recognition. Pattern Recogn Lett 28:197–206
32. Wei CP, Wang P, Zhang YZ (2011) Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications. Inf Sci 181:4273–4286
33. Wang H, Smarandache F, Zhang YQ, Sunderraman R (2010) Single valued neutrosophic sets. Multispace Multistruct 4:410–413
34. Wang H, Smarandache F, Zhang YQ, Sunderraman R (2005) Interval neutrosophic sets and logic: theory and applications in computing. Hexis, Arizona
35. Ye J (2013) Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment. Int J Gen Syst 42(4):386–394
36. Ye J (2014) Similarity measures between interval neutrosophic sets and their applications in Multi-criteria decision-making. J Intell Fuzzy Syst 26:165–172
37. Ye J (2014) Single valued neutrosophic cross-entropy for multi-criteria decision making problems. Appl Math Model 38(3):1170–1175
38. Ye J (2014) A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. J Intell Fuzzy Syst 26(5):2459–2466
39. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
40. Zadeh LA (1968) Probability measures of fuzzy events. J Math Anal Appl 23:421–427
41. Zhang HY, Wang JQ, Chen XH (2014) Interval neutrosophic sets and their application in multicriteria decision making problems. Sci World J 2014:645953
42. Zhang QS, Jiang S, Jia B, Luo S (2010) Some information measures for interval-valued intuitionistic fuzzy sets. Inf Sci 180:5130–5145