1. Home
  2. Issues
  3. Volume 29, Issue 1 (2018)
  4. The Generalized Dice Similarity Measures ...

Informatica


The Generalized Dice Similarity Measures for Picture Fuzzy Sets and Their Applications
Volume 29, Issue 1 (2018), pp. 107–124
Pub. online: 1 January 2018      Type: Research Article      Open accessOpen Access
Received
1 January 2017
Accepted
1 November 2017
Published
1 January 2018

Abstract

The picture fuzzy set is characterized by three functions expressing the degree of membership, the degree of neutral membership and the degree of non-membership. It was proposed as a generalization of an intuitionistic fuzzy set in order to deal with indeterminate and inconsistent information. In this work, we shall present some novel Dice similarity measures of picture fuzzy sets and the generalized Dice similarity measures of picture fuzzy sets and indicate that the Dice similarity measures and asymmetric measures (projection measures) are the special cases of the generalized Dice similarity measures in some parameter values. Then, we propose the generalized Dice similarity measures-based patterns recognition models with picture fuzzy information. Then, we apply the generalized Dice similarity measures between picture fuzzy sets to building material recognition. Finally, an illustrative example is given to demonstrate the efficiency of the similarity measures for building material recognition.

References

 
Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96.
 
Atanassov, K. (1989). More on intuitionistic fuzzy sets. Fuzzy Sets and Systems, 3, 37–46.
 
Chen, T.Y. (2016). An interval-valued intuitionistic fuzzy permutation method with likelihood-based preference functions and its application to multiple criteria decision analysis. Applied Soft Computing, 2, 390–409.
 
Cuong, B. (2013). Picture fuzzy sets-first results. Part 1. In: Seminar Neuro-Fuzzy Systems with Applications. Clarendon Press, Hanoi.
 
Dice, L.R. (1945a). Measures of the amount of ecologic association between species. Ecology, 6, 297–302.
 
Dice, L.R. (1945b). Measures of the amount of ecologic association between species. Ecology, 26, 297–302.
 
Garg, H. (2016). A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem. Journal of Intelligent and Fuzzy Systems, 1(1), 529–540.
 
Hu, J.H., Zhang, Y., Chen, X.H. (2013). Multi-criteria decision making method based on possibility degree of interval type-2 fuzzy number. Knowledge-Based Systems, 3, 21–29.
 
Hung, W.L., Yang, M.S. (2007). Similarity measures of intuitionistic fuzzy sets based on Lp metric. International Journal of Approximate Reasoning, 6, 120–136.
 
Jaccard, P. (1901). Distribution de la flore alpine dans le Bassin des Drouces et dans quelques regions voisines. Bulletin de la Société Sciences Nat, 7(140), 241–272.
 
Li, D.F., Ren, H.P. (2015). Multi-attribute decision making method considering the amount and reliability of intuitionistic fuzzy information. Journal of Intelligent and Fuzzy Systems, 8(4), 1877–1883.
 
Liu, H.W. (2005). New similarity measures between intuitionistic fuzzy sets and between elements. Mathematical and Computer Modelling, 2, 61–70.
 
Lu, M., Wei, G.W., Alsaadi, F.E., Hayat, T., Alsaedi, A. (2017a). Bipolar 2-tuple linguistic aggregation operators in multiple attribute decision making. Journal of Intelligent and Fuzzy Systems, 3(2), 1197–1207.
 
Lu, M., Wei, G.W., Alsaadi, F.E., Hayat, T., Alsaedi, A. (2017b). Hesitant pythagorean fuzzy hamacher aggregation operators and their application to multiple attribute decision making. Journal of Intelligent and Fuzzy Systems, 3(2), 1105–1117.
 
Peng, X., Yang, Y. (2015). Some results for pythagorean fuzzy sets. International Journal of Intelligent System, 30, 1133–1160.
 
Rajarajeswari, P., Uma, N. (2013). Intuitionistic fuzzy multi similarity measure based on cotangent function. International Journal of Engineering Research & Technology, 2(11), 1323–1329.
 
Salton, G., McGill, M.J. (1987). Introduction to Modern Information Retrieval. Clarendon Press, Hanoi.
 
Singh, P. (2014). Correlation coefficients for picture fuzzy sets. Journal of Intelligent & Fuzzy Systems, 7, 2857–2868.
 
Son, L. (2015). DPFCM: a novel distributed picture fuzzy clustering method on picture fuzzy sets. Expert System with Applications, 2, 51–66.
 
Szmidt, E. (2014). Distances and similarities in intuitionistic fuzzy sets. In: Studies in Fuzziness and Soft Computing, Vol. 307. Springer.
 
Szmidt, E., Kacprzyk, J. (2000). Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems, 114, 505–518.
 
Thong, N.T. (2015). HIFCF: An effective hybrid model between picture fuzzy clustering and intuitionistic fuzzy recommender systems for medical diagnosis expert systems with applications. Expert Systems with Applications, 2(7), 3682–3701.
 
Thong, P.H., Son, L.H. (2015). A new approach to multi-variables fuzzy forecasting using picture fuzzy clustering and picture fuzzy rules interpolation method. In: 6th International Conference on Knowledge and Systems Engineering. Hanoi, Vietnam, pp. 679–690.
 
Tian, M.Y. (2013). A new fuzzy similarity based on cotangent function for medical diagnosis. Advanced Modeling and Optimization, 5(2), 151–156.
 
Wei, G.W. (2009). Some geometric aggregation functions and their application to dynamic multiple attribute decision making in intuitionistic fuzzy setting. International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 7, 179–196.
 
Wei, G.W. (2010). Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making. Applied Soft Computing, 10, 423–431.
 
Wei, G.W. (2011). Gray relational analysis method for intuitionistic fuzzy multiple attribute decision making. Expert Systems with Applications, 38(9), 11671–11677.
 
Wei, G.W. (2015). Approaches to interval intuitionistic trapezoidal fuzzy multiple attribute decision making with incomplete weight information. International Journal of Fuzzy Systems, 17(3), 484–489.
 
Wei, G.W. (2016a). Interval valued hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making. International Journal of Machine Learning and Cybernetics, 6, 1093–1114.
 
Wei, G.W. (2016b). Picture fuzzy cross-entropy for multiple attribute decision making problems. Journal of Business Economics and Management, 17(4), 491–502.
 
Wei, G.W. (2017a). Interval-valued dual hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making. Journal of Intelligent and Fuzzy Systems, 3(3), 1881–1893.
 
Wei, G.W. (2017b). Picture 2-tuple linguistic Bonferroni mean operators and their application to multiple attribute decision making. International Journal of Fuzzy System, 19(4), 997–1010.
 
Wei, G.W. (2017c). Picture fuzzy aggregation operators and their application to multiple attribute decision making. Journal of Intelligent and Fuzzy Systems, 33(2), 713–724.
 
Wei, G.W. (2017d). Pythagorean fuzzy interaction aggregation operators and their application to multiple attribute decision making. Journal of Intelligent and Fuzzy Systems, 3(4), 2119–2132.
 
Wei, G.W. (2017e). Some cosine similarity measures for picture fuzzy sets and their applications to strategic decision making. Informatica, 28(3), 547–564.
 
Wei, G.W. (2018). Picture 2-tuple linguistic aggregation operators in multiple attribute decision making. Soft Computing, 22(3), 989–1002. 2018.
 
Wei, G.W., Lu, M. (2017). Dual hesitant Pythagorean fuzzy Hamacher aggregation operators in multiple attribute decision making. Archives of Control Sciences, 7(3), 365–395.
 
Wei, G.W., Lu, M. (2018). Pythagorean fuzzy power aggregation operators in multiple attribute decision making. International Journal of Intelligent Systems, 33(1), 169–186.
 
Wei, G.W., Wang, J.M. (2017). A comparative study of robust efficiency analysis and data envelopment analysis with imprecise data. Expert Systems with Applications, 1, 28–38.
 
Wei, G.W., Alsaadi, F.E., Hayat, T. (2016a). Projection models for multiple attribute decision making with picture fuzzy information. International Journal of Machine Learning and Cybernetics. https://doi.org/10.1007/s13042-016-0604-1.
 
Wei, G.W., Alsaadi, F.E., Hayat, T., Alsaedi, A. (2016b). Hesitant fuzzy linguistic arithmetic aggregation operators in multiple attribute decision making. Iranian Journal of Fuzzy Systems, 3(4), 1–16.
 
Wei, G.W., Alsaadi, F.E., Hayat, T., Alsaedi, A. (2017a). Hesitant bipolar fuzzy aggregation operators in multiple attribute decision making. Journal of Intelligent and Fuzzy Systems, 3(2), 1119–1128.
 
Wei, G.W., Alsaadi, F.E., Hayat, T., Alsaedi, A. (2017b). A linear assignment method for multiple criteria decision analysis with hesitant fuzzy sets based on fuzzy measure. International Journal of Fuzzy Systems, 9(3), 607–614.
 
Wei, G.W., Lu, M., Alsaadi, F.E., Hayat, T., Alsaedi, A. (2017c). Pythagorean 2-tuple linguistic aggregation operators in multiple attribute decision making. Journal of Intelligent and Fuzzy Systems, 33(2), 1129–1142.
 
Wu, S.J., Wei, G.W. (2017). Picture uncertain linguistic aggregation operators and their application to multiple attribute decision making. International Journal of Knowledge-Based and Intelligent Engineering Systems, 21(4), 243–256.
 
Xu, Z.S., Cai, X. (2008). Intuitionistic Fuzzy Information Aggregation: Theory and Applications. Science Press.
 
Xu, Z.S., Chen, J. (2008). An overview of distance and similarity measures of intuitionistic fuzzy sets. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 6(4), 529–455.
 
Xu, Z.S., Ma, Z.M. (2016). Symmetric pythagorean fuzzy weighted geometric averaging operators and their application in multicriteria decision-making problems. International Journal of Intelligent Systems, 31, 1198–1219.
 
Xu, Z.S., Xia, M.M. (2010). Some new similarity measures for intuitionistic fuzzy values and their application in group decision making. Journal of System Science and Engineering, 19, 430–452.
 
Ye, J. (2011). Cosine similarity measures for intuitionistic fuzzy sets and their applications. Mathematical and Computer Modelling, 53(1–2), 91–97.
 
Ye, J. (2012a). Multicriteria decision-making method using the Dice similarity measure between expected intervals of trapezoidal fuzzy numbers. Journal of Decision Systems, 1(4), 307–317.
 
Ye, J. (2012b). Multicriteria group decision-making method using vector similarity measures for trapezoidal intuitionistic fuzzy numbers. Group Decision and Negotiation, 21(4), 519–530.
 
Ye, J. (2014). Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making. International Journal of Fuzzy Systems, 6(2), 204–211.
 
Ye, J. (2016a). The generalized Dice measures for multiple attribute decision making under simplified neutrosophic environments. Journal of Intelligent and Fuzzy Systems, 1(1), 663–671.
 
Ye, J. (2016b). Similarity measures of intuitionistic fuzzy sets based on cosine function for the decision making of mechanical design schemes. Journal of Intelligent and Fuzzy Systems, 30(1), 151–158.
 
Zeng, S., Marqués, D.P., Zhu, F. (2016). A new model for interactive group decision making with intuitionistic fuzzy preference relations. Informatica, 27(4), 911–928.
 
Zeng, S.Z., Merigó, J.M., Marqués, D.P. (2017). Intuitionistic fuzzy induced ordered weighted averaging distance operator and its application to decision making. Journal of Intelligent and Fuzzy Systems, 2(1), 11–22.
 
Zhang, X.L., Xu, Z.S. (2014). Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. International Journal of Intelligent System, 9, 1061–1078.
 
Zhang, X.L., Xu, Z.S. (2015). Soft computing based on maximizing consensus and fuzzy TOPSIS approach to interval-valued intuitionistic fuzzy group decision making. Applied Soft Computing, 6, 42–56.

Biographies

Wei Guiwu
weiguiwu@163.com

G. Wei has an MSc and a PhD degree in applied mathematics from SouthWest Petroleum University, business administration from school of Economics and Management at SouthWest Jiaotong University, China, respectively. From May 2010 to April 2012, he was a postdoctoral researcher with the School of Economics and Management, Tsinghua University, Beijing, China. He is a professor in the School of Business at Sichuan Normal University. He has published more than 100 papers in journals, books and conference proceedings including journals such as Omega, Decision Support Systems, Expert Systems with Applications, Applied Soft Computing, Knowledge and Information Systems, Computers & Industrial Engineering, Knowledge-Based Systems, International Journal of Intelligent Systems, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, International Journal of Computational Intelligence Systems, Soft Computing and Information: An International Interdisciplinary Journal. He has published 1 book. He has participated in several scientific committees and serves as a reviewer in a wide range of journals including Computers & Industrial Engineering, International Journal of Information Technology and Decision Making, Knowledge-Based Systems, Information Sciences, International Journal of Computational Intelligence Systems and European Journal of Operational Research. He is currently interested in aggregation operators, decision making and computing with words.

Gao Hui

H. Gao has an MSc degree in management sciences and engineering from school of Economics and Management at University of Electronic Science and Technology of China, China. She is an associate professor in the School of Business at Sichuan Normal University.


Full article Cited by PDF XML
Full article Cited by PDF XML

Copyright
© 2018 Vilnius University
Open access article under the CC BY license.

Keywords
generalized Dice similarity measures Dice similarity measures picture fuzzy set asymmetric measures projection measures patterns recognition building material recognition

Metrics
since January 2020
2537

Article info
views

952

Full article
views

964

PDF
downloads

324

XML
downloads


Share


RSS