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Informatica


A New Decision Making Method Using Interval-Valued Intuitionistic Fuzzy Cosine Similarity Measure Based on the Weighted Reduced Intuitionistic Fuzzy Sets
Volume 31, Issue 2 (2020), pp. 399–433
Pub. online: 27 March 2020      Type: Research Article      Open accessOpen Access
Received
1 March 2019
Accepted
1 February 2020
Published
27 March 2020

Abstract

In this paper, we develop a new flexible method for interval-valued intuitionistic fuzzy decision-making problems with cosine similarity measure. We first introduce the interval-valued intuitionistic fuzzy cosine similarity measure based on the notion of the weighted reduced intuitionistic fuzzy sets. With this cosine similarity measure, we are able to accommodate the attitudinal character of decision-makers in the similarity measuring process. We study some of its essential properties and propose the weighted interval-valued intuitionistic fuzzy cosine similarity measure.
Further, the work uses the idea of GOWA operator to develop the ordered weighted interval-valued intuitionistic fuzzy cosine similarity (OWIVIFCS) measure based on the weighted reduced intuitionistic fuzzy sets. The main advantage of the OWIVIFCS measure is that it provides a parameterized family of cosine similarity measures for interval-valued intuitionistic fuzzy sets and considers different scenarios depending on the attitude of the decision-makers. The measure is demonstrated to satisfy some essential properties, which prepare the ground for applications in different areas. In addition, we define the quasi-ordered weighted interval-valued intuitionistic fuzzy cosine similarity (quasi-OWIVIFCS) measure. It includes a wide range of particular cases such as OWIVIFCS measure, trigonometric-OWIVIFCS measure, exponential-OWIVIFCS measure, radical-OWIVIFCS measure. Finally, the study uses the OWIVIFCS measure to develop a new decision-making method to solve real-world decision problems with interval-valued intuitionistic fuzzy information. A real-life numerical example of contractor selection is also given to demonstrate the effectiveness of the developed approach in solving real-life problems.

References

 
Aggarwal, A., Khan, I. (2016). On solving Atanassov’s I-fuzzy linear programming problems: some variants of Angelov’s model. Opsearch, 53(2), 375–389.
 
Atanassov, K.T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.
 
Atanassov, K.T. (1994). Operators over interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 64(2), 159–174.
 
Atanassov, K.T., Gargov, G. (1989). Interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31(3), 343–349.
 
Atanassov, K.T., Pasi, G., Yager, R.R. (2005). Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. International Journal of System Science, 36(14), 859–868.
 
Bhattacharya, A. (1946). On a measure of divergence of two multinomial populations. Sankhya: The Indian Journal of Statistics, 7(4), 401–406.
 
Chen, H.Y., Liu, C.L., Sheng, Z.H. (2004). Induced ordered weighted harmonic averaging (IOWHA) operator and its application to combination forecasting method. Chinese Journal of Management Science, 12(5), 35–40.
 
Chiclana, F., Tapia García, J.M., del Moral, M.J., Herrera-Viedma, E. (2013). A statistical comparative study of different similarity measures of consensus in group decision making. Information Sciences, 221, 110–123.
 
De, S.K., Biswas, R., Roy, A.R. (2001). An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets and Systems, 117(2), 209–213.
 
Denfeng, L., Chuntian, C. (2002). New similarity measures of intuitionistic fuzzy sets and application to pattern recognition. Pattern Recognition Letters, 23(1–3), 221–225.
 
Del Moral, M.J., Chiclana, F., Tapia, J.M., Herrera-Viedma, E. (2018). A comparative study on consensus measures in group decision making. International Journal of Intelligent Systems, 33(8), 1624–1638.
 
Dong, Y., Zhao, S., Zhang, H., Chiclana, F., Herrera-Viedma, E. (2018). A self-management mechanism for non-cooperative behaviors in large-scale group consensus reaching processes. IEEE Transactions on Fuzzy Systems, 26(6), 3276–3288.
 
Fodor, J., Marichal, J.L., Roubens, M. (1995). Characterization of the ordered weighted averaging operators. IEEE Transactions on Fuzzy Systems, 3(2), 236–240.
 
Hong, D.H., Kim, C. (1995). A note on similarity measures between vague sets and between elements. Information Sciences, 115(1–4), 83–96.
 
Hung, W.L., Yang, M.S. (2004). Similarity measures of intuitionistic fuzzy sets based on Hausdorff distances. Pattern Recognition Letter, 25(14), 1603–1611.
 
Hung, K.C., Wang, P. (2012). A new intuitionistic fuzzy cosine similarity measures for medical pattern recognition. In: Proceedings of International Conference on Business and Information (BAI-2012), Sapporo, Japan, July 3–5, 2012, pp. 1252–1261.
 
Liang, Z., Shi, P. (2003). Similarity measures on intuitionistic fuzzy sets. Pattern Recognition Letters, 24(15), 2687–2693.
 
Liu, C., Peng, B. (2017). A method for group decision making based on interval-valued intuitionistic fuzzy geometric distance measures. Informatica, 28(3), 453–470.
 
Liu, D., Chen, X., Peng, D. (2017). Interval-valued intuitionistic fuzzy ordered weighted cosine similarity measure and its application in investment decision making. Complexity. https://doi.org/10.1155/2017/1891923.
 
Merigó, J.M. (2012). Probabilities in the OWA operator. Expert Systems with Applications, 39(13), 11456–11467.
 
Merigó, J.M., Gil-Lafuente, A.M. (2010). New decision-making techniques and their application in the selection of financial products. Information Sciences, 180(11), 2085–2094.
 
Merigó, J.M., Casanovas, M. (2011). Decision making with distance measures and induced aggregation operators. Computer and Industrial Engineering, 60(1), 66–76.
 
Merigó, J.M., Gil-Lafuente, A.M. (2011a). Fuzzy induced generalized aggregation operators and its application in multi-person decision making. Expert Systems with Applications, 38(8), 9761–9772.
 
Merigó, J.M., Gil-Lafuente, A.M. (2011b). Decision making in sport management based on OWA operator. Expert Systems with Applications, 38(8), 10408–10413.
 
Merigó, J.M., Yager, R.R. (2013). Generalized moving averages, distance measures and OWA operators. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21(4), 533–559.
 
Mitchell, H.B. (2003). On the Dengfeng-Chuntian similarity measure and its application to pattern recognition. Pattern Recognition Letters, 24(16), 3101–3104.
 
Park, D.G., Kwun, Y.C., Park, J.H., Park, Y. (2009). Correlation coefficient of interval-valued intuitionistic fuzzy sets and its application to multiple attribute group decision-making problems. Mathematical and Computer Modelling, 50(9–10), 1279–1293.
 
Salton, G., McGill, M.J. (1983). Introduction to Modern Information Retrieval. McGraw-Hill Book Company, New York.
 
Singh, P. (2012). A new method on measure of similarity between interval-valued intuitionistic fuzzy sets for pattern recognition. Journal of Applied & Computational Mathematics, 1(1), 1–5.
 
Su, W., Yang, Y., Zhang, C., Zeng, S. (2013). Intuitionistic fuzzy decision making with similarity measures and OWA operator. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21(2), 245–262.
 
Szmidt, E., Kacprzyk, J. (2013). Geometric similarity measures for intuitionistic fuzzy sets. In: Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13), pp. 840–847.
 
Ureña, R., Kou, G., Dong, Y., Chiclana, F., Herrera-Viedma, E. (2019). A review on trust propagation and opinion dynamics in social networks and group decision-making frameworks. Information Sciences, 478, 461–475.
 
Verma, R.K., Sharma, B.D. (2011). Intuitionistic fuzzy sets: some new results. Notes on intuitionistic fuzzy sets, 17(3), 1–10.
 
Verma, R.K., Sharma, B.D. (2012). On generalized intuitionistic fuzzy divergence (relative information) and their properties. Journal of Uncertain Systems, 6(4), 308–320.
 
Verma, R.K., Sharma, B.D. (2013a). A new measure of inaccuracy with its application to multi-criteria decision making under intuitionistic fuzzy environment. Journal of Intelligent and Fuzzy Systems, 27(4), 1811–1824.
 
Verma, R.K., Sharma, B.D. (2013b). Intuitionistic fuzzy Jensen-Rényi divergence: applications to multiple-attribute decision making. Informatica, 37(4), 399–409.
 
Verma, R.K., Sharma, B.D. (2013c). Exponential entropy on intuitionistic fuzzy sets. Kybernetika, 49(1), 111–127.
 
Verma, R., Merigó, J.M. (2019). Variance measures with ordered weighted aggregation operators. International Journal of Intelligent Systems, 34(6), 1184–1205.
 
Vlochos, I.K., Sergiadis, G.D. (2007). Intuitionistic fuzzy information: applications to pattern recognition. Pattern Recognition Letters, 28(2), 197–206.
 
Wei, C.P., Wang, P., Zhang, Y. (2011). Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications. Information Sciences, 181(19), 4273–4286.
 
Xu, Z. (2005). An overview of methods for determining OWA weights. International Journal of Intelligent Systems, 20(8), 843–865.
 
Xu, Z. (2007). On similarity measures of interval-valued intuitionistic fuzzy sets and their application to pattern recognition. Journal of Southeast University, 23(1), 139–143.
 
Xu, Z. (2008). An overview of distance and similarity measures of intuitionistic fuzzy sets. International Journal of Uncertainty, Fuzziness, and Knowledge-Based Systems, 16(4), 529–555.
 
Xu, Z. (2010). A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Information Sciences, 180(1), 181–190.
 
Xu, Z. (2012). Fuzzy ordered distance measures. Fuzzy Optimization and Decision Making, 11(1), 73–97.
 
Xu, Z., Chen, J. (2008). Ordered weighted distance measure. Journal of Systems Science and Systems Engineering, 17(4), 432–445.
 
Xu, Z., Da, Q.L. (2002). The ordered weighted geometric averaging operators. International Journal of Intelligent Systems, 17(7), 709–716.
 
Yager, R.R. (1988). On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transactions on Systems, Man and Cybernetics, 18(1), 183–190.
 
Yager, R.R. (1996). On the inclusion of variance in decision making under uncertainty. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 4(5), 401–409.
 
Yager, R.R. (2002). Heavy OWA operator. Fuzzy Optimization and Decision Making, 1(4), 379–397.
 
Yager, R.R. (2004). Generalized OWA aggregation operators. Fuzzy Optimization and Decision Making, 3(1), 93–107.
 
Yager, R.R. (2006). Generalizing variance to allow the inclusion of decision attitude in decision making under uncertainty. International Journal of Approximate Reasoning, 42(3), 137–158.
 
Ye, J. (2011). Cosine similarity measures for intuitionistic fuzzy sets and their applications. Mathematical and Computer Modelling, 53(1–2), 91–97.
 
Ye, J. (2012). Multicriteria decision-making method using the dice similarity measure based on the reduced interval-valued intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets. Applied Mathematical Modelling, 36(9), 4466–4472.
 
Ye, J. (2013). Interval-valued intuitionistic fuzzy cosine similarity measures for multiple attribute decision-making. International Journal of General Systems, 42(8), 883–891.
 
Yu, Y., Xu, A., Merigó, J.M., Wang, H. (2015). Hesitant fuzzy linguistic ordered weighted distance operators for group decision making. Journal of Applied Mathematics and Computing, 49(1–2), 285–308.
 
Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.
 
Zeng, S., Palacios-Marques, D., Zhu, F. (2016). A new model for interactive group decision making with intuitionistic fuzzy preference relations. Informatica, 27(4), 911–928.
 
Zeng, S., Merigó, J.M., Palacios-Marqués, D., Jin, H., Gu, F. (2017). Intuitionistic fuzzy induced ordered weighted averaging distance operator and its application to decision making. Journal of Intelligent and Fuzzy Systems, 32(1), 11–22.
 
Zhang, Q., Yao, H., Zhang, Z. (2011). Some similarity measures of interval-valued intuitionistic fuzzy sets and application to pattern recognition. Applied Mechanics and Materials, 44–47, 3888–3892.
 
Zhang, H., Dong, Y., Herrera-Viedma, E. (2018). Consensus building for the heterogeneous large-scale GDM with the individual concerns and satisfactions. IEEE Transactions on Fuzzy Systems, 26(2), 884–898.
 
Zhang, C., Chen, C., Streimikiene, D., Balezentis, T. (2019). Intuitionistic fuzzy MULTIMOORA approach for multi-criteria assessment of the energy storage technologies. Applied Soft Computing, 79, 410–423.
 
Zhao, N., Xu, Z. (2016). Entropy measures for interval-valued intuitionistic fuzzy information from a comparative perspective and their application to decision making. Informatica, 27(1), 203–228.
 
Zhou, L., Chen, H., Liu, J. (2013). Continuous ordered weighted distance measure and its application to multiple attribute group decision making. Group Decision and Negotiation, 22(4), 739–758.
 
Zhou, L., Tao, Z., Chen, H., Liu, J. (2014). Intuitionistic fuzzy ordered weighted cosine similarity measure. Group Decision and Negotiation, 23(4), 879–900.

Biographies

Verma Rajkumar
[email protected]

R. Verma received the MSc degree in mathematics from Chaudhary Charan Singh University University, Meerut (U.P.), India, in 2006, and the PhD degree in applied mathematics with a speciality in information theory and computational intelligence techniques from Jaypee Institute of Information Technology (Deemed University), Noida (U.P.), India, in 2014. He is currently a postdoctoral research fellow at the Department of Management Control and Information Systems, University of Chile, Santiago, Chile. He has authored over 45 research articles published in refereed international journals including the International Journal of Intelligent Systems, Kybernetika, Journal of Intelligent and Fuzzy Systems, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, International Journal of Machine Learning and Cybernetics, Neural Computing and Applications, Informatica. He has also authored five book chapters. He is currently interested in information measures, aggregation operators, multiple attribute group decision making, computational intelligence techniques, and computing with words.

Merigó José M.
[email protected]

J. M.Merigó (PhD 2009) is a professor at the School of Information, Systems, and Modelling at the Faculty of Engineering and Information Technology at the University of Technology, Sydney (Australia). Before joining UTS, he was a full professor at the Department of Management Control and Information Systems at the University of Chile. Previously, he was a senior research fellow at the Manchester Business School, University of Manchester (UK) and an assistant professor at the Department of Business Administration at the University of Barcelona (Spain). He holds a masters and a PhD degree in business administration from the University of Barcelona. He also holds a bachelors degree of science and of social sciences in economics and a masters degree in European business administration and business law from Lund University (Sweden).

He has published more than 400 articles in journals, books and conference proceedings. He is on the editorial board of several journals. He has also been a guest editor for several international journals, member of the scientific committee of several conferences and reviewer in a wide range of international journals. Recently (2015–2018), Clarivate Analytics (previously Thomson & Reuters) has distinguished him as a highly cited researcher in computer science. He is currently interested in decision making, aggregation operators, computational intelligence, bibliometrics and applications in business and economics.


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Copyright
© 2020 Vilnius University
Open access article under the CC BY license.

Keywords
interval-valued intuitionistic fuzzy sets weighted reduced intuitionistic fuzzy sets cosine similarity measure ordered weighted average operator multiple attribute decision-making

Funding
The first author would like to acknowledge the Postdoctoral Research Financial support from Project 3170556 provided by the Chilean Government (Conicyt) through the Fondecyt Postdoctoral Program.

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