The concept of fuzzy numbers has been generalized to intuitionistic fuzzy interval numbers (IFINs) to solve problems with imprecision in the information modeling. Similarity measure is an important tool to measure the degree of resemblance between any two objects in real-life situations and is applied in many areas such as decision making, image processing, pattern recognition, etc. In this paper, a new distance-based similarity measure between IFINs is proposed using which a similarity measure on incomplete imprecise interval information is attempted. Some properties of the proposed distance measure and similarity measure are studied using illustrative examples. The nominal decreasing and increasing properties based on the proposed distance measure and similarity measure are proved. Further, the superiority of the proposed similarity measure over familiar existing methods is shown by different numerical examples and the proposed measure is applied to technique for order preference by similarity to ideal solution method under interval-valued intuitionistic fuzzy environment. Finally, the applicability of the proposed method in pattern recognition problems is illustrated.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–356
Atanassov K, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31(3):343–349
Nayagam VLG, Muralikrishnan S, Sivaraman G (2011) Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets. Expert Syst Appl 38:1464–1467
Xu ZS, Chen J (2007) An approach to group decision making based on interval-valued intuitionistic judgement matrices. Syst Eng Theory Pract 27:126–133
Xu ZS (2007) Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making. Fuzzy Optim Decis Mak 6:109–121
Ye J (2013) Interval-valued intuitionistic fuzzy cosine similarity measures for multiple attribute decision-making. Int J Gen Syst 42(8):883–891
Chen SM, Cheng SH, Lan TC (2016) A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition. Inf Sci 343–344:15–40
Li DF, Cheng CT (2002) New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognit Lett 23:221–225
Mitchell HB (2003) On the Dengfeng–Chuntian similarity measure and its application to pattern recognition. Pattern Recognit Lett 24:3101–3104
Xu ZS (2007) On similarity measures of interval-valued intuitionistic fuzzy sets and their application to pattern recognitions. J Southeast Univ (Engl Ed) 23(1):139–143
Boran FE, Akay D (2014) A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition. Inf Sci 255:45–57
Chen SM (1995) Measures of similarity between vague sets. Fuzzy Sets Syst 74(2):217–223
Chen SM (1997) Similarity measures between vague sets and between elements. IEEE Trans Syst Man Cybern 27(1):153–158
Egghe L (2010) Good properties of similarity measures and their complementarity. J Am Soc Inf Sci Technol 61(10):2151–2160
Hong DH, Kim C (1999) A note on similarity measures between vague sets and between elements. Inf Sci 115:83–96
Hung WL, Yang MS (2004) Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recognit Lett 25:1603–1611
Hung WL, Yang MS (2007) Similarity measures of intuitionistic fuzzy sets based on Lp metric. Int J Approx Reason 46:120–136
Liang Z, Shi P (2003) Similarity measures on intuitionistic fuzzy sets. Pattern Recognit Lett 24:2687–2693
Liu W (2005) New similarity measures between intuitionistic fuzzy sets and between elements. Math Comput Model 42:61–70
Song Y, Wang X (2015) A new similarity measure between intuitionistic fuzzy sets and the positive definiteness of the similarity matrix. Pattern Anal Appl. https://doi.org/10.1007/s10044-015-0490-2
Ye J (2011) Cosine similarity measures for intuitionistic fuzzy sets and their applications. Math Comput Model 53(1–2):91–97
Wei C-P, Wang P, Zhang Y-Z (2011) Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications. Inf Sci 181:4273–4286
Szmidt E, Kacprzyk J (2000) Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst 114(3):505–518
Wang WQ, Xin XL (2005) Distance measure between intuitionistic fuzzy sets. Pattern Recognit Lett 26(13):2063–2069
Xu ZS, Chen J (2008) An overview of distance and similarity measures of intuitionistic sets. Int J Uncertain Fuzziness Knowl Based Syst 16(4):529–555
Lee W, Shen HW, Zhang G (2009) Research on fault diagnosis of turbine based on similarity measures between interval-valued intuitionistic fuzzy sets. In: IEEE international conference on measuring technology and mechatronics automation, pp 700–703
Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96
Atanassov K (1994) Operators over interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 64:159–174
Xu ZS, Chen J (2007) On geometric aggregation over interval-valued intuitionistic fuzzy information. In: Proceedings of fourth international conference on fuzzy systems and knowledge discovery (FSKD 2007), vol 2, pp 466–471
Sivaraman G, Nayagam VLG, Ponalagusamy R (2014) A complete ranking of incomplete interval information. Expert Syst Appl 41:1947–1954
Hwang CL, Yoon K (1981) Multiple attributes decision making methods and applications. Springer, Berlin
Dhanasekaran P, Jeevaraj S, Nayagam VLG (2018) A complete ranking of trapezoidal fuzzy numbers and its applications to multi-criteria decision making. Neural Comput Appl 30(11):3303–3315
Nayagam VLG, Sivaraman G (2011) Ranking of interval-valued intuitionistic fuzzy sets. Appl Soft Comput 11:3368–3372
Nayagam VLG, Jeevaraj S, Dhanasekaran P (2017) An intuitionistic fuzzy multi criteria decision making method based on non-hesitance score for interval-valued intuitionistic fuzzy sets. Soft Comput 21(23):7077–7082
Nayagam VLG, Dhanasekaran P, Jeevaraj S (2016) A complete ranking of incomplete trapezoidal information. J Intell Fuzzy Syst 30(6):3209–3225
Nayagam VLG, Jeevaraj S, Dhanasekaran P (2016) A linear ordering on the class of trapezoidal intuitionistic fuzzy numbers. Expert Syst Appl 60:269–279
Nayagam VLG, Jeevaraj S, Dhanasekaran P (2017) A new ranking principle for ordering trapezoidal intuitionistic fuzzy numbers. Complexity, Article ID 3049041, 1–24
Nayagam VLG, Jeevaraj S, Dhanasekaran P (2018) An improved ranking method for comparing trapezoidal intuitionistic fuzzy numbers and its applications to multicriteria decision making. Neural Comput Appl 30(2):671–682
Nayagam VLG, Jeevaraj S, Geetha S (2016) Total ordering for intuitionistic fuzzy numbers. Complexity 21(S2):54–66
Nayagam VLG, Jeevaraj S, Sivaraman G (2016) Complete ranking of intuitionistic fuzzy numbers. Fuzzy Inf Eng 8:237–254
Nayagam VLG, Jeevaraj S, Sivaraman G (2016) Total ordering defined on the set of all intuitionistic fuzzy numbers. J Intell Fuzzy Syst 30(4):2015–2028
Nayagam VLG, Jeevaraj S, Sivaraman G (2017) Rank Incomplete trapezoidal information. Soft Comput 21:7125–7140
Nayagam VLG, Venkateshwari G, Sivaraman G (2008) Ranking of intuitionistic fuzzy numbers. In: IEEE International conference on fuzzy systems (IEEE World Congress on Computational Intelligence 2008), pp 1971–1974
Conflict of interest
The authors declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Nayagam, V.L.G., Ponnialagan, D. & Jeevaraj, S. Similarity measure on incomplete imprecise interval information and its applications. Neural Comput & Applic 32, 3749–3761 (2020). https://doi.org/10.1007/s00521-019-04277-8
- Interval-valued intuitionistic fuzzy number
- Similarity measure
- TOPSIS method
- Pattern recognition