The intuitionistic fuzzy InterCriteria analysis (ICrA) is a new method for correlation analysis, which is based on the concepts of index matrices (IMs) and intuitionistic fuzzy sets (IFSs), aiming at detecting of the dependencies between pairs of rating criteria in both clear and uncertain environments. In the present paper, which is an extension of [39], our aim is to extend ICrA to multidimensional ICrA (n-D ICrA) under intuitionistic fuzzy environment for situations where the evaluations of the objects against multidimensional criteria are completely unknown and to show its efficiency through an application in identifying correlations between pairs of criteria when referred to actual data gathered through estimates of a restaurant’s kitchen staff over a three-year period in Bulgaria. We also present a comparative analysis of the correlations between the evaluated criteria of the kitchen staff, on the basis the application of the correlation methods of ICrA, Pearson (PCA), Spearman (SCA) and Kendall (KCA). The four-correlation analysis yielded very similar correlation coefficients, but only the ICrA can be applied to intuitionistic fuzzy evaluations. It is observed that considerable divergence of the ICrA results from those obtained by the other classical correlation analyzes, is only found when the input data contains mistakes.
DoaneD. and SewardL., Applied statistics in business and economics, McGraw-Hill Education, New York, USA, 2016.
2.
HongD.H. and HwangS.Y., Correlation of intuitionistic fuzzy sets in probability spaces, Fuzzy Sets and Systems75 (1995), 77–81.
3.
MendelsonE., Introduction to Mathematical Logic, NJ: D. Van Nostrand, Princeton, 1964.
4.
SzmidtE. and KacprzykJ., The Spearman and Kendall rank correlation coefficients between intuitionistic fuzzy sets, in: Proc. 7th conf. European Society for Fuzzy logic and technology. Atlantis Press, Aix-Les-Bains, France, 2011, pp. 521–528.
5.
SzmidtE. and KacprzykJ., Amount of information and its reliability in the ranking of Atanassov intuitionistic fuzzy alternatives, in: Rakus-Andersson, E., Yager, R., Ichalkaranje, N., Jain, L.C. (eds.) Recent Advances in Decision Making, SCI 222, Springer, Heidelberg, 2009, pp. 7–19.
6.
SzmidtE., KacprzykJ. and BujnowskiP., Correlation between Intuitionistic Fuzzy Sets: Some Conceptual and Numerical Extensions, in: WCCI 2012 IEEE World Congress on Computational Intelligence, Brisbane, QLD, 2012, pp. 1–7.
7.
ÇuvalcıoğluG., BurevaV. and MichalíkováA., Intercriteria analysis applied to university ranking system of Turkey, Notes on Intuitionistic Fuzzy Sets25(4) (2019), 90–97.
8.
MitchellH.B., A correlation coefficient for intuitionistic fuzzy sets, International Journal of Intelligent Systems19 (2004), 483–490.
9.
BelovskiI., PetkovT., SotirovS. and AleksandrovA., Prediction of the parameters of a Thermoelectric Battery with Neural Network, in: 9th National Conference with International Participation. Electronica 2018 – Proceedings, IEEE, 2018.
10.
AtanassovK., Intuitionistic fuzzy sets, in Proceedings of VII ITKR’s Session, Sofia, 1983 (in Bulgarian).
11.
AtanassovK., Generalized index matrices, Comptes rendus de l’Academie Bulgare des Sciences40(11) (1987), 3–10.
12.
AtanassovK., Interval-valued intuitionistic fuzzy sets, Studies in Fuzziness and Soft Computing, Springer, Cham 838, 2020.
13.
AtanassovK., Intuitionistic Fuzzy Logics, Studies in Fuzziness and Soft Computing, Springer, Cham 351, (2017), 138.
AtanassovK., SzmidtE. and KacprzykJ., On intuitionistic fuzzy pairs, Notes on Int. Fuzzy Sets19(3) (2013), 1–13.
16.
AtanassovK., Index Matrices: Towards an Augmented Matrix Calculus, Studies in Comp. Intelligence573, Springer, 2014.
17.
AtanassovK., n-Dimensional extended index matrices Part 1, Advanced Studies in Contemporary Mathematics28(2) (2018), 245–259.
18.
AtanassovK., Extended interval-valued intuitionistic fuzzy index matrices, submitted by Springer, 2019 (in press).
19.
AtanassovK., AtanassovaV. and GluhchevG., InterCriteria Analysis: ideas and problems, Notes on Intuitionistic Fuzzy Sets21(1) (2015), 81–88.
20.
AtanassovK., MavrovD. and AtanassovaV., InterCriteria decision making. A new approach for multicriteria decision making, based on index matrices and intuitionistic fuzzy sets, Issues in Intuitionistic Fuzzy Sets and Generalized Nets11 (2014), 1–8.
21.
AtanassovK., MarinovP. and AtanassovaV., InterCriteria analysis with Interval-valued Intuitionistic fuzzy evaluations, in: Cuzzocrea A., Greco S., Larsen H., Saccà D., Andreasen T., Christiansen H. (eds) Flexible Query Answering Systems. FQAS 2019, Lecture Notes in Computer Science, Springer, Cham, 11529 (2019), pp. 329–338.
22.
ZadehL., Fuzzy Sets, Information and Control8(3) (1965), 338–353.
23.
HinovN., GochevaP. and GochevV., Mathematical Modelling of Electronic Circuits with Index Matrices, in: Proceedings of the 33rd International Conference on Information Technologies (InfoTech-2019), 19–20 September 2019, Bulgaria, pp. 1–4.
24.
IkonomovN., VassilevP. and RoevaO., ICrAData – Software for InterCriteria Analysis, Int Journal Bioautomation22(1) (2018), 1–10.
25.
ZhangQ. and JiangS., Statistical Correlation of Intuitionistic Fuzzy Sets, in: Proc. of the Eighth International Conference on Machine Learning and Cybernetics, Baoding, 2009, pp. 817–821.
26.
FidanovaS. and RoevaO., Comparison of different metaheuristic algorithms based on intercriteria analysis, J Comput Appl Math340 (2018), 615–628.
27.
SotirovS., AtanassovaV., SotirovaE., et al., Application of the Intuitionistic Fuzzy InterCriteria Analysis Method with Triples to a Neural Network Preprocessing Procedure, Computational Intelligence and Neuroscience2017 (2017), 1–8.
28.
TodinovaS., MavrovD., KrumovaS., MarinovP., AtanassovaV., AtanassovK. and TanevaS., Blood plasma thermograms dataset analysis by means of InterCriteria and correlation analyses for the case of colorectal cancer, Int J Bioautomation20(1) (2016), 115–124.
29.
GerstenkornT. and MankoJ., Correlation of intuitionistic fuzzy sets, Fuzzy Sets and Systems44 (1991), 39–43.
30.
AtanassovaV. and RoevaO., Computational complexity and influence of numerical precision on the results of intercriteria analysis in the decision making process, Notes on Intuitionistic Fuzzy Sets24(3) (2018), 53–63.
31.
AtanassovaV., DoukovskaL., KacprzykJ., SotirovaE., RadevaI. and VassilevP., InterCriteria analysis of the global competitiveness reports: from efficiency-to innovation-driven economies, J Multiple-Valued Logic Soft Comput31(5– 6) (2018), 469–494.
32.
BurevaV., SotirovaE., SotirovS. and MavrovD., Application of the InterCriteria decision making method to Bulgarian universities ranking, Notes of Int. Fuzzy Sets21(2) (2018), 111–117.
33.
BurevaV., SotirovaE., AtanassovaV., AngelovaN. and AtanassovK., Intercriteria Analysis over Intuitionistic Fuzzy Data, Lecture Notes in Computer Science10665, Springer International Publishing AG (2018), 333–340.
34.
TranevaV., On 3-dimensional intuitionistic fuzzy index matrices, Notes on Intuitionistic Fuzzy Sets20(4) (2014), 59–64.
35.
TranevaV., SotirovaE., BurevaV. and AtanassovK., Aggregation operations over 3-D extended index matrices, Advanced Studies in Contemporary Mathematics25(3) (2015), 407–416.
36.
TranevaV., AtanassovK. and RangasamiP., On 3-dimensional index matrices, International Journal of Research in Science1(2) (2014), 64–68.
37.
TranevaV. and TranevS., Index Matrices as a Tool for Managerial Decision Making, Publ. House of the Union of Scientists, Bulgaria, 2017. (in Bulgarian)
38.
TranevaV. and TranevS., An Intuitionistic Fuzzy Zero Suffix Method for Solving the Transportation Problem, in: S. Fidanova (eds.), Proceeding of HPC 2019, Studies in Computational Intelligence, 2020. (in press)
39.
TranevaV. and TranevS., Intuitionistic Fuzzy InterCriteria Approach to the Assessment in a Fast Food Restaurant, in: Kahraman C., Cebi S., Cevik S., Oztaysi B., Tolga A., Sari I. (eds.) Intelligent and Fuzzy Techniques in Big Data Analytics and DecisionMaking. INFUS 2019. Advances in Intelligent Systems and Computing, 1029. Springer, Cham, 2020, pp. 589–597.
40.
TranevaV., TranevS., SzmidtE. and AtanassovK., Three Dimensional Intercriteria Analysis over Intuitionistic Fuzzy Data, in: Kacprzyk J., Szmidt E., Zadrożny S., Atanassov K., Krawczak M. (eds) Advances in Fuzzy Logic and Technology 2017. IWIFSGN 2017, EUSFLAT 2017. Advances in Intelligent Systems and Computing 643, Springer, Cham, 2017, pp. 442–449.
41.
TranevaV., TranevS., S., StoenchevM. and AtanassovK., Scaled aggregation operations over two- and three-dimensional index matrices, Soft computing22(15) (2018), 5115–5120.
42.
HungW.L. and WuJ.W., Correlation of intuitionistic fuzzy sets by centroid method, Information Sciences144 (2002), 219–225.
43.
ZengW. and LiH., Correlation coefficient of intuitionistic fuzzy sets, Journal of Industrial Engineering International3(5) (2002), 33–40.
