Abstract
Likert scale is the most widely used psychometric scale for obtaining feedback. The major disadvantage of Likert scale is information distortion and information loss problem that arise due to its ordinal nature and closed format. Real-world responses are mostly inconsistent, imprecise and indeterminate depending on the customers’ emotions. To capture the responses realistically, the concept of neutrosophy (study of neutralities and indeterminacy) is used. Indeterminate Likert scale based on neutrosophy is introduced in this paper. Clustering according to customer feedback is an effective way of classifying customers and targeting them accordingly. Clustering algorithm for feedback obtained using indeterminate Likert scaling is proposed in this paper. While dealing real-world scenarios, indeterminate Likert scaling is better in capturing the responses accurately.
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References
Armstrong RL (1987) The midpoint on a five-point likert-type scale. Percept Mot Skills 64(2):359–362. https://doi.org/10.2466/pms.1987.64.2.359
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
Brown CN, Guskiewicz KM, Bleiberg J (2007) Athlete characteristics and outcome scores for computerized neuropsychological assessment: a preliminary analysis. J Athl Train 42(4):515
Cheng HD, Guo Y (2008) A new neutrosophic approach to image thresholding. New Math Nat Comput 4(03):291–308. https://doi.org/10.1142/S1793005708001082
Kandasamy I (2018a) Double-valued neutrosophic sets, their minimum spanning trees, and clustering algorithm. J Intell Syst 27(2):163–182. https://doi.org/10.1515/jisys-2016-0088
Kandasamy I (2018b) Indeterminate likert scale—sample dataset—customer feedback of restaurant. Mendeley Data, v1. https://doi.org/10.17632/ywjxpyw95w.1
Kandasamy I, Smarandache E (2016a) Multicriteria decision making using double refined indeterminacy neutrosophic cross entropy and indeterminacy based cross entropy. Appl Mech Mater 859:129–143. https://doi.org/10.4028/www.scientific.net/AMM.859.129
Kandasamy I, Smarandache F (2016b) Triple refined indeterminate neutrosophic sets for personality classification. In: 2016 IEEE Symposium Series on Computational Intelligence (SSCI). IEEE, pp 1–8. https://doi.org/10.1109/SSCI.2016.7850153
Khan Q, Liu P, Mahmood T (2018) Some generalized dice measures for double-valued neutrosophic sets and their applications. Mathematics 6(7):121. https://doi.org/10.3390/math6070121
Kiedrowski PJ (2006) Quantitative assessment of a senge learning organization intervention. Learn Organ 13(4):369–383. https://doi.org/10.1108/09696470610667742
Li Q (2013) A novel likert scale based on fuzzy sets theory. Expert Syst Appl 40(5):1609–1618. https://doi.org/10.1016/j.eswa.2012.09.015
Likert R (1932) A technique for the measurement of attitudes. Arch Psychol 22:5–55
Liu P, Li H (2017) Multiple attribute decision-making method based on some normal neutrosophic Bonferroni mean operators. Neural Comput Appl 28:179–194. https://doi.org/10.1007/s00521-015-2048-z
Liu P, 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. https://doi.org/10.1007/s00521-014-1736-4
Liu P, Teng F (2017) Multiple attribute group decision making methods based on some normal neutrosophic number Heronian mean operators. J Intell Fuzzy Syst 32(3):2375–2391. https://doi.org/10.3233/JIFS-16345
Liu P, 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. https://doi.org/10.1007/s00521-014-1688-8
Orr MG, Ohlsson S (2005) Relationship between complexity and liking as a function of expertise. Music Percept Interdiscip J 22(4):583–611. https://doi.org/10.1525/mp.2005.22.4.583
Postma TC (2007) Screening tools to prioritize routine dental care in an institutional environment. Mil Med 172(12):1287–1292
Rus CL, Chirică S, Raţiu L, Băban A (2014) Learning organization and social responsibility in Romanian higher education institutions. Procedia Soc Behav Sci 142:146–153. https://doi.org/10.1016/j.sbspro.2014.07.628
Russell CJ, Bobko P (1992) Moderated regression analysis and likert scales: too coarse for comfort. J Appl Psychol 77(3):336
Salama A, Haitham A, Manie A, Lotfy M (2014) Utilizing neutrosophic set in social network analysis e-learning systems. Int J Inf Sci Intell Syst 3(2):61–72
Sengur A, Guo Y (2011) Color texture image segmentation based on neutrosophic set and wavelet transformation. Comput Vis Image Underst 115(8):1134–1144. https://doi.org/10.1016/j.cviu.2011.04.001
Smarandache F (2000) A unifying field in logics: neutrosophic logic. Neutrosophy, neutrosophic set, probability, and statistics. American Research Press, Rehoboth. https://arxiv.org/pdf/math/0101228
Smarandache F (2013) n-valued refined neutrosophic logic and its applications in physics. Prog Phys 4:143–146
Vasantha W, Smarandache F (2003) Fuzzy cognitive maps and neutrosophic cognitive maps. Xiquan. https://arxiv.org/pdf/math/0311063
Vasantha W, Smarandache F (2004) Analysis of social aspects of migrant labourers living with HIV/AIDS using fuzzy theory and neutrosophic cognitive maps: with special reference to Rural Tamil Nadu in India. Xiquan. https://arxiv.org/pdf/math/0406304
Vasantha WB, Kandasamy I, Smarandache F (2018a) Algebraic structure of neutrosophic duplets in neutrosophic rings. Neutrsophic Sets Syst 23:85–95
Vasantha WB, Kandasamy I, Smarandache F (2018b) A classical group of neutrosophic triplet groups using Z2p. Symmetry 10(6):194. https://doi.org/10.3390/sym10060194
Vasantha WB, Kandasamy I, Smarandache F (2018c) Neutrosophic duplets of Zpn, and Zpq, and their properties. Symmetry 10(8):344. https://doi.org/10.3390/sym10080345
Wang H, Smarandache F, Zhang Y, Sunderraman R (2010) Single valued neutrosophic sets. Review p. 10. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.309.9470&rep=rep1&type=pdf
Ye J (2013) Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment. Int J Gen Syst 42(4):386–394. https://doi.org/10.1080/03081079.2012.761609
Ye J (2014a) A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. J Intell Fuzzy Syst 26(5):2459–2466. https://doi.org/10.3233/IFS-130916
Ye J (2014b) Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making. J Intell Fuzzy Syst 26(1):165–172. https://doi.org/10.3233/IFS-120724
Ye J (2014c) Single valued neutrosophic cross-entropy for multicriteria decision making problems. Appl Math Model 38(3):1170–1175. https://doi.org/10.1016/j.apm.2013.07.020
Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353
Zhang M, Zhang L, Cheng H (2010) A neutrosophic approach to image segmentation based on watershed method. Signal Process 90(5):1510–1517. https://doi.org/10.1016/j.sigpro.2009.10.021
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Kandasamy, I., Kandasamy, W.B.V., Obbineni, J.M. et al. Indeterminate Likert scale: feedback based on neutrosophy, its distance measures and clustering algorithm. Soft Comput 24, 7459–7468 (2020). https://doi.org/10.1007/s00500-019-04372-x
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DOI: https://doi.org/10.1007/s00500-019-04372-x