{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T22:49:40Z","timestamp":1774306180316,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,7,10]],"date-time":"2019-07-10T00:00:00Z","timestamp":1562716800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computers"],"abstract":"<jats:p>We perform a theoretical and empirical analysis of a set of Cascading Style Sheets (CSS) document complexity metrics. The metrics are validated using a practical framework that demonstrates their viability. The theoretical analysis is performed using the Weyuker\u2019s properties\u2212a widely adopted approach to conducting empirical validations of metrics proposals. The empirical analysis is conducted using visual and statistical analysis of distribution of metric values, Cliff\u2019s delta, Chi-square and Liliefors statistical normality tests, and correlation analysis on our own dataset of CSS documents. The results show that five out of the nine metrics (56%) satisfy Weyuker\u2019s properties except for the Number of Attributes Defined per Rule Block (NADRB) metric, which satisfies six out of nine (67%) properties. In addition, the results from the statistical analysis show good statistical distribution characteristics (only the Number of Extended Rule Blocks (NERB) metric exceeds the rule-of-thumb threshold value of the Cliff\u2019s delta). The correlation between the metric values and the size of the CSS documents is insignificant, suggesting that the presented metrics are indeed complexity rather than size metrics. The practical application of the presented CSS complexity metric suite is to assess the risk of CSS documents. The proposed CSS complexity metrics suite allows identification of CSS files that require immediate attention of software maintenance personnel.<\/jats:p>","DOI":"10.3390\/computers8030054","type":"journal-article","created":{"date-parts":[[2019,7,10]],"date-time":"2019-07-10T11:56:51Z","timestamp":1562759811000},"page":"54","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Complexity Metrics Suite for Cascading Style Sheets"],"prefix":"10.3390","volume":"8","author":[{"given":"Adewole","family":"Adewumi","sequence":"first","affiliation":[{"name":"Department of Computer and Information Sciences, Covenant University, Canaanland, Ota 0123, Nigeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sanjay","family":"Misra","sequence":"additional","affiliation":[{"name":"Department of Computer and Information Sciences, Covenant University, Canaanland, Ota 0123, Nigeria"},{"name":"Department of Computer Engineering, Atilim University, 06830 Ankara, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9990-1084","authenticated-orcid":false,"given":"Robertas","family":"Dama\u0161evi\u010dius","sequence":"additional","affiliation":[{"name":"Department of Software Engineering, Kaunas University of Technology, 51368 Kaunas, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,10]]},"reference":[{"key":"ref_1","unstructured":"Pressman, R.S. (2005). Software Engineering: A Practitioner\u2019s Approach, McGraw-Hill."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Kumari, M., Misra, A., Misra, S., Sanz, L.F., Damasevicius, R., and Singh, V.B. (2019). Quantitative quality evaluation of software products by considering summary and comments entropy of a reported bug. Entropy, 21.","DOI":"10.3390\/e21010091"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Gupta, A., Suri, B., Kumar, V., Misra, S., Bla\u017eauskas, T., and Dama\u0161evi\u010dius, R. (2018). Software code smell prediction model using shannon, r\u00e9nyi and tsallis entropies. Entropy, 20.","DOI":"10.3390\/e20050372"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.5381\/jot.2016.15.1.a2","article-title":"When do software complexity metrics mean nothing?-when examined out of context","volume":"15","author":"Gil","year":"2016","journal-title":"J. Object Technol."},{"key":"ref_5","unstructured":"Wang, Y. (2003, January 20\u201320). On Cognitive Informatics. Proceedings of the Second IEEE International Conference on Cognitive Informatics (ICCI 2002), London, UK."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/s12046-011-0028-2","article-title":"An Inheritance Complexity Metric for Object Oriented Code: A Cognitive Approach","volume":"36","author":"Misra","year":"2011","journal-title":"SADHANA"},{"key":"ref_7","first-page":"1689","article-title":"Weighted Class Complexity: A Measure of Complexity for Object Oriented Systems","volume":"24","author":"Misra","year":"2008","journal-title":"J. Inf. Sci. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1109\/CJECE.2003.1532511","article-title":"A New Measure of Software Complexity based on Cognitive Weights","volume":"28","author":"Wang","year":"2003","journal-title":"Can. J. Electr. Comput. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"8782","DOI":"10.1109\/ACCESS.2018.2791344","article-title":"A suite of object oriented cognitive complexity metrics","volume":"6","author":"Misra","year":"2018","journal-title":"IEEE Access"},{"key":"ref_10","unstructured":"Halstead, M.H. (1977). Elements of Software Science, Operating, and Programming Systems Series, Elsevier."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1109\/TSE.1976.233837","article-title":"A complexity measure","volume":"4","author":"McCabe","year":"1976","journal-title":"IEEE Trans. Softw. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1109\/32.295895","article-title":"A Metrics Suite for Object Oriented Design","volume":"20","author":"Chidamber","year":"1994","journal-title":"IEEE Trans. Softw. Eng."},{"key":"ref_13","first-page":"770","article-title":"Metrics for evaluation of metaprogram complexity","volume":"7","year":"2010","journal-title":"Comput. Sci. Inf. Syst."},{"key":"ref_14","first-page":"16","article-title":"Entropy as a Measure of Quality of XML Schema Document","volume":"8","author":"Basci","year":"2011","journal-title":"Int. Arab J. Inf. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"9","DOI":"10.4316\/aece.2009.02002","article-title":"Data Complexity Metrics for XML Web Services","volume":"9","author":"Basci","year":"2009","journal-title":"Adv. Electr. Comput. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1049\/iet-sen.2010.0089","article-title":"Metrics Suite for Maintainability of XML Web Services","volume":"5","author":"Basci","year":"2011","journal-title":"IET Softw."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1145\/1384139.1384144","article-title":"Entropy Metric for XML DTD Documents","volume":"33","author":"Basci","year":"2008","journal-title":"ACM SIGSOFT Softw. Eng. Notes"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Norta, A., Gaaloul, W., Gangadharan, G., and Dam, H. (2015). Estimating the complexity of software services using an entropy based metric, 2016. Service-Oriented Computing\u2014ICSOC 2015 Workshops, Springer. Lecture Notes in Computer Science.","DOI":"10.1007\/978-3-662-50539-7"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1271","DOI":"10.2298\/CSIS140815077P","article-title":"XML schema metrics for quality evaluation","volume":"11","author":"Budimac","year":"2014","journal-title":"Comput. Sci. Inf. Syst."},{"key":"ref_20","unstructured":"Falola, O., Misra, S., Adewumi, A., and Damasevi\u010dius, R. (2017). Evaluation and comparison of metrics for XML schema languages. International Conference of the Catalan Association for Artificial Intelligence. Frontiers in Artificial Intelligence and Applications 300, IOS Press."},{"key":"ref_21","first-page":"255","article-title":"Separation of Concerns in Multi-language Specifications","volume":"13","author":"Damasevicius","year":"2002","journal-title":"Informatica"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1109\/2.803645","article-title":"Today\u2019s Style Sheet Standards: The Great Vision Blinded","volume":"32","author":"Marden","year":"1999","journal-title":"Computer"},{"key":"ref_23","unstructured":"Keller, M., and Nussbaumer, M. (2010, January 29). CSS Code Quality: A Metric for Abstractness. Proceedings of the Seventh International Conference on the Quality of Information and Communications Technology, Porto, Portugal."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Mesbah, A., and Mirshokraie, S. (2012, January 2\u20139). Automated Analysis of CSS Rules to Support Style Maintenance. Proceedings of the 34th International Conference on Software Engineering, Zurich, Switzerland.","DOI":"10.1109\/ICSE.2012.6227174"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Adewumi, A., Misra, S., and Ikhu-Omoregbe, N. (2012, January 18\u201321). Complexity Metrics for Cascading Style Sheets. Proceedings of the 12th International conference on Computational Science and Its Applications, ICCSA 2012, Salvador de Bahia, Brazil.","DOI":"10.1007\/978-3-642-31128-4_18"},{"key":"ref_26","unstructured":"Misra, S. (2006, January 11\u201315). Modified Set of Weyuker\u2019s properties. Proceedings of the IEEE (ICCI \u201806), Istanbul, Turkey."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Misra, S. (July, January 29). Weyuker\u2019s properties, language independency and object oriented metrics. Proceedings of the International Conference on Computational Science and Its Applications, ICCSA 2009, Seoul, Korea.","DOI":"10.1007\/978-3-642-02457-3_6"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1109\/32.6178","article-title":"Evaluating software complexity measure","volume":"14","author":"Weyuker","year":"1988","journal-title":"IEEE Trans. Softw. Eng."},{"key":"ref_29","first-page":"55","article-title":"An Analysis of Weyuker\u2019s Properties and Measurement Theory","volume":"76","author":"Misra","year":"2010","journal-title":"Proc. Indian Natl. Sci. Acad."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1109\/32.87287","article-title":"On Weyuker\u2019s axioms for software complexity measures","volume":"17","author":"Cherniavsky","year":"1991","journal-title":"IEEE Trans. Softw. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1007\/s10664-011-9162-z","article-title":"Calculation and optimization of thresholds for sets of software metrics","volume":"16","author":"Herbold","year":"2011","journal-title":"Empir. Softw. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Yamashita, K., Huang, C., Nagappan, M., Kamei, Y., Mockus, A., Hassan, A.E., and Ubayashi, N. (2016, January 1\u20133). Thresholds for Size and Complexity Metrics: A Case Study from the Perspective of Defect Density. Proceedings of the IEEE Int Conference on Software Quality, Reliability and Security (QRS), Vienna, Austria.","DOI":"10.1109\/QRS.2016.31"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1109\/TSE.2010.9","article-title":"A quantitative investigation of the acceptable risk levels of object-oriented metrics in open-source systems","volume":"36","author":"Shatnawi","year":"2010","journal-title":"IEEE Trans. Softw. Eng. (TSE)"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Alves, T.L., Ypma, C., and Visser, J. (2010, January 12\u201318). Deriving metric thresholds from benchmark data. Proceedings of the IEEE International Conference on Software Maintenance, Timisoara, Romania.","DOI":"10.1109\/ICSM.2010.5609747"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"486","DOI":"10.5812\/ijem.3505","article-title":"Normality tests for statistical analysis: A guide for non-statisticians","volume":"10","author":"Ghasemi","year":"2012","journal-title":"Int. J. Endocrinol. Metab."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Zhang, F., Mockus, A., Zou, Y., Khomh, F., and Hassan, A.E. (2013, January 1). How Does Context Affect the Distribution of Software Maintainability Metrics?. Proceedings of the 29th IEEE International Conference on Software Maintenance, Eindhoven, The Netherlands.","DOI":"10.1109\/ICSM.2013.46"},{"key":"ref_37","unstructured":"Sheskin, D.J. (2007). Handbook of Parametric and Nonparametric Statistical Procedures, Chapman Hall\/CRC. [4th ed.]."},{"key":"ref_38","unstructured":"Cliff, N. (1996). Ordinal Methods for Behavioral Data Analysis, Erlbaum."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.tjem.2018.08.001","article-title":"User\u2019s guide to correlation coefficients","volume":"18","author":"Akoglu","year":"2018","journal-title":"Turk. J. Emerg. Med."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"17","DOI":"10.2298\/CSIS0801017M","article-title":"Applicability of weyuker\u2019s properties on oo metrics: Some misunderstandings","volume":"5","author":"Misra","year":"2008","journal-title":"ComSIS"},{"key":"ref_41","unstructured":"He, P., Ma, Y., and Li, B. (2016). TDSelector: A Training Data Selection Method for Cross-Project Defect Prediction. arXiv."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1109\/TSE.2002.1000452","article-title":"The optimal class size for object-oriented software","volume":"28","author":"Benlarbi","year":"2002","journal-title":"IEEE Trans. Softw. Eng."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1109\/TSE.2009.32","article-title":"Examining the potentially confounding effect of class size on the associations between object-oriented metrics and change-proneness","volume":"35","author":"Zhou","year":"2009","journal-title":"IEEE Trans. Softw. Eng."},{"key":"ref_44","unstructured":"Jiarpakdee, J., Tantithamthavorn, C., and Hassan, A.E. (2019). The Impact of Correlated Metrics on the Interpretation of Defect Models. IEEE Trans.Softw. Eng."},{"key":"ref_45","unstructured":"Yin, R.K. (2002). Case Study Research: Design and Methods, SAGE Publications. [3rd ed.]."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1002\/smr.1720","article-title":"A conceptual framework of challenges and solutions for managing global software maintenance","volume":"27","author":"Ulziit","year":"2015","journal-title":"J. Softw. Evol. Proc."},{"key":"ref_47","unstructured":"Hecht, M., Tang, D., Hecht, H., and Brill, R.W. (1997, January 16\u201319). Quantitative reliability and availability assessment for critical systems including software. Proceedings of the COMPASS \u201997, Annual Conference on Computer Assurance, Gaithersburg, MD, USA."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Li, L., Lu, M., and Gu, T. (2018, January 17\u201319). A systematic modeling approach for failure indicators of complex software-intensive systems. Proceedings of the 12th International Conference on Reliability, Maintainability, and Safety, ICRMSS, Shanghai, China.","DOI":"10.1109\/ICRMS.2018.00019"}],"container-title":["Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-431X\/8\/3\/54\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:04:23Z","timestamp":1760187863000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-431X\/8\/3\/54"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,10]]},"references-count":48,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,9]]}},"alternative-id":["computers8030054"],"URL":"https:\/\/doi.org\/10.3390\/computers8030054","relation":{},"ISSN":["2073-431X"],"issn-type":[{"value":"2073-431X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,10]]}}}