{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T05:49:35Z","timestamp":1778824175791,"version":"3.51.4"},"reference-count":23,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,3,14]],"date-time":"2018-03-14T00:00:00Z","timestamp":1520985600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61363001"],"award-info":[{"award-number":["61363001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>As the virtual mirror of complex real-time business processes of organisations\u2019 underlying information systems, the workflow management system (WfMS) has emerged in recent decades as a new self-autonomous paradigm in the open, dynamic, distributed computing environment. In order to construct a trustworthy workflow management system (TWfMS), the design of a software behaviour trustworthiness measurement algorithm is an urgent task for researchers. Accompanying the trustworthiness mechanism, the measurement algorithm, with uncertain software behaviour trustworthiness information of the WfMS, should be resolved as an infrastructure. Based on the framework presented in our research prior to this paper, we firstly introduce a formal model for the WfMS trustworthiness measurement, with the main property reasoning based on calculus operators. Secondly, this paper proposes a novel measurement algorithm from the software behaviour entropy of calculus operators through the principle of maximum entropy (POME) and the data mining method. Thirdly, the trustworthiness measurement algorithm for incomplete software behaviour tests and runtime information is discussed and compared by means of a detailed explanation. Finally, we provide conclusions and discuss certain future research areas of the TWfMS.<\/jats:p>","DOI":"10.3390\/e20030195","type":"journal-article","created":{"date-parts":[[2018,3,15]],"date-time":"2018-03-15T05:06:43Z","timestamp":1521090403000},"page":"195","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Trustworthiness Measurement Algorithm for TWfMS Based on Software Behaviour Entropy"],"prefix":"10.3390","volume":"20","author":[{"given":"Qiang","family":"Han","sequence":"first","affiliation":[{"name":"School of Computer Science and Engineering, North Minzu University, Yinchuan 750021, China"},{"name":"Key Laboratory of Trustworthy Distributed Computing and Services (Ministry of Education), Beijing University of Posts and Telecommunications, Beijing 100871, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,14]]},"reference":[{"key":"ref_1","unstructured":"Qu, R. (2002). Case-Based Reasoning for Couse Timetabling Problems. [Ph.D. Thesis, University of Nottingham]."},{"key":"ref_2","first-page":"145","article-title":"Overview on Major Research Plan of Trustworthy Software","volume":"22","author":"Liu","year":"2008","journal-title":"Bull. Natl. Sci. Found. China"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1016\/j.compind.2010.01.001","article-title":"A workflow net similarity measure based on transition adjacency relations","volume":"61","author":"Zha","year":"2010","journal-title":"Comput. Ind."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zha, H., Wang, J., Wen, L., and Wang, C. (2009, January 7\u201311). A label-free similarity measure between workflow nets. Proceedings of the IEEE Asia-Pacific Services Computing Conference (IEEE APSCC 2009), Singapore.","DOI":"10.1109\/APSCC.2009.5394086"},{"key":"ref_5","unstructured":"M\u00fchlen, M. (2001). Workflow-based process controlling-or: What you can measure you can control. Workflow Handbook 2001, Workflow Management Coalition, Future Strategies."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ins.2015.03.055","article-title":"Cost and accuracy aware scientific workflow retrieval based on distance measure","volume":"314","author":"Ma","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_7","unstructured":"Chin, D.-M. (2005). A Definition and Measure of Workflow Modularity. [Master\u2019s Thesis, Florida International University]."},{"key":"ref_8","first-page":"54","article-title":"A new focus on process and measure: Raising data quality with a standard coding workflow and benchmarks","volume":"79","author":"Wilson","year":"2008","journal-title":"J. AHIMA"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Wang, Y., Li, M., Cao, J., Lin, X., and Tang, F. (2007, January 24\u201327). Workflow similarity measure for process clustering in grid. Proceedings of the International Conference on Fuzzy Systems and Knowledge Discovery, Haikou, China.","DOI":"10.1109\/FSKD.2007.618"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Wei, L., Handley, J., Martin, N., Sun, T., and Keogh, E. (2006, January 18\u201322). Clustering workflow requirements using compression dissimilarity measure. Proceedings of the Sixth IEEE International Conference Data Mining Workshops (ICDM Workshops), Hong Kong, China.","DOI":"10.1109\/ICDMW.2006.44"},{"key":"ref_11","unstructured":"Bo, T.K., Gundersen, M., and Berge, T.O. (2014, January 25\u201327). To measure workflow and waste: A concept for continuous improvement. Proceedings of the 22th Annual Conference of the International Group for Lean Construction (IGLC 2014), Oslo, Norway."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1109\/TSE.2007.70739","article-title":"Uncertainty Analysis in Software Reliability Modeling by Bayesian Analysis with Maximum-Entropy Principle","volume":"33","author":"Dai","year":"2007","journal-title":"IEEE Trans. Softw. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Lollai, S.A. (2017). Quality Systems. A Thermodynamics-Related Interpretive Model. Entropy, 19.","DOI":"10.3390\/e19080418"},{"key":"ref_14","first-page":"181","article-title":"Information Theory and Statistics Mechanics","volume":"106","author":"Jaynes","year":"1963","journal-title":"Stat. Phys."},{"key":"ref_15","unstructured":"Kapur, J. (1989). Maximum-Entropy Models in Science and Engineering, John Wiley & Sons."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1109\/JSYST.2009.2017397","article-title":"Towards a Conceptual Framework for Resilience Engineering","volume":"3","author":"Madni","year":"2009","journal-title":"IEEE Syst. J."},{"key":"ref_17","first-page":"47","article-title":"Research on trustworthiness measurement approaches of component based BPRAS","volume":"35","author":"Han","year":"2014","journal-title":"J. Commun."},{"key":"ref_18","unstructured":"Han, Q. (2017, January 30\u201331). TWfMS: A framework of trustworthy workflow management system. Proceedings of the International Conference on Subject-Oriented Business Process Management (S-BPM) ONE 2017, Darmstadt, Germany."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Han, Q. (2017, January 25\u201329). Resilience engineering for trustworthy workflow management system. Proceedings of the IEEE International Conference on Software Quality, Reliability and Security Companion (QRS-C), Prague, Czech Republic.","DOI":"10.1109\/QRS-C.2017.57"},{"key":"ref_20","first-page":"817","article-title":"A Software Behavior Trustworthiness Measurement Method based on Data Mining","volume":"4","author":"Yuan","year":"2011","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_21","first-page":"293","article-title":"A Data Mining Based Measurement Method for Software Trustworthiness","volume":"21","author":"Yuan","year":"2012","journal-title":"Chin. J. Electron."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4818","DOI":"10.3390\/e16094818","article-title":"A Trustworthiness Evaluation Method for Software Architectures Based on the Principle of Maximum Entropy (POME) and the Grey Decision-Making Method (GDMM)","volume":"16","author":"Rong","year":"2014","journal-title":"Entropy"},{"key":"ref_23","unstructured":"Hong, M., and Jian, L. (2016). A Software Architecture Centric Engineering Approach for Internetware, Springer."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/3\/195\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:57:07Z","timestamp":1760194627000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/3\/195"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,14]]},"references-count":23,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,3]]}},"alternative-id":["e20030195"],"URL":"https:\/\/doi.org\/10.3390\/e20030195","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,14]]}}}