{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T19:31:49Z","timestamp":1767987109096,"version":"3.49.0"},"reference-count":35,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,11,28]],"date-time":"2021-11-28T00:00:00Z","timestamp":1638057600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The aim of the article is to propose a new method of valuation of a company, considering its ownership relations with other companies. For this purpose, the concept of the Shapley value from cooperative game theory is used as the basis for assessing such dependent companies. The paper presents proposals for Shapley value calculation algorithms for our model. We expand our model by discussing personal relations in addition to ownership relations and point out how intuitionistic fuzzy sets may be helpful in this context. As a result, we propose two new expanded models. In the first probabilistic model, we apply Pearson\u2019s correlation coefficient, in the second, we use a correlation coefficient between intuitionistic fuzzy sets to determine the personal relationships. Finally, we present and interpret results for a real-world economic network with 17 companies.<\/jats:p>","DOI":"10.3390\/e23121598","type":"journal-article","created":{"date-parts":[[2021,11,29]],"date-time":"2021-11-29T05:23:02Z","timestamp":1638163382000},"page":"1598","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Shapley-Based Estimation of Company Value\u2014Concept, Algorithms and Parameters"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7278-0155","authenticated-orcid":false,"given":"Jacek","family":"Mercik","sequence":"first","affiliation":[{"name":"Faculty of Finance and Management, WSB University in Wroc\u0142aw, Fabryczna 29-31, 53-609 Wroc\u0142aw, Poland"}]},{"given":"Barbara","family":"G\u0142adysz","sequence":"additional","affiliation":[{"name":"Department of Operations Research and Business Intelligence, Faculty of Management, Wroc\u0142aw University of Science and Technology, Wybrze\u017ce Wyspia\u0144skiego 27, 50-370 Wroc\u0142aw, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9243-8653","authenticated-orcid":false,"given":"Izabella","family":"Stach","sequence":"additional","affiliation":[{"name":"Department of Business Informatics and Management Engineering, Faculty of Management, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krak\u00f3w, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0619-4606","authenticated-orcid":false,"given":"Jochen","family":"Staudacher","sequence":"additional","affiliation":[{"name":"Fakult\u00e4t Informatik, Kempten University; Bahnhofstr. 61, 87435 Kempten, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,28]]},"reference":[{"key":"ref_1","first-page":"307","article-title":"A value for n-person games","volume":"Volume 28","author":"Kuhn","year":"1953","journal-title":"Contributions to the Theory of Games II, Annals of Mathematical Studies"},{"key":"ref_2","first-page":"317","article-title":"Weighted voting doesn\u2019t work: A mathematical analysis","volume":"19","author":"Banzhaf","year":"1965","journal-title":"Rutgers Law Rev."},{"key":"ref_3","first-page":"304","article-title":"One man, 3.312 votes: A mathematical analysis of the electoral college","volume":"13","author":"Banzhaf","year":"1968","journal-title":"Villanova Law Rev."},{"key":"ref_4","unstructured":"Liberman, B. (1971). Control of collectivities and the power of a collectivity to act. Social Choice, Gorden and Breach."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"40","DOI":"10.2307\/1954283","article-title":"Decision rules and individual values in constitutional choice","volume":"63","author":"Rae","year":"1969","journal-title":"Am. Political Sci. Rev."},{"key":"ref_6","unstructured":"Brams, S.J., and Lake, M. (1977, January 10\u201317). Power and satisfaction in a representative democracy. Proceedings of the Conference on Game Theory and Political Science, Hyannis, MA, USA."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/BF01753239","article-title":"A new index of power for simple n-person games","volume":"7","author":"Deegan","year":"1979","journal-title":"Int. J. Game Theory"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1111\/j.1467-9248.1982.tb00537.x","article-title":"Forming coalitions and measuring voting power","volume":"30","author":"Holler","year":"1982","journal-title":"Political Stud."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1068\/a100907","article-title":"On the measurement of power: Some reactions to Lawer","volume":"10","author":"Johnston","year":"1978","journal-title":"Environ. Plan. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/BF00435662","article-title":"Division of power in legislatures with two cohesive subgroups","volume":"3","author":"Gehrlein","year":"1986","journal-title":"Soc. Choice Welf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1006\/game.1994.1008","article-title":"The Shapley value for n-person games in generalized characteristic function form","volume":"6","author":"Nowak","year":"1994","journal-title":"Games Econ. Behav."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Holler, M., and Owen, G. (2001). Index of power for cabinet. Power Indices and Coalition Formation, Kluwer Academic Publishers.","DOI":"10.1007\/978-1-4757-6221-1"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/s00182-012-0361-7","article-title":"\u201cProcedural\u201d values for cooperative games","volume":"42","author":"Malawski","year":"2013","journal-title":"Int. J. Game Theory"},{"key":"ref_14","first-page":"75","article-title":"Sub-coalitional approach to values","volume":"Volume 10480","author":"Nguyen","year":"2017","journal-title":"Transactions on Computational Collective Intelligence XXVII"},{"key":"ref_15","first-page":"97","article-title":"Measurement of control power in corporate networks","volume":"1","author":"Stach","year":"2021","journal-title":"Oper. Res. Decis."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"787","DOI":"10.2307\/1951053","article-title":"A method of evaluating the distribution of power in a committee system","volume":"48","author":"Shapley","year":"1954","journal-title":"Am. Political Sci. Rev."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"53","DOI":"10.2307\/2981392","article-title":"The elementary statistics of majority voting","volume":"109","author":"Penrose","year":"1946","journal-title":"J. R. Stat. Soc."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1002\/nav.3800220409","article-title":"Multilinear extensions and the Banzhaf value","volume":"22","author":"Owen","year":"1975","journal-title":"Nav. Res. Logist. Q."},{"key":"ref_19","unstructured":"Straffin, P.D. (1980). Topics in the Theory of Voting, Birkh\u00e4user."},{"key":"ref_20","unstructured":"Holubiec, J.W., and Mercik, J.W. (1994). Inside Voting Procedures, Accedo Verlag."},{"key":"ref_21","unstructured":"Bergstr\u00f6m, C., and Rydquist, K. (1991). Concentration of Voting Power in Publicly-Traded Firms, Stockholm School of Economics."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Felsenthal, D.S., and Machover, M. (1998). The Measurement of Voting Power, Edward Elgar.","DOI":"10.4337\/9781840647761"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1287\/moor.2.3.225","article-title":"Graphs and cooperation in games","volume":"2","author":"Myerson","year":"1977","journal-title":"Math. Oper. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/BF01769885","article-title":"Monotonic solutions of cooperative games","volume":"14","author":"Young","year":"1985","journal-title":"Int. J. Game Theory"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","author":"Attanasov","year":"1986","journal-title":"Fuzzy Sets Syst."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Attanassov, K.T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications, Physica-Verlag, Springer.","DOI":"10.1007\/978-3-7908-1870-3_6"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/0165-0114(91)90031-K","article-title":"Correlation of intuitionistic fuzzy sets","volume":"44","author":"Gerstenkorn","year":"1991","journal-title":"Fuzzy Sets Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1142\/S0218488501000910","article-title":"Using statistical viewpoint in developing correlation of intuitionistic fuzzy sets","volume":"9","author":"Hung","year":"2001","journal-title":"Int. J. Uncertain. Fuzziness Knowl. Based Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.3233\/IFS-151824","article-title":"A new correlation measure of the intuitionistic fuzzy sets","volume":"30","author":"Liu","year":"2016","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1959","DOI":"10.3233\/JIFS-171589","article-title":"A new correlation coefficient of the intuitionistic fuzzy sets and its application","volume":"35","year":"2018","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_31","unstructured":"Staudacher, J., and Anwander, J. (2021, September 12). Using the R Package CoopGame for the Analysis, Solution and Visualization of Cooperative Games with Transferable Utility. R Vignette for Package Version 0.2.2. Available online: https:\/\/cran.r-project.org\/package=CoopGame."},{"key":"ref_32","first-page":"123","article-title":"Computing power indices for weighted voting games via dynamic programming","volume":"31","author":"Staudacher","year":"2021","journal-title":"Oper. Res. Decis."},{"key":"ref_33","first-page":"213","article-title":"The Shapley value for multigraphs","volume":"Volume 11056","author":"Nguyen","year":"2018","journal-title":"Computational Collective Intelligence. ICCCI 2018"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1007\/978-3-662-62245-2_8","article-title":"Some propositions of approaches for measuring indirect control power of firms and mutual connections in corporate shareholding structures","volume":"Volume 12330","author":"Nguyen","year":"2020","journal-title":"Transactions on Computational Collective Intelligence XXXV"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1007\/978-3-662-58464-4_7","article-title":"On measurement of control in corporate structures","volume":"Volume 11290","author":"Nguyen","year":"2018","journal-title":"Transactions on Computational Collective Intelligence XXXI"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/12\/1598\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:36:59Z","timestamp":1760168219000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/12\/1598"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,28]]},"references-count":35,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["e23121598"],"URL":"https:\/\/doi.org\/10.3390\/e23121598","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,28]]}}}