{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T15:12:32Z","timestamp":1762182752966,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T00:00:00Z","timestamp":1762041600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This research proposes a method based on the greatest and shortest eigen fuzzy sets of fuzzy relations to evaluate the effectiveness of policies and strategies implemented in urban settlements aimed at increasing the livability and well-being of citizens. This assessment is performed by extracting population census data collected at the beginning and end of the analyzed period and grouping them by subzone, that is, for each of the urban areas into which the urban settlement is divided. The greatest eigen fuzzy set (GEFS) and the smallest eigen fuzzy set (SEFS) are determined symmetrically as min-max and max-min solutions of fuzzy relations; they are calculated to estimate the average impact of urban strategies on generating symptoms of growth in citizen well-being during the investigated period. The method is implemented on a GIS (Geographic Information System) platform and was tested to assess the effectiveness of local policies applied between 2011 and 2021 on the growth of employment rates and educational attainment in the city of Naples (Italy), partitioned by neighborhood. Our model, unlike other fuzzy-based models for evaluating the effectiveness of actions and strategies to improve the quality of life in urban settlements, does not allow for subjective interpretations based on the knowledge or experience of different stakeholders, but relies solely on measurements over time of characteristics collected during census activities. Furthermore, it is integrated into a GIS-based platform, providing additional capabilities for identifying the urban areas where the impact of local strategies and policies has been most significant and those most critical. The test results show that the proposed framework can be a valuable tool for supporting decision makers in evaluating the effectiveness of local actions and policies aimed at improving the livability and well-being of citizens.<\/jats:p>","DOI":"10.3390\/sym17111840","type":"journal-article","created":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T13:47:58Z","timestamp":1762177678000},"page":"1840","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A New Method Based on the Symmetrical Calculus of GEFS and SEFS of Fuzzy Relations to Assess the Effectiveness of Local Policies for Increasing the Well-Being of Citizens"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9844-9513","authenticated-orcid":false,"given":"Barbara","family":"Cardone","sequence":"first","affiliation":[{"name":"Department of Architecture, University of Naples Federico II, Via Toledo 402, 80134 Napoli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5690-5384","authenticated-orcid":false,"given":"Ferdinando","family":"Di Martino","sequence":"additional","affiliation":[{"name":"Department of Architecture, University of Naples Federico II, Via Toledo 402, 80134 Napoli, Italy"},{"name":"Center for Interdepartmental Research Alberto Calza Bini, University of Naples Federico II, Via Toledo 402, 80134 Napoli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/0165-0114(78)90033-7","article-title":"Resolution of eigen fuzzy sets equation","volume":"1","author":"Sanchez","year":"1978","journal-title":"Fuzzy Sets Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/0022-247X(81)90073-1","article-title":"Eigen fuzzy sets and fuzzy relations","volume":"81","author":"Sanchez","year":"1981","journal-title":"J. Math. Anal. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/S0165-0114(86)80031-8","article-title":"On the construction of fuzzy eigen solutions in given regions","volume":"20","author":"Wagenknecht","year":"1986","journal-title":"Fuzzy Sets Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/0165-0114(95)00212-X","article-title":"Convergence, eigen fuzzy sets and stability analysis of relation matrices","volume":"81","author":"Bourke","year":"1996","journal-title":"Fuzzy Sets Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1007\/s10700-009-9059-0","article-title":"A survey on fuzzy relational equations, part I: Classification and solvability","volume":"8","author":"Li","year":"2009","journal-title":"Fuzzy Optim. Decis. Mak."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Nobuhara, H., and Hirota, K. (2003, January 27\u201330). Eigen fuzzy sets of various compositions and their application to image analysis. Proceedings of the Seventh World Multi Conference on Systemics, Cybernetics and Informatics SCI\u20192003, Orlando, FL, USA. CD Proceedings.","DOI":"10.1109\/ISP.2003.1275808"},{"key":"ref_7","unstructured":"Nobuhara, H., and Hirota, K. (2003, January 6). A solution for eigen fuzzy sets of adjoint max-min decomposition and its application to image analysis. Proceedings of the IEEE International Symposium on Intelligent Signal Processing, 2003, Budapest, Hungary."},{"key":"ref_8","unstructured":"Nobuhara, H., Hirota, K., and Bede, B. (2004, January 25\u201329). Generation of various eigen fuzzy sets by permutation fuzzy matrix and its application to image analysis. Proceedings of the 2004 IEEE International Conference on Fuzzy Systems, Budapest, Hungary."},{"key":"ref_9","unstructured":"Di Martino, F., Nobuhara, H., and Sessa, S. (2004, January 25\u201329). Eigen fuzzy sets and image information retrieval. Proceedings of the 2004 IEEE International Conference on Fuzzy Systems, Budapest, Hungary."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Pedrycz, W., Skowron, A., and Kreinovich, V. (2008). Eigen fuzzy sets and image information retrieval. Handbook of Granular Computing, Wiley.","DOI":"10.1002\/9780470724163"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2988","DOI":"10.1016\/j.ins.2005.11.008","article-title":"On various eigen fuzzy sets and their application to image reconstruction","volume":"176","author":"Nobuhara","year":"2006","journal-title":"Inf. Sci."},{"key":"ref_12","unstructured":"Nobuhara, H., Iyoda, E.M., Bede, B., and Hirota, K. (2004, January 22\u201324). A solution for generalized eigen fuzzy sets equations by genetic algorithms and its application to image analysis. Proceedings of the 2nd International IEEE Conference on \u2018Intelligent Systems\u2019, Proceedings (IEEE Cat. No.04EX791), Varna, Bulgaria."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1007\/978-3-540-73400-0_43","article-title":"A genetic algorithm based on eigen fuzzy sets for image reconstruction","volume":"Volume 4578","author":"Masulli","year":"2007","journal-title":"Applications of Fuzzy Sets Theory"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Di Martino, F., and Sessa, S. (2023). A Novel Image Similarity Measure Based on Greatest and Smallest Eigen Fuzzy Sets. Symmetry, 15.","DOI":"10.3390\/sym15051104"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/0165-0114(94)90187-2","article-title":"An application of fuzzy set theory to differentiating the effectiveness of drugs in treatment of inflammation of genital organs","volume":"68","author":"Gerstenkorn","year":"1994","journal-title":"Fuzzy Sets Syst."},{"key":"ref_16","unstructured":"Rakus-Andersson, E. (2003, January 1\u20134). An application of fuzzy numbers in eigen fuzzy set problem to differentiating the effectiveness of drugs. Proceedings of the International Conference on Fuzzy Information Processing: Theories and Applications, Beijing, China."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., and \u017burada, J.M. (2006). The greatest and the least eigen fuzzy sets in evaluation of the drug effectiveness levels. Artificial Intelligence and Soft Computing\u2014ICAISC 2006, Springer. Lecture Notes in Computer Science.","DOI":"10.1007\/11785231"},{"key":"ref_18","unstructured":"Rakus-Andersson, E. (2007). Fuzzy and rough techniques in medical diagnosis and medication. Studies in Fuzziness and Soft Computing, Springer."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"7041","DOI":"10.1007\/s00521-018-3521-2","article-title":"An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets","volume":"31","author":"Mahmood","year":"2019","journal-title":"Neural Comput. Appl."},{"key":"ref_20","first-page":"516","article-title":"Eigen spherical fuzzy sets and its application in decision making problem, Scientia Iranica","volume":"28","author":"Guleria","year":"2019","journal-title":"Sci. Iran."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Di Martino, F., and Sessa, S. (2020). Eigen Fuzzy Sets and their Application to Evaluate the Effectiveness of Actions in Decision Problems. Mathematics, 8.","DOI":"10.3390\/math8111999"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1840\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T14:19:13Z","timestamp":1762179553000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1840"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,2]]},"references-count":21,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["sym17111840"],"URL":"https:\/\/doi.org\/10.3390\/sym17111840","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,2]]}}}