{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T16:16:55Z","timestamp":1771949815218,"version":"3.50.1"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2021,5,22]],"date-time":"2021-05-22T00:00:00Z","timestamp":1621641600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,5,22]],"date-time":"2021-05-22T00:00:00Z","timestamp":1621641600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Deutscher Akademischer Austauschdienst","award":["57214224"],"award-info":[{"award-number":["57214224"]}]},{"DOI":"10.13039\/501100012320","name":"Otto-von-Guericke-Universit\u00e4t Magdeburg","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100012320","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Swarm Intell"],"published-print":{"date-parts":[[2021,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Collective perception allows sparsely distributed agents to form a global view on a common spatially distributed problem without any direct access to global knowledge and only based on a combination of locally perceived information. However, the evidence gathered from the environment is often subject to spatial correlations and depends on the movements of the agents. The latter is not always easy to control and the main question is how to share and to combine the estimated information to achieve the most precise global estimate in the least possible time. The current article aims at answering this question with the help of evidence theory, also known as Dempster\u2013Shafer theory, applied to the collective perception scenario as a collective decision-making problem. We study eight most common belief combination operators to address the arising conflict between different sources of evidence in a highly dynamic multi-agent setting, driven by modulation of positive feedback. In comparison with existing approaches, such as voter models, the presented framework operates on quantitative belief assignments of the agents based on the observation time of the options according to the agents\u2019 opinions. The evaluated results on an extended benchmark set for multiple options (<jats:inline-formula><jats:alternatives><jats:tex-math>$$n&gt;2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>&gt;<\/mml:mo>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>) indicate that the proportional conflict redistribution (PCR) principle allows a collective of small size (<jats:inline-formula><jats:alternatives><jats:tex-math>$$N=20$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>N<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>20<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>), occupying <jats:inline-formula><jats:alternatives><jats:tex-math>$$3.5\\%$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mn>3.5<\/mml:mn>\n                    <mml:mo>%<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> of the surface, to successfully resolve the conflict between clustered areas of features and reach a consensus with almost <jats:inline-formula><jats:alternatives><jats:tex-math>$$100\\%$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mn>100<\/mml:mn>\n                    <mml:mo>%<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> certainty up to <jats:inline-formula><jats:alternatives><jats:tex-math>$$n=5$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>5<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s11721-021-00192-8","type":"journal-article","created":{"date-parts":[[2021,5,22]],"date-time":"2021-05-22T18:02:28Z","timestamp":1621706548000},"page":"83-110","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Multi-featured collective perception with Evidence Theory: tackling spatial correlations"],"prefix":"10.1007","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5908-8196","authenticated-orcid":false,"given":"Palina","family":"Bartashevich","sequence":"first","affiliation":[]},{"given":"Sanaz","family":"Mostaghim","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,5,22]]},"reference":[{"key":"192_CR1","doi-asserted-by":"publisher","unstructured":"Albani, D., IJsselmuiden, J., Haken, R., & Trianni, V. (2017). Monitoring and mapping with robot swarms for agricultural applications. In 2017 14th IEEE International Conference on Advanced Video and Signal Based Surveillance (AVSS), (pp. 1\u20136), https:\/\/doi.org\/10.1109\/AVSS.2017.8078478.","DOI":"10.1109\/AVSS.2017.8078478"},{"key":"192_CR2","doi-asserted-by":"publisher","unstructured":"Ali, S., Veltri, R., Epstein, J.\u00a0A., Christudass, C., & Madabhushi, A. (2013). Cell cluster graph for prediction of biochemical recurrence in prostate cancer patients from tissue microarrays. In Medical Imaging 2013: Digital Pathology, International Society for Optics and Photonics, SPIE, vol 8676, (pp. 164 \u2013 174), https:\/\/doi.org\/10.1117\/12.2008695.","DOI":"10.1117\/12.2008695"},{"key":"192_CR3","first-page":"197","volume-title":"Computational methods for a mathematical theory of evidence","author":"JA Barnett","year":"2008","unstructured":"Barnett, J. A. (2008). Computational methods for a mathematical theory of evidence (pp. 197\u2013216). Springer."},{"key":"192_CR4","doi-asserted-by":"publisher","unstructured":"Bartashevich, P., & Mostaghim, S. (2019a). Benchmarking collective perception: New task difficulty metrics for collective decision-making. In Progress in Artificial Intelligence, Springer International Publishing, (pp. 699\u2013711), https:\/\/doi.org\/10.1007\/978-3-030-30241-2_58.","DOI":"10.1007\/978-3-030-30241-2_58"},{"key":"192_CR5","doi-asserted-by":"publisher","unstructured":"Bartashevich, P., & Mostaghim, S. (2019b). Ising model as a switch voting mechanism in collective perception. In Progress in Artificial Intelligence, Springer International Publishing, Cham, (pp. 617\u2013629), https:\/\/doi.org\/10.1007\/978-3-030-30244-3_51.","DOI":"10.1007\/978-3-030-30244-3_51"},{"key":"192_CR6","doi-asserted-by":"publisher","unstructured":"Bartashevich, P., & Mostaghim, S. (2019c). Positive impact of isomorphic changes in the environment on collective decision-making. In Proceedings of the Genetic and Evolutionary Computation Conference Companion, Association for Computing Machinery, GECCO \u201919, (p. 105\u2013106), https:\/\/doi.org\/10.1145\/3319619.3321984.","DOI":"10.1145\/3319619.3321984"},{"key":"192_CR7","doi-asserted-by":"publisher","unstructured":"Berdahl A.\u00a0M., Kao A.\u00a0B., Flack A., Westley P. A.\u00a0H., Codling E.\u00a0A., Couzin I.\u00a0D., Dell A.\u00a0I., Biro D. (2018) Collective animal navigation and migratory culture: from theoretical models to empirical evidence. Philosophical Transactions of the Royal Society B: Biological Sciences 373(1746), https:\/\/doi.org\/10.1098\/rstb.2017.0009.","DOI":"10.1098\/rstb.2017.0009"},{"issue":"5","key":"192_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1371\/journal.pone.0019888","volume":"6","author":"A Campo","year":"2011","unstructured":"Campo, A., Garnier, S., D\u00e9driche, O., Zekkri, M., & Dorigo, M. (2011). Self-organized discrimination of resources. PLOS ONE, 6(5), 1\u20137. https:\/\/doi.org\/10.1371\/journal.pone.0019888.","journal-title":"PLOS ONE"},{"key":"192_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2018\/5858272","volume":"2018","author":"L Chen","year":"2018","unstructured":"Chen, L., Diao, L., & Sang, J. (2018). Weighted evidence combination rule based on evidence distance and uncertainty measure: An application in fault diagnosis. Mathematical Problems in Engineering, 2018, 1\u201310. https:\/\/doi.org\/10.1155\/2018\/5858272.","journal-title":"Mathematical Problems in Engineering"},{"key":"192_CR10","doi-asserted-by":"publisher","unstructured":"Crosscombe, M., Lawry, J., & Bartashevich, P. (2019). Evidence propagation and consensus formation in noisy environments. In Scalable Uncertainty Management, Springer International Publishing, (pp. 310\u2013323), https:\/\/doi.org\/10.1007\/978-3-030-35514-2_23.","DOI":"10.1007\/978-3-030-35514-2_23"},{"issue":"2","key":"192_CR11","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1016\/j.artint.2007.05.008","volume":"172","author":"T Den\u00e6ux","year":"2008","unstructured":"Den\u00e6ux, T. (2008). Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence. Artificial Intelligence, 172(2), 234\u2013264. https:\/\/doi.org\/10.1016\/j.artint.2007.05.008.","journal-title":"Artificial Intelligence"},{"key":"192_CR12","unstructured":"Dezert, J., Moras, J., & Pannetier, B. (2015). Environment perception using grid occupancy estimation with belief functions. In 2015 18th international conference on information fusion (Fusion), IEEE, (pp. 1070\u20131077), https:\/\/ieeexplore.ieee.org\/document\/7266677."},{"key":"192_CR13","unstructured":"Ebert, J.\u00a0T., Gauci, M., Nagpal, R. (2018). Multi-feature collective decision making in robot swarms. In Proceedings of the 17th International Conference on Autonomous Agents and Multi-Agent Systems, AAMAS \u201918, (p. 1711\u20131719), https:\/\/dl.acm.org\/doi\/10.5555\/3237383.3237953."},{"key":"192_CR14","doi-asserted-by":"publisher","unstructured":"Ebert, J.\u00a0T., Gauci, M., Mallmann-Trenn, F., & Nagpal, R. (2020). Bayes bots: Collective bayesian decision-making in decentralized robot swarms. In 2020 IEEE International Conference on Robotics and Automation (ICRA), (pp. 7186\u20137192), https:\/\/doi.org\/10.1109\/ICRA40945.2020.9196584.","DOI":"10.1109\/ICRA40945.2020.9196584"},{"key":"192_CR15","unstructured":"Florea, M. C., Dezert, J., Valin, P., Smarandache, F., & Jousselme, A.-L. (2006). Adaptative combination rule and proportional conflict redistribution rule for information fusion. ArXiv. arXiv:cs\/0604042."},{"key":"192_CR16","first-page":"255","volume-title":"Spatial autocorrelation","author":"A Getis","year":"2010","unstructured":"Getis, A. (2010). Spatial autocorrelation (pp. 255\u2013278). Berlin, Heidelberg: Springer."},{"key":"192_CR17","doi-asserted-by":"crossref","unstructured":"Goovaerts, P. (2011). Fate and transport: Geostatistics and environmental contaminants. In Encyclopedia of environmental health. Elsevier (pp. 701\u2013714).","DOI":"10.1016\/B978-0-444-52272-6.00123-9"},{"key":"192_CR18","first-page":"3109","volume-title":"Social learning in animals","author":"L Huber","year":"2012","unstructured":"Huber, L. (2012). Social learning in animals (pp. 3109\u20133113). Boston: Springer."},{"key":"192_CR19","first-page":"99","volume-title":"Context assumptions for threat assessment systems","author":"SA Israel","year":"2016","unstructured":"Israel, S. A., & Blasch, E. (2016). Context assumptions for threat assessment systems (pp. 99\u2013124). Berlin: Springer."},{"issue":"2","key":"192_CR20","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/S1566-2535(01)00026-4","volume":"2","author":"A-L Jousselme","year":"2001","unstructured":"Jousselme, A.-L., Grenier, D., & Boss\u00e9, \u00c9loi. (2001). A new distance between two bodies of evidence. Information Fusion, 2(2), 91\u2013101. https:\/\/doi.org\/10.1016\/S1566-2535(01)00026-4.","journal-title":"Information Fusion"},{"issue":"8","key":"192_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1371\/journal.pcbi.1003762","volume":"10","author":"AB Kao","year":"2014","unstructured":"Kao, A. B., Miller, N., Torney, C., Hartnett, A., & Couzin, I. D. (2014). Collective learning and optimal consensus decisions in social animal groups. PLOS Computational Biology, 10(8), 1\u201311. https:\/\/doi.org\/10.1371\/journal.pcbi.1003762.","journal-title":"PLOS Computational Biology"},{"key":"192_CR22","doi-asserted-by":"publisher","unstructured":"Ke, X., Ma, L., & Wang, Y. (2014). Some notes on canonical decomposition and separability of a belief function. In Belief functions: Theory and applications, Springer International Publishing, (pp. 153\u2013160), https:\/\/doi.org\/10.1007\/978-3-319-11191-9_17.","DOI":"10.1007\/978-3-319-11191-9_17"},{"key":"192_CR23","doi-asserted-by":"publisher","first-page":"16","DOI":"10.3389\/frobt.2019.00016","volume":"6","author":"Y Khaluf","year":"2019","unstructured":"Khaluf, Y., Simoens, P., & Hamann, H. (2019). The neglected pieces of designing collective decision-making processes. Frontiers in Robotics and AI, 6, 16. https:\/\/doi.org\/10.3389\/frobt.2019.00016.","journal-title":"Frontiers in Robotics and AI"},{"key":"192_CR24","doi-asserted-by":"publisher","unstructured":"Kirchner, A., Dambreville, F., Celeste, F., Dezert, J., & Smarandache, F. (2007). Application of probabilistic PCR5 fusion rule for multisensor target tracking. In The 10th international conference on information fusion, IEEE, (pp. 1\u20138), https:\/\/doi.org\/10.1109\/ICIF.2007.4408058.","DOI":"10.1109\/ICIF.2007.4408058"},{"issue":"1","key":"192_CR25","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/BF01440734","volume":"39","author":"J Kohlas","year":"1994","unstructured":"Kohlas, J., & Monney, P.-A. (1994). Theory of evidence -a survey of its mathematical foundations, applications and computational aspects. Zeitschrift f\u00fcr Operations Research, 39(1), 35\u201368. https:\/\/doi.org\/10.1007\/BF01440734.","journal-title":"Zeitschrift f\u00fcr Operations Research"},{"key":"192_CR26","doi-asserted-by":"crossref","unstructured":"Martin, A., & Osswald, C. (2007). Toward a combination rule to deal with partial conflict and specificity in belief functions theory. In 2007 10th international conference on information fusion (pp. 1\u20138), https:\/\/ieeexplore.ieee.org\/document\/4408007.","DOI":"10.1109\/ICIF.2007.4408007"},{"key":"192_CR27","first-page":"67","volume":"3","author":"A Martin","year":"2008","unstructured":"Martin, A., Osswald, C., Dezert, J., & Smarandache, F. (2008). General combination rules for qualitative and quantitative beliefs. Journal of Advances in Information Fusion, 3, 67\u201389.","journal-title":"Journal of Advances in Information Fusion"},{"key":"192_CR28","unstructured":"Mousavi, S.\u00a0R. (2012). Dempster-shafer theory and modified rules to determine uncertainty in mineral prospection. PhD thesis, TU Clausthal, Clausthal-Zellerfeld, http:\/\/d-nb.info\/1019265132\/34."},{"key":"192_CR29","unstructured":"Scholte, K.\u00a0A., & Norden, W.\u00a0L. (2009). Applying the PCR6 Rule of combination in real time classification systems. In 2009 12th international conference on information fusion, IEEE, (pp. 1665\u20131672), https:\/\/ieeexplore.ieee.org\/document\/5203676."},{"key":"192_CR30","volume-title":"Advances and applications of dsmt for information fusion (collected works)","author":"F Smarandache","year":"2004","unstructured":"Smarandache, F., & Dezert, J. (2004a). Advances and applications of dsmt for information fusion (collected works). USA: American Research Press."},{"key":"192_CR31","unstructured":"Smarandache F., Dezert J. (2004b) An algorithm for quasi-associative and quasi-markovian rules of combination in information fusion. ArXiv.arxiv:0408021"},{"key":"192_CR32","doi-asserted-by":"publisher","unstructured":"Smarandache, F., & Dezert, J. (2005). Information fusion based on new proportional conflict redistribution rules. In 2005 7th international conference on information fusion, IEEE, vol\u00a02, (pp. 1\u20138), https:\/\/doi.org\/10.1109\/ICIF.2005.1591955.","DOI":"10.1109\/ICIF.2005.1591955"},{"key":"192_CR33","unstructured":"Smarandache, F., & Dezert, J. (2013). On the consistency of PCR6 with the averaging rule and its application to probability estimation. In proceedings of the 16th international conference on information fusion, FUSION 2013, July 9-12, 2013, IEEE, (pp. 1119\u20131126), https:\/\/ieeexplore.ieee.org\/document\/6641121."},{"issue":"4","key":"192_CR34","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1016\/j.inffus.2006.04.003","volume":"8","author":"P Smets","year":"2007","unstructured":"Smets, P. (2007). Analyzing the combination of conflicting belief functions. Information Fusion, 8(4), 387\u2013412. https:\/\/doi.org\/10.1016\/j.inffus.2006.04.003.","journal-title":"Information Fusion"},{"key":"192_CR35","first-page":"693","volume-title":"The transferable belief model","author":"P Smets","year":"2008","unstructured":"Smets, P., & Kennes, R. (2008). The transferable belief model (pp. 693\u2013736). Berlin, Heidelberg: Springer."},{"key":"192_CR36","doi-asserted-by":"publisher","unstructured":"Soorati, M.\u00a0D., Krome, M., Mora-Mendoza, M., Ghofrani, J., & Hamann, H. (2019). Plasticity in collective decision-making for robots: Creating global reference frames, detecting dynamic environments, and preventing lock-ins. In 2019 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), (pp. 4100\u20134105), https:\/\/doi.org\/10.1109\/IROS40897.2019.8967777.","DOI":"10.1109\/IROS40897.2019.8967777"},{"key":"192_CR37","unstructured":"Strobel, V., Castell\u00f3\u00a0Ferrer, E., & Dorigo, M. (2018). Managing byzantine robots via blockchain technology in a swarm robotics collective decision making scenario. In proceedings of the 17th international conference on autonomous agents and multi-agent systems, AAMAS \u201918, (p. 541\u2013549), https:\/\/dl.acm.org\/doi\/10.5555\/3237383.3237464."},{"key":"192_CR38","doi-asserted-by":"publisher","unstructured":"Trabattoni, M., Valentini, G., & Dorigo, M. (2018). Hybrid control of swarms for resource selection. In Swarm Intelligence, Springer International Publishing, (pp. 57\u201370), https:\/\/doi.org\/10.1007\/978-3-030-00533-7_5.","DOI":"10.1007\/978-3-030-00533-7_5"},{"key":"192_CR39","doi-asserted-by":"crossref","unstructured":"Valentini, G. (2017). Achieving consensus in robot swarms: Design and analysis of strategies for the best-of-$$n$$Problem. Studies in computational intelligence, vol 706. Springer International Publishing, https:\/\/dl.acm.org\/doi\/book\/10.5555\/3092589.","DOI":"10.1007\/978-3-319-53609-5_3"},{"key":"192_CR40","doi-asserted-by":"publisher","unstructured":"Valentini, G., Brambilla, D., Hamann, H., & Dorigo, M. (2016a). Collective perception of environmental features in a robot swarm. In Swarm Intelligence, Springer International Publishing, (pp. 65\u201376), https:\/\/doi.org\/10.1007\/978-3-319-44427-7_6.","DOI":"10.1007\/978-3-319-44427-7_6"},{"issue":"3","key":"192_CR41","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1007\/s10458-015-9323-3","volume":"30","author":"G Valentini","year":"2016","unstructured":"Valentini, G., Ferrante, E., Hamann, H., & Dorigo, M. (2016b). Collective decision with 100 Kilobots: Speed versus accuracy in binary discrimination problems. Autonomous Agents and Multi-Agent Systems, 30(3), 553\u2013580. https:\/\/doi.org\/10.1007\/s10458-015-9323-3.","journal-title":"Autonomous Agents and Multi-Agent Systems"}],"container-title":["Swarm Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11721-021-00192-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11721-021-00192-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11721-021-00192-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,26]],"date-time":"2021-06-26T14:11:16Z","timestamp":1624716676000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11721-021-00192-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,22]]},"references-count":41,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["192"],"URL":"https:\/\/doi.org\/10.1007\/s11721-021-00192-8","relation":{},"ISSN":["1935-3812","1935-3820"],"issn-type":[{"value":"1935-3812","type":"print"},{"value":"1935-3820","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,22]]},"assertion":[{"value":"29 April 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 May 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}