{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:11:21Z","timestamp":1760227881685,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,4,30]],"date-time":"2022-04-30T00:00:00Z","timestamp":1651276800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003819","name":"Natural Science Foundation of Hubei Province","doi-asserted-by":"publisher","award":["2019CFB782"],"award-info":[{"award-number":["2019CFB782"]}],"id":[{"id":"10.13039\/501100003819","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Completeness is one of the basic assumptions about the rational preference relation in classical decision theory. Strongly and weakly consistent preferences are presented by abandoning the completeness of the rational preference relation. Some expansion and contraction conditions are proposed and the relationships between these conditions of rationality are discussed. The relationships between the conditions of rationality and boundedly rational choice behavior based on strongly and weakly consistent preferences are analyzed and discussed. Furthermore, an example about the choices of chocolates with interval ordinal numbers is given to explain some of the main conclusions in this paper. The results can be used as references for the study of boundedly rational decisions.<\/jats:p>","DOI":"10.3390\/sym14050918","type":"journal-article","created":{"date-parts":[[2022,5,4]],"date-time":"2022-05-04T08:21:25Z","timestamp":1651652485000},"page":"918","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Boundedly Rational Decision-Making Model Based on Weakly Consistent Preference Relations"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1716-156X","authenticated-orcid":false,"given":"Xinlin","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Hubei University of Education, Wuhan 430205, China"},{"name":"Institute of Big Data Modeling and Intelligent Computing, Hubei University of Education, Wuhan 430205, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiyan","family":"Xiao","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hubei University of Education, Wuhan 430205, China"},{"name":"Institute of Big Data Modeling and Intelligent Computing, Hubei University of Education, Wuhan 430205, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"61","DOI":"10.2307\/2548836","article-title":"A note on the pure theory of consumer\u2019s behaviour","volume":"5","author":"Samuelson","year":"1938","journal-title":"Economica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"121","DOI":"10.2307\/2550390","article-title":"Rational choice functions and orderings","volume":"26","author":"Arrow","year":"1959","journal-title":"Economica"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"635","DOI":"10.2307\/1909773","article-title":"Revealed preference theory","volume":"34","author":"Richter","year":"1966","journal-title":"Econometrica"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"307","DOI":"10.2307\/2296384","article-title":"Choice functions and revealed preference","volume":"38","author":"Sen","year":"1971","journal-title":"Rev. Econ. Stud."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1037\/h0031207","article-title":"Reversals of preference between bids and choice in gambling decisions","volume":"89","author":"Lichtenstein","year":"1971","journal-title":"J. Exp. Psychol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"263","DOI":"10.2307\/1914185","article-title":"Prospect theory: An analysis of decision making under risk","volume":"47","author":"Kahneman","year":"1979","journal-title":"Econometrica"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"99","DOI":"10.2307\/1884852","article-title":"A behavioral model of rational choice","volume":"69","author":"Simon","year":"1955","journal-title":"Q. J. Econ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/s102030200006","article-title":"Knightian decision theory. Part I","volume":"25","author":"Bewley","year":"2002","journal-title":"Decis. Econ. Financ."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1016\/j.jet.2015.02.002","article-title":"Variational Bewley preferences","volume":"157","author":"Faro","year":"2015","journal-title":"J. Econ. Theory"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.econlet.2017.07.031","article-title":"A taxonomy of rationalization by incomplete preferences","volume":"159","author":"Barokas","year":"2017","journal-title":"Econ. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/j.jet.2019.03.002","article-title":"Revealed preferences under uncertainty: Incomplete preferences and preferences for randomization","volume":"181","author":"Cettolin","year":"2019","journal-title":"J. Econ. Theory"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s00199-015-0869-8","article-title":"Partially dominant choice","volume":"61","author":"Gerasimou","year":"2016","journal-title":"Econ. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/s40505-017-0113-8","article-title":"Partially dominant choice with transitive preferences","volume":"5","author":"Qin","year":"2017","journal-title":"Econ. Theory Bull."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.econlet.2017.12.037","article-title":"On the indifference relation in Bewley preferences","volume":"164","author":"Gerasimou","year":"2018","journal-title":"Econ. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1257\/aer.20111046","article-title":"Revealed (P)reference theory","volume":"105","author":"Ok","year":"2015","journal-title":"Am. Econ. Rev."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.mathsocsci.2014.12.006","article-title":"Sequential rationalization of multivalued choice","volume":"74","author":"Alcantud","year":"2015","journal-title":"Math. Soc. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.jmp.2015.12.006","article-title":"(m, n)-rationalizable choices","volume":"73","author":"Cantone","year":"2016","journal-title":"J. Math. Psychol."},{"key":"ref_18","first-page":"1911","article-title":"Rationalizability of choice functions: Domain Conditions","volume":"37","author":"Pal","year":"2017","journal-title":"Econ. Bull."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1007\/s11238-017-9634-8","article-title":"This or that? Sequential rationalization of indecisive choice behaviour","volume":"84","author":"Kops","year":"2018","journal-title":"Theory Decis."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.geb.2020.07.003","article-title":"Rationalizable choice functions","volume":"123","author":"Yang","year":"2020","journal-title":"Games Econ. Behav."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.jet.2007.01.019","article-title":"Cognitive constraints, contraction consistency, and the satisficing criterion","volume":"138","author":"Tyson","year":"2008","journal-title":"J. Econ. Theory"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1007\/s00199-017-1043-2","article-title":"Rationalizability of menu preferences","volume":"65","author":"Tyson","year":"2018","journal-title":"Econ. Theory"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s00199-018-1157-1","article-title":"Rational preference and rationalizable choice","volume":"69","author":"Giarlotta","year":"2020","journal-title":"Econ. Theory"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.mathsocsci.2020.01.003","article-title":"Weak pseudo-rationalizability","volume":"104","author":"Stewart","year":"2020","journal-title":"Math. Soc. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"102439","DOI":"10.1016\/j.jmp.2020.102439","article-title":"A hyper-relation characterization of weak pseudo-rationalizability","volume":"99","author":"Stewart","year":"2020","journal-title":"J. Math. Psychol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1002\/mar.20269","article-title":"Testing the boundaries of the choice overload phenomenon: The effect of number of options and time pressure on decision difficulty and satisfaction","volume":"26","author":"Haynes","year":"2009","journal-title":"Psychol. Mark."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1037\/0022-3514.79.6.995","article-title":"When choice is demotivating: Can one desire too much of a good thing?","volume":"79","author":"Iyengar","year":"2000","journal-title":"J. Personal. Soc. Psychol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1037\/0003-066X.58.9.697","article-title":"A perspective on judgment and choice: Mapping bounded rationality","volume":"58","author":"Kahneman","year":"2003","journal-title":"Am. Psychol."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Augier, M., and March, J.G. (2004). Is bounded rationality unboundedly rational? Some ruminations. Models of a Man: Essays in Memory of Simon H A, MIT Press.","DOI":"10.7551\/mitpress\/4709.001.0001"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1111\/j.1756-8765.2010.01094.x","article-title":"Moral satisficing: Rethinking moral behavior as bounded rationality","volume":"2","author":"Gigerenzer","year":"2010","journal-title":"Top. Cogn. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Rubinstein, A. (1998). Modelling Bounded Rationality, MIT Press.","DOI":"10.7551\/mitpress\/4702.001.0001"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1002\/sres.2120","article-title":"Retracted: Intrinsic preferences, revealed preferences and bounded rational decisions","volume":"33","author":"Zhao","year":"2016","journal-title":"Syst. Res. Behav. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.knosys.2017.12.010","article-title":"On priority weights and consistency for incomplete hesitant fuzzy preference relations","volume":"143","author":"Zhang","year":"2018","journal-title":"Knowl.-Based Syst."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Zhang, Z., and Li, Z.L. (IEEE Trans. Syst. Man Cybern. Syst., 2022). Personalized individual semantics-based consistency control and consensus reaching in linguistic group decision making, IEEE Trans. Syst. Man Cybern. Syst., in press.","DOI":"10.1109\/TSMC.2021.3129510"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Wang, J., Rao, C.J., Goh, M., and Xiao, X.P. (Artif. Intell. Rev., 2022). Risk assessment of coronary heart disease based on cloud-random forest, Artif. Intell. Rev., in press.","DOI":"10.1007\/s10462-022-10170-z"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/918\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:04:51Z","timestamp":1760137491000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/918"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,30]]},"references-count":35,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["sym14050918"],"URL":"https:\/\/doi.org\/10.3390\/sym14050918","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,4,30]]}}}