{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T05:10:53Z","timestamp":1772341853214,"version":"3.50.1"},"reference-count":49,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2017,9,11]],"date-time":"2017-09-11T00:00:00Z","timestamp":1505088000000},"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>The daily fluctuation trends of a stock market are illustrated by three statuses: up, equal, and down. These can be represented by a neutrosophic set which consists of three functions\u2014truth-membership, indeterminacy-membership, and falsity-membership. In this paper, we propose a novel forecasting model based on neutrosophic set theory and the fuzzy logical relationships between the status of historical and current values. Firstly, the original time series of the stock market is converted to a fluctuation time series by comparing each piece of data with that of the previous day. The fluctuation time series is then fuzzified into a fuzzy-fluctuation time series in terms of the pre-defined up, equal, and down intervals. Next, the fuzzy logical relationships can be expressed by two neutrosophic sets according to the probabilities of different statuses for each current value and a certain range of corresponding histories. Finally, based on the neutrosophic logical relationships and the status of history, a Jaccard similarity measure is employed to find the most proper logical rule to forecast its future. The authentic Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) time series datasets are used as an example to illustrate the forecasting procedure and performance comparisons. The experimental results show that the proposed method can successfully forecast the stock market and other similar kinds of time series. We also apply the proposed method to forecast the Shanghai Stock Exchange Composite Index (SHSECI) to verify its effectiveness and universality.<\/jats:p>","DOI":"10.3390\/sym9090191","type":"journal-article","created":{"date-parts":[[2017,9,11]],"date-time":"2017-09-11T10:28:46Z","timestamp":1505125726000},"page":"191","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Forecasting Model Based on Neutrosophic Logical Relationship and Jaccard Similarity"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7335-5871","authenticated-orcid":false,"given":"Hongjun","family":"Guan","sequence":"first","affiliation":[{"name":"School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuang","family":"Guan","sequence":"additional","affiliation":[{"name":"Rensselaer Polytechnic Institute, Troy, NY 12180, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aiwu","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Management, Jiangsu University, Zhenjiang 212013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,9,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Robinson, P.M. (2003). Time Series with Long Memory, Oxford University Press.","DOI":"10.1093\/oso\/9780199257294.001.0001"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1981","DOI":"10.1016\/j.eswa.2012.10.001","article-title":"Forecasting seasonal time series with computational intelligence: On recent methods and the potential of their combinations","volume":"40","author":"Stepnicka","year":"2013","journal-title":"Expert Syst. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1109\/TPWRS.2005.846054","article-title":"Day-ahead electricity price forecasting using the wavelet transform and ARIMA models","volume":"20","author":"Conejo","year":"2005","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"987","DOI":"10.2307\/1912773","article-title":"Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation","volume":"50","author":"Engle","year":"1982","journal-title":"Econometrica"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/0304-4076(86)90063-1","article-title":"Generalized autoregressive conditional heteroscedasticity","volume":"31","author":"Bollerslev","year":"1986","journal-title":"J. Econom."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0165-0114(93)90355-L","article-title":"Forecasting enrollments with fuzzy time series\u2014Part I","volume":"54","author":"Song","year":"1993","journal-title":"Fuzzy Sets Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/0165-0114(93)90372-O","article-title":"Fuzzy time series and its models","volume":"54","author":"Song","year":"1993","journal-title":"Fuzzy Sets Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0165-0114(94)90067-1","article-title":"Forecasting enrollments with fuzzy time series\u2014Part II","volume":"62","author":"Song","year":"1994","journal-title":"Fuzzy Sets Syst."},{"key":"ref_9","first-page":"405","article-title":"Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and the probabilities of trends of fuzzy logical relationships","volume":"45","author":"Chen","year":"2015","journal-title":"IEEE Trans. Cybern."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.ins.2016.11.004","article-title":"Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups, similarity measures and PSO techniques","volume":"391\u2013392","author":"Chen","year":"2017","journal-title":"Inf. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.eswa.2017.01.049","article-title":"Improving stock index forecasts by using a new weighted fuzzy-trend time series method","volume":"76","author":"Rubio","year":"2017","journal-title":"Expert Syst. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1016\/j.asoc.2014.11.043","article-title":"A new linguistic out-sample approach of fuzzy time series for daily forecasting of Malaysian electricity load demand","volume":"28","author":"Efendi","year":"2015","journal-title":"Appl. Soft Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.ijar.2017.01.006","article-title":"Short-term load forecasting method based on fuzzy time series, seasonality and long memory process","volume":"83","author":"Sadaei","year":"2017","journal-title":"Int. J. Approx. Reason."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2121","DOI":"10.1016\/j.eswa.2014.09.036","article-title":"A high-order multi-variate fuzzy time series forecasting algorithm based on fuzzy clustering","volume":"42","author":"Askari","year":"2015","journal-title":"Expert Syst. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.jocs.2015.11.011","article-title":"Intraday stock prime forecasting based on variational mode decomposition","volume":"12","author":"Lahrimi","year":"2016","journal-title":"J. Comput. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.eswa.2016.02.025","article-title":"A variational mode decomposition approach for analysis and forecasting of economic and financial time series","volume":"55","author":"Lahrimi","year":"2016","journal-title":"Expert Syst. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Jia, J.Y., Zhao, A.W., and Guan, S. (2017). Forecasting based on high-order fuzzy-fluctuation trends and particle swarm optimization machine learning. Symmetry, 9.","DOI":"10.20944\/preprints201707.0006.v1"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/S0165-0114(00)00057-9","article-title":"Effective lengths of intervals to improve forecasting in fuzzy time series","volume":"123","author":"Huarng","year":"2001","journal-title":"Fuzzy Sets Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"15","DOI":"10.3233\/IFS-2010-0470","article-title":"A new approach based on the optimization of the length of intervals in fuzzy time series","volume":"22","author":"Egrioglu","year":"2011","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"5052","DOI":"10.1016\/j.eswa.2009.12.006","article-title":"Finding an optimal interval length in high order fuzzy time series","volume":"37","author":"Egrioglu","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5673","DOI":"10.1016\/j.eswa.2013.04.026","article-title":"Effective intervals determined by information granules to improve forecasting in fuzzy time series","volume":"40","author":"Wang","year":"2013","journal-title":"Expert Syst. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1016\/j.asoc.2008.09.002","article-title":"A new approach for determining the length of intervals for fuzzy time series","volume":"9","author":"Yolcu","year":"2009","journal-title":"Appl. Soft Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2795","DOI":"10.3233\/JIFS-169161","article-title":"A computational fuzzy time series forecasting model based on GEM-based discretization and hierarchical fuzzy logical rules","volume":"31","author":"Zhao","year":"2016","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1109\/TSMCB.2005.857093","article-title":"Ratio-based lengths of intervals to improve fuzyy time series forecasting","volume":"36","author":"Huarng","year":"2006","journal-title":"IEEE Trans. Syst. Man Cybern. Part B Cybern."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1016\/j.physa.2004.11.006","article-title":"Weighted fuzzy time series models for TAIEX forecasting","volume":"349","author":"Yu","year":"2005","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4228","DOI":"10.1016\/j.eswa.2008.04.001","article-title":"Forecasting in high order fuzzy time series by using neural networks to define fuzzy relations","volume":"36","author":"Aladag","year":"2009","journal-title":"Expert Syst. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.knosys.2014.11.003","article-title":"A new fuzzy time series forecasting model combined with ant colony optimization and auto-regression","volume":"74","author":"Cai","year":"2015","journal-title":"Knowl. Based Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4772","DOI":"10.1016\/j.ins.2010.08.026","article-title":"Multi-variable fuzzy forecasting based on fuzzy clustering and fuzzy rule interpolation techniques","volume":"180","author":"Chen","year":"2010","journal-title":"Inf. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TFUZZ.2010.2073712","article-title":"TAIEX forecasting based on fuzzy time series and fuzzy variation groups","volume":"19","author":"Chen","year":"2011","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1485","DOI":"10.1109\/TSMCA.2012.2190399","article-title":"TAIEX forecasting using fuzzy time series and automatically generated weights of multiple factors","volume":"42","author":"Chen","year":"2012","journal-title":"IEEE Trans. Syst. Man Cybern. Part A Syst. Hum."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.ins.2016.05.038","article-title":"A novel forecasting method based on multi-order fuzzy time series and technical analysis","volume":"367\u2013368","author":"Ye","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1126","DOI":"10.1016\/j.eswa.2006.12.021","article-title":"Fuzzy time-series based on adaptive expectation model for TAIEX forecasting","volume":"34","author":"Cheng","year":"2008","journal-title":"Expert Syst. Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"935815","DOI":"10.1155\/2013\/935815","article-title":"An ARMA type fuzzy time series forecasting method based on particle swarm optimization","volume":"2013","author":"Egrioglu","year":"2013","journal-title":"Math. Probl. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"128097","DOI":"10.1155\/2015\/128097","article-title":"A new high order fuzzy ARMA time series forecasting method by using neural networks to define fuzzy relations","volume":"2015","author":"Kocak","year":"2015","journal-title":"Math. Probl. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.asoc.2017.04.021","article-title":"ARMA(p,q) type high order fuzzy time series forecast method based on fuzzy logic relations","volume":"59","author":"Kocak","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_36","unstructured":"Smarandache, F. (1999). A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability, American Research Press. [2nd ed.]."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Fu, J., and Ye, J. (2017). Simplified neutrosophic exponential similarity measures for the initial evaluation\/diagnosis of benign prostatic hyperplasia symptoms. Symmetry, 9.","DOI":"10.3390\/sym9080154"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Chen, J., and Ye, J. (2017). Vector similarity measures between refined simplified neutrosophic sets and their multiple attribute decision-making method. Symmetry, 9.","DOI":"10.3390\/sym9080153"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.3233\/IFS-130810","article-title":"On similarity and entropy of neutrosophic sets","volume":"26","author":"Majumdar","year":"2014","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1016\/j.asoc.2014.08.070","article-title":"An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets","volume":"25","author":"Peng","year":"2014","journal-title":"Appl. Soft Comput."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2001","DOI":"10.1007\/s00521-014-1688-8","article-title":"Multiple attribute decision making method based on single-valued neutrosophic normalized weighted Bonferroni mean","volume":"25","author":"Liu","year":"2014","journal-title":"Neural Comput. Appl."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.cmpb.2015.10.002","article-title":"Multi-period medical diagnosis method using a single valued neutrosophic similarity measure based on tangent function","volume":"123","author":"Ye","year":"2015","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/0165-0114(95)00107-7","article-title":"A model of consensus in group decision making under linguistic assessments","volume":"79","author":"Herrera","year":"1996","journal-title":"Fuzzy Sets Syst."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/j.ins.2014.09.038","article-title":"A hybrid fuzzy time series model based on granular computing for stock price forecasting","volume":"294","author":"Chen","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1388","DOI":"10.1016\/j.asoc.2010.04.010","article-title":"A hybrid ANFIS model based on AR and volatility for TAIEX Forecasting","volume":"11","author":"Chang","year":"2011","journal-title":"Appl. Soft Comput."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1102","DOI":"10.1109\/TSMCB.2012.2223815","article-title":"Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and particle swarm optimization techniques","volume":"43","author":"Chen","year":"2013","journal-title":"IEEE Trans. Cybern."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1016\/j.econmod.2012.09.047","article-title":"OWA-based ANFIS model for TAIEX forecasting","volume":"30","author":"Cheng","year":"2013","journal-title":"Econ. Model."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2510","DOI":"10.1016\/j.asoc.2010.09.007","article-title":"Forecasting stock markets using wavelet trans-forms and recurrent neural networks: An integrated system based on artificial bee colony algorithm","volume":"11","author":"Hsieh","year":"2011","journal-title":"Appl. Soft Comput."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1080\/07350015.1995.10524599","article-title":"Comparing predictive accuracy","volume":"13","author":"Diebold","year":"1995","journal-title":"J. Bus. Econ. Stat."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/9\/191\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:44:35Z","timestamp":1760208275000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/9\/191"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,11]]},"references-count":49,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2017,9]]}},"alternative-id":["sym9090191"],"URL":"https:\/\/doi.org\/10.3390\/sym9090191","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,11]]}}}