{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T06:09:06Z","timestamp":1768543746488,"version":"3.49.0"},"publisher-location":"Cham","reference-count":27,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319596136","type":"print"},{"value":"9783319596143","type":"electronic"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-59614-3_4","type":"book-chapter","created":{"date-parts":[[2017,10,17]],"date-time":"2017-10-17T05:02:48Z","timestamp":1508216568000},"page":"57-79","source":"Crossref","is-referenced-by-count":10,"title":["Ordered Fuzzy Numbers: Definitions and Operations"],"prefix":"10.1007","author":[{"given":"Piotr","family":"Prokopowicz","sequence":"first","affiliation":[]},{"given":"Dominik","family":"\u015al\u0229zak","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,10,18]]},"reference":[{"issue":"6","key":"4_CR1","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/s005000100155","volume":"6","author":"JJ Buckley","year":"2002","unstructured":"Buckley, J.J., Feuring, T., Hayashi, Y.: Linear systems of first order ordinary differential equations: fuzzy initial conditions. Soft Comput. 6(6), 415\u2013421 (2002)","journal-title":"Soft Comput."},{"issue":"1","key":"4_CR2","doi-asserted-by":"crossref","first-page":"47","DOI":"10.14708\/ma.v41i1.380","volume":"41","author":"A Chwastyk","year":"2013","unstructured":"Chwastyk, A., Kosi\u0144ski, W.: Fuzzy calculus with aplications. Mathematica Applicanda 41(1), 47\u201396 (2013)","journal-title":"Mathematica Applicanda"},{"key":"4_CR3","doi-asserted-by":"crossref","unstructured":"Czerniak, J.M., Dobrosielski, W., Apiecionek, \u0141., Ewald, D.: Representation of a trend in OFN during fuzzy observance of the water level from the crisis control center. In: Ganzha, M., Maciaszek, L., Paprzycki, M. (eds.) Proceedings of FedCSIS 2015. pp. 443\u2013447. IEEE, New York (2015)","DOI":"10.15439\/2015F217"},{"issue":"6","key":"4_CR4","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1080\/00207727808941724","volume":"9","author":"D Dubois","year":"1978","unstructured":"Dubois, D., Prade, H.: Operations on fuzzy numbers. Int. J. Syst. Sci. 9(6), 613\u2013626 (1978)","journal-title":"Int. J. Syst. Sci."},{"issue":"2","key":"4_CR5","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/S0165-0114(97)00080-8","volume":"90","author":"D Dubois","year":"1997","unstructured":"Dubois, D., Prade, H.: Fuzzy sets: where do we stand? where do we go? the three semantics of fuzzy sets. Fuzzy Sets Syst. 90(2), 141\u2013150 (1997)","journal-title":"Fuzzy Sets Syst."},{"issue":"1","key":"4_CR6","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/0165-0114(86)90026-6","volume":"18","author":"R Goetschel","year":"1986","unstructured":"Goetschel, R., Voxman, W.: Elementary fuzzy calculus. Fuzzy Sets Syst. 18(1), 31\u201343 (1986)","journal-title":"Fuzzy Sets Syst."},{"key":"4_CR7","doi-asserted-by":"crossref","unstructured":"Kacprzak, M., Kosi\u0144ski, W., W\u0119grzyn-Wolska, K.: Diversity of opinion evaluated by ordered fuzzy numbers. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., \u017burada, J.M. (eds.) Proceedings of ICAISC 2013, Part I. Lecture Notes in Computer Science, vol. 7894, pp. 271\u2013281. Springer, Berlin (2013)","DOI":"10.1007\/978-3-642-38658-9_25"},{"key":"4_CR8","doi-asserted-by":"crossref","unstructured":"Kaucher, E.: In: Alefeld, G., Grigorieff, R.D. (eds.) Interval Analysis in the Extended Interval Space IR, Fundamentals of Numerical Computation (Computer-Oriented Numerical Analysis), Computing Supplementum, vol.\u00a02, pp. 33\u201349. Springer, Berlin (1980)","DOI":"10.1007\/978-3-7091-8577-3_3"},{"key":"4_CR9","doi-asserted-by":"crossref","unstructured":"Kole\u015bnik, R., Prokopowicz, P., Kosi\u0144ski, W.: Fuzzy calculator \u2013 useful tool for programming with fuzzy algebra. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) Proceedings ICAISC 2004. Lecture Notes in Computer Science, vol. 3070, pp. 320\u2013325. Springer, Berlin (2004)","DOI":"10.1007\/978-3-540-24844-6_45"},{"issue":"5","key":"4_CR10","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1016\/j.engappai.2007.03.003","volume":"20","author":"W Kosi\u0144ski","year":"2007","unstructured":"Kosi\u0144ski, W.: Evolutionary algorithm determining defuzzyfication operators. Eng. Appl. AI 20(5), 619\u2013627 (2007)","journal-title":"Eng. Appl. AI"},{"key":"4_CR11","doi-asserted-by":"crossref","unstructured":"Kosi\u0144ski, W., Frischmuth, K., Wilczy\u0144ska-Sztyma, D.: A new fuzzy approach to ordinary differential equations. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., \u017burada, J.M. (eds.) Proceedings of ICAISC 2010, Part I. Lecture Notes in Computer Science, vol. 6113, pp. 120\u2013127 (2010)","DOI":"10.1007\/978-3-642-13208-7_16"},{"key":"4_CR12","doi-asserted-by":"crossref","unstructured":"Kosi\u0144ski, W., Prokopowicz, P., Kacprzak, D.: Fuzziness \u2013 representation of dynamic changes by ordered fuzzy numbers. In: Seising, R. (ed.) Views on Fuzzy Sets and Systems from Different Perspectives: Philosophy and Logic, Criticisms and Applications, Studies in Fuzziness and Soft Computing, vol. 243, pp. 485\u2013508. Springer, Berlin (2009)","DOI":"10.1007\/978-3-540-93802-6_24"},{"key":"4_CR13","doi-asserted-by":"crossref","unstructured":"Kosi\u0144ski, W., Prokopowicz, P., \u015al\u0119zak, D.: Fuzzy reals with algebraic operations: algorithmic approach. In: K\u0142opotek, M.A., Wierzcho\u0144, S.T., Michalewicz, M. (eds.) Proceedings of IIS 2002. Advances in Soft Computing, pp. 311\u2013320. Physica-Verlag (2002)","DOI":"10.1007\/978-3-7908-1777-5_33"},{"key":"4_CR14","doi-asserted-by":"crossref","unstructured":"Kosi\u0144ski, W., Prokopowicz, P., \u015al\u0119zak, D.: Calculus with fuzzy numbers. In: Bolc, L., Michalewicz, Z., Nishida, T. (eds.) Proceedings of IMTCI 2004. Lecture Notes in Computer Science, vol. 3490, pp. 21\u201328. Springer, Berlin (2004)","DOI":"10.1007\/11558637_3"},{"issue":"3","key":"4_CR15","first-page":"327","volume":"51","author":"W Kosi\u0144ski","year":"2003","unstructured":"Kosi\u0144ski, W., Prokopowicz, P., \u015al\u0119zak, D.: Ordered fuzzy numbers. Bull. Pol. Acad. Sci. Math. 51(3), 327\u2013338 (2003)","journal-title":"Bull. Pol. Acad. Sci. Math."},{"issue":"3","key":"4_CR16","first-page":"285","volume":"41","author":"W Kosi\u0144ski","year":"1993","unstructured":"Kosi\u0144ski, W., S\u0142ysz, P.: Fuzzy numbers and their quotient space with algebraic operations. Bull. Pol. Acad. Sci. Math. 41(3), 285\u2013295 (1993)","journal-title":"Bull. Pol. Acad. Sci. Math."},{"issue":"2","key":"4_CR17","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/S0165-0114(97)00136-X","volume":"91","author":"M Mares","year":"1997","unstructured":"Mares, M.: Weak arithmetics of fuzzy numbers. Fuzzy Sets Syst. 91(2), 143\u2013153 (1997)","journal-title":"Fuzzy Sets Syst."},{"key":"4_CR18","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.ins.2014.03.026","volume":"273","author":"A Marsza\u0142ek","year":"2014","unstructured":"Marsza\u0142ek, A., Burczy\u0144ski, T.: Modeling and forecasting financial time series with ordered fuzzy candlesticks. Inf. Sci. 273, 144\u2013155 (2014)","journal-title":"Inf. Sci."},{"key":"4_CR19","unstructured":"Mosak, R.D.: Banach Algebras. Chicago Lectures in Mathematics. University of Chicago Press, Chicago (1975)"},{"issue":"5","key":"4_CR20","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1093\/comjnl\/45.5.494","volume":"45","author":"BJ Oommen","year":"2002","unstructured":"Oommen, B.J., Rueda, L.G.: The efficiency of histogram-like techniques for database query optimization. Comput. J. 45(5), 494\u2013510 (2002)","journal-title":"Comput. J."},{"key":"4_CR21","doi-asserted-by":"crossref","unstructured":"Prokopowicz, P.: Flexible and simple methods of calculations on fuzzy numbers with the ordered fuzzy numbers model. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., \u017burada, J.M. (eds.) Proceedings of ICAISC 2013, Part I, Lecture Notes in Computer Science, vol. 7894, pp. 365\u2013375. Springer, Berlin (2013)","DOI":"10.1007\/978-3-642-38658-9_33"},{"key":"4_CR22","doi-asserted-by":"crossref","unstructured":"Prokopowicz, P.: Analysis of the changes in processes using the Kosi\u0144ski\u2019s fuzzy numbers. In: Ganzha, M., Maciaszek, L., Paprzycki, M. (eds.) Proceedings of FedCSIS 2016. pp. 121\u2013128. IEEE, New York (2016)","DOI":"10.15439\/2016F140"},{"issue":"3","key":"4_CR23","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1515\/bams-2016-0009","volume":"12","author":"P Prokopowicz","year":"2016","unstructured":"Prokopowicz, P., Miko\u0142ajewski, D.: Fuzzy-based computational simulations of brain functions - preliminary concept. Bio-Algorithms Med-Syst. 12(3), 99\u2013104 (2016)","journal-title":"Bio-Algorithms Med-Syst."},{"key":"4_CR24","doi-asserted-by":"crossref","unstructured":"\u015al\u0119zak, D., Synak, P., Wr\u00f3blewski, J., Borkowski, J., Toppin, G.: Rough optimizations of complex expressions in infobright\u2019s RDBMS. In: Yao, J., Yang, Y., S\u0142owi\u0144ski, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) Proceedings of RSCTC 2012. Lecture Notes in Computer Science, vol. 7413, pp. 94\u201399. Springer, Berlin (2012)","DOI":"10.1007\/978-3-642-32115-3_10"},{"issue":"1","key":"4_CR25","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/S0165-0114(00)00096-8","volume":"123","author":"M Wagenknecht","year":"2001","unstructured":"Wagenknecht, M., Hampel, R., Schneider, V.: Computational aspects of fuzzy arithmetics based on archimedean t-norms. Fuzzy Sets Syst. 123(1), 49\u201362 (2001)","journal-title":"Fuzzy Sets Syst."},{"issue":"3","key":"4_CR26","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0020-0255(75)90036-5","volume":"8","author":"LA Zadeh","year":"1975","unstructured":"Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning I. Inf. Sci. 8(3), 199\u2013249 (1975)","journal-title":"Inf. Sci."},{"issue":"1","key":"4_CR27","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0165-0114(78)90029-5","volume":"1","author":"LA Zadeh","year":"1978","unstructured":"Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1(1), 3\u201328 (1978)","journal-title":"Fuzzy Sets Syst."}],"container-title":["Studies in Fuzziness and Soft Computing","Theory and Applications of Ordered Fuzzy Numbers"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-59614-3_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,27]],"date-time":"2023-08-27T03:12:51Z","timestamp":1693105971000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-59614-3_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319596136","9783319596143"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-59614-3_4","relation":{},"ISSN":["1434-9922","1860-0808"],"issn-type":[{"value":"1434-9922","type":"print"},{"value":"1860-0808","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017]]}}}