{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T01:05:52Z","timestamp":1722992752725},"reference-count":29,"publisher":"Fuji Technology Press Ltd.","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Adv. Comput. Intell. Intell. Inform.","JACIII"],"published-print":{"date-parts":[[2009,9,20]]},"abstract":"In this paper, we will discuss interval-valued and intuitionistic fuzzy sets as a model for grayscale images, taking into account the uncertainty regarding the measured grayscale values, which in some cases is also related to the uncertainty regarding the spatial position of an object in an image. We will demonstrate the practical potential of this image model by introducing an interval-valued morphological theory and by illustrating its application with some examples. The results show that the uncertainty that is present during the image capture not only can be modelled, but can also be propagated such that the information regarding the uncertainty is never lost.<\/jats:p>","DOI":"10.20965\/jaciii.2009.p0529","type":"journal-article","created":{"date-parts":[[2016,4,14]],"date-time":"2016-04-14T06:08:34Z","timestamp":1460614114000},"page":"529-536","source":"Crossref","is-referenced-by-count":3,"title":["Modelling Numerical and Spatial Uncertainty in GrayscaleImage Capture Using Fuzzy Set Theory"],"prefix":"10.20965","volume":"13","author":[{"given":"Mike","family":"Nachtegae","sequence":"first","affiliation":[]},{"name":"Dept. of Applied Mathematics and Computer Science, Ghent University, Fuzziness and Uncertainty Modelling Research Unit","sequence":"first","affiliation":[]},{"given":"Peter","family":"Sussner","sequence":"additional","affiliation":[]},{"given":"Tom","family":"M\u00e9lange","sequence":"additional","affiliation":[]},{"given":"Etienne E.","family":"Kerre","sequence":"additional","affiliation":[]},{"name":"Dept. of Applied Mathematics, University of Campinas, Campinas, SP 13083 859, Brazil","sequence":"additional","affiliation":[]}],"member":"8550","published-online":{"date-parts":[[2009,9,20]]},"reference":[{"key":"key-10.20965\/jaciii.2009.p0529-1","doi-asserted-by":"crossref","unstructured":"L. Zadeh, \u201cFuzzy Sets,\u201d in: Information Control, Vol.8, pp. 338-353, 1965.","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"key-10.20965\/jaciii.2009.p0529-2","doi-asserted-by":"crossref","unstructured":"S. Schulte, M. Nachtegael, V. DeWitte, D. Van der Weken, and E. E. Kerre, \u201cFuzzy impulse noise reduction methods for color images,\u201d in: Proc. of FUZZY DAYS 2006 (Int. Conf. on Computational Intelligence), Dortmund (Germany), pp. 711-720.","DOI":"10.1007\/3-540-34783-6_69"},{"key":"key-10.20965\/jaciii.2009.p0529-3","doi-asserted-by":"crossref","unstructured":"S. Schulte, V. De Witte, M. Nachtegael, T. M\u00e9lange, and E. E. Kerre, \u201cA new fuzzy additive noise reduction method,\u201d in: Lecture Notes in Computer Science, Vol.4633 (Image Analysis and Recognition \u2014 Proc. of ICIAR 2007), pp. 12-23, 2007, ISBN 978-3-540-74258-6.","DOI":"10.1007\/978-3-540-74260-9_2"},{"key":"key-10.20965\/jaciii.2009.p0529-4","doi-asserted-by":"crossref","unstructured":"E. Vansteenkiste, D. Van der Weken, W. Philips, and E. E. Kerre, \u201cEvaluation of the perceptual performance of fuzzy image quality measures,\u201d in: Lecture Notes in Computer Science, Vol.4251, pp. 623-630, 2006.","DOI":"10.1007\/11892960_75"},{"key":"key-10.20965\/jaciii.2009.p0529-5","unstructured":"J. Serra, \u201cImage analysis and mathematical morphology,\u201d Academic Press Inc, London, 1982."},{"key":"key-10.20965\/jaciii.2009.p0529-6","doi-asserted-by":"crossref","unstructured":"B. De Baets, \u201cFuzzy morphology: a logical approach,\u201d in: B. M. Ayyub and M. M. Gupta (Eds.), Uncertainty Analysis in Engineering and Sciences: Fuzzy Logic, Statistics, and Neural Network Approach, Kluwer Academic Publishers, Boston, pp. 53-67, 1997.","DOI":"10.1007\/978-1-4615-5473-8_4"},{"key":"key-10.20965\/jaciii.2009.p0529-7","doi-asserted-by":"crossref","unstructured":"M. Nachtegael and E. E. Kerre, \u201cConnections between binary, grayscale and fuzzy mathematical morphologies,\u201d in: Fuzzy Sets and Systems, Vol.124, No.1, pp. 73-86, 2001.","DOI":"10.1016\/S0165-0114(01)00013-6"},{"key":"key-10.20965\/jaciii.2009.p0529-8","doi-asserted-by":"crossref","unstructured":"P. Sussner and M. E. Valle, \u201cClassification of Fuzzy Mathematical Morphologies Based on Concepts of Inclusion Measure and Duality,\u201d in: Journal of Mathematical Imaging and Vision, accepted for publication, 2008.","DOI":"10.1007\/s10851-008-0094-1"},{"key":"key-10.20965\/jaciii.2009.p0529-9","unstructured":"I. Bloch, \u201cMathematical Morphology on Bipolar Fuzzy Sets,\u201d in: Proc. of ISMM 2007 (Int. Symposium on Mathematical Morphology), pp. 3-4, 2007."},{"key":"key-10.20965\/jaciii.2009.p0529-10","doi-asserted-by":"crossref","unstructured":"I. Bloch, \u201cDilation and Erosion of Spatial Bipolar Fuzzy Sets,\u201d in: Lecture Notes in Artificial Intelligence, Vol.4578 (Proc. of WILF 2007), pp. 385-393, 2007.","DOI":"10.1007\/978-3-540-73400-0_49"},{"key":"key-10.20965\/jaciii.2009.p0529-11","unstructured":"M. Nachtegael, P. Sussner, T. M\u00e9lange, and E. E. Kerre, \u201cSome Aspects of Interval-valued and Intuitionistic Fuzzy Mathematical Morphology,\u201d accepted for IPCV 2008 \u2014 Int. Conf. on Image Processing, Computer Vision and Pattern Recognition (July 14-17, 2008, Las Vegas, US)."},{"key":"key-10.20965\/jaciii.2009.p0529-12","doi-asserted-by":"crossref","unstructured":"M. Nachtegael, P. Sussner, T. M\u00e9lange, and E. E. Kerre, \u201cAn Interval-valued Fuzzy Morphological Model based on Lukasiewicz-Operators,\u201d accepted for ACIVS 2008 \u2014 Int. Conf. on Advanced Concepts for Intelligent Vision Systems (October 21-24, 2008, Juan-les-Pins, France).","DOI":"10.1007\/978-3-540-88458-3_54"},{"key":"key-10.20965\/jaciii.2009.p0529-13","doi-asserted-by":"crossref","unstructured":"J. M. Mendel, \u201cComputing With Words: Zadeh, Turing, Popper and Occam,\u201d in: IEEE Computational Intelligence Magazine, Vol.2, No.4, pp. 10-17, 2007.","DOI":"10.1109\/MCI.2007.9066897"},{"key":"key-10.20965\/jaciii.2009.p0529-14","doi-asserted-by":"crossref","unstructured":"O. Castillo and P. Melin, \u201cIntelligent Systems with Interval Type-2 Fuzzy Logic,\u201d in: Int. Journal of Innovative Computing, Information and Control, Vol.4, No.4, pp. 771-783, 2008.","DOI":"10.1002\/9780470724163.ch26"},{"key":"key-10.20965\/jaciii.2009.p0529-15","doi-asserted-by":"crossref","unstructured":"G. Deschrijver and E. E. Kerre, \u201cOn the Relationship Between some Extensions of Fuzzy Set Theory,\u201d in: Fuzzy Sets and Systems, Vol.133, pp. 227-235, 2003.","DOI":"10.1016\/S0165-0114(02)00127-6"},{"key":"key-10.20965\/jaciii.2009.p0529-16","doi-asserted-by":"crossref","unstructured":"I. B. Turksen and Z. Zhong, \u201cAn Approximate Analogical Reasoning Schema based on Similarity Measures and Interval-Valued Fuzzy Sets,\u201d in: Fuzzy Sets and Systems, Vol.34, No.3, pp. 323-346, 1990.","DOI":"10.1016\/0165-0114(90)90218-U"},{"key":"key-10.20965\/jaciii.2009.p0529-17","unstructured":"S. D. Cabrera, K. Iyer, G. Xiang, and V. Kreinovich, \u201cOn Inverse Halftoning: Computational Complexity and Interval Computations,\u201d in: Proc. of CISS 2005 (39th Conf. on Information Sciences and Systems), The John Hopkins University, paper 164, 2005."},{"key":"key-10.20965\/jaciii.2009.p0529-18","doi-asserted-by":"crossref","unstructured":"A. E. Brito and O. Kosheleva, \u201cInterval + Image =Wavelet: For Image Processing under Interval Uncertainty, Wavelets are Optimal,\u201d in: Reliable Computing, Vol.4, No.3, pp. 291-301, 1998.","DOI":"10.1023\/A:1009959714229"},{"key":"key-10.20965\/jaciii.2009.p0529-19","unstructured":"E. Barrenechea, \u201cImage Processing with interval-valued Fuzzy Sets- Edge Detection - Contrast,\u201d Ph.D. thesis, Public University of Navarra, 2005."},{"key":"key-10.20965\/jaciii.2009.p0529-20","doi-asserted-by":"crossref","unstructured":"K. Atanassov, \u201cIntuitionistic Fuzzy Sets,\u201d Physica Verlag, Heidelberg (Germany), 1999.","DOI":"10.1007\/978-3-7908-1870-3"},{"key":"key-10.20965\/jaciii.2009.p0529-21","doi-asserted-by":"crossref","unstructured":"I. K. Vlachos and D. G. Sergiadis, \u201cTowards Intuitionistic Fuzzy Image Processing,\u201d in: Proc. of the Int. Conf. on Computational Intelligence for Modelling, Control and Automation and Int. Conf. on Intelligent Agents, Web Technologies and Internet Commerce, pp. 2-7, 2005.","DOI":"10.1109\/CIMCA.2005.1631233"},{"key":"key-10.20965\/jaciii.2009.p0529-22","doi-asserted-by":"crossref","unstructured":"I. K. Vlachos and D. G. Sergiadis, \u201cIntuitionistic Fuzzy Information \u2014 Applications to Pattern Recognition,\u201d in: Pattern Recognition Letters, Vol.28, pp. 197-206, 2006.","DOI":"10.1016\/j.patrec.2006.07.004"},{"key":"key-10.20965\/jaciii.2009.p0529-23","doi-asserted-by":"crossref","unstructured":"I. K. Vlachos and D. G. Sergiadis, \u201cHesitancy Histogram Equalization,\u201d in: Proc. of FUZZ-IEEE 2007, pp. 1-6, 2007.","DOI":"10.1109\/FUZZY.2007.4295620"},{"key":"key-10.20965\/jaciii.2009.p0529-24","doi-asserted-by":"crossref","unstructured":"J. Goguen, \u201cL-fuzzy sets,\u201d in: Journal of Mathematical Analysis and Applications, Vol.18, pp. 145-174, 1967.","DOI":"10.1016\/0022-247X(67)90189-8"},{"key":"key-10.20965\/jaciii.2009.p0529-25","doi-asserted-by":"crossref","unstructured":"R. M. Haralick, S. R. Sternberg, and X. Zhuang, \u201cImage analysis using mathematical morphology,\u201d in: IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol.9, No.4, pp. 532-550, 1987.","DOI":"10.1109\/TPAMI.1987.4767941"},{"key":"key-10.20965\/jaciii.2009.p0529-26","doi-asserted-by":"crossref","unstructured":"C. Cornelis, G. Deschrijver, and E. E. Kerre, \u201cImplication in Intuitionistic and Interval-valued Fuzzy Set Theory: Construction, Classification, Application,\u201d in: Int. Journal of Approximate Reasoning, Vol.35, pp. 55-95, 2004.","DOI":"10.1016\/S0888-613X(03)00072-0"},{"key":"key-10.20965\/jaciii.2009.p0529-27","doi-asserted-by":"crossref","unstructured":"G. Deschrijver, C. Cornelis, and E. E. Kerre, \u201cOn the Representation of Intuitionistic Fuzzy t-norms and t-conorms,\u201d in: IEEE Transactions on Fuzzy Systems, Vol.12, No.1, pp. 45-61, 2004.","DOI":"10.1109\/TFUZZ.2003.822678"},{"key":"key-10.20965\/jaciii.2009.p0529-28","doi-asserted-by":"crossref","unstructured":"G. Deschrijver and C. Cornelis, \u201cRepresentability in Interval-valued Fuzzy Set Theory,\u201d in: Int. Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol.15, No.3, pp. 345-361, 2007.","DOI":"10.1142\/S0218488507004716"},{"key":"key-10.20965\/jaciii.2009.p0529-29","doi-asserted-by":"crossref","unstructured":"G. Deschrijver, \u201cArithmetic Operators in Interval-valued Fuzzy Set Theory,\u201d in: Information Sciences, Vol.177, No.14, pp. 2906-2924, 2007.","DOI":"10.1016\/j.ins.2007.02.003"}],"container-title":["Journal of Advanced Computational Intelligence and Intelligent Informatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.fujipress.jp\/main\/wp-content\/themes\/Fujipress\/phyosetsu.php?ppno=JACII001300050003","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,15]],"date-time":"2024-06-15T18:32:45Z","timestamp":1718476365000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.fujipress.jp\/jaciii\/jc\/jacii001300050529"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9,20]]},"references-count":29,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2009,9,20]]},"published-print":{"date-parts":[[2009,9,20]]}},"URL":"https:\/\/doi.org\/10.20965\/jaciii.2009.p0529","relation":{},"ISSN":["1883-8014","1343-0130"],"issn-type":[{"type":"electronic","value":"1883-8014"},{"type":"print","value":"1343-0130"}],"subject":[],"published":{"date-parts":[[2009,9,20]]}}}