caa a22 4500 605468559 CHVBK 20210128100317.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00500-014-1302-0 doi (NATIONALLICENCE)springer-10.1007/s00500-014-1302-0 Martin T. Machine Intelligence and Uncertainty Group, Intelligent Systems Lab, University of Bristol, BS8 1TR, Bristol, UK aut The X-mu representation of fuzzy sets [Elektronische Daten] [T. Martin] Fuzzy sets are a good model of the flexible definitions used in human language, but do not always give results in accordance with human reasoning. One reason is that operations on fuzzy sets do not obey all identities from crisp set algebra, such as the law of the excluded middle. Additionally, when used to represent fuzzy numbers they lead to a generalised interval arithmetic rather than a fuzzy version of standard arithmetic. In this paper, we outline the $$X\hbox {-}\mu $$ X - μ approach, a new method of representing, visualizing and calculating functions of fuzzy values. This fuzzy representation retains standard Boolean operations and leads to standard arithmetic when applied to numerical quantities. It includes the idea of strict fuzzy values, which do not incorporate set or interval-based uncertainty. Using simple examples, we illustrate the $$X\hbox {-}\mu $$ X - μ approach and outline the notion of a strict fuzzy value. Springer-Verlag Berlin Heidelberg, 2014 $$X\hbox {-}mu$$ X - m u representation nationallicence Strict fuzzy values nationallicence Fuzzy numbers nationallicence Fuzzy excluded middle nationallicence Gradual elements nationallicence Soft Computing Springer Berlin Heidelberg 19/6(2015-06-01), 1497-1509 1432-7643 19:6<1497 2015 19 500 https://doi.org/10.1007/s00500-014-1302-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00500-014-1302-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Martin T. Machine Intelligence and Uncertainty Group, Intelligent Systems Lab, University of Bristol, BS8 1TR, Bristol, UK aut NATIONALLICENCE 773 0- Soft Computing Springer Berlin Heidelberg 19/6(2015-06-01), 1497-1509 1432-7643 19:6<1497 2015 19 500