International Journal of Information Engineering and Electronic Business (IJIEEB)
IJIEEB Vol. 7, No. 5, 8 Sep. 2015
Cover page and Table of Contents: PDF (size: 709KB)
An Introduction of Two and Three Dimensional Imprecise Numbers
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Author(s)
Index Terms
Reference function, imprecise number, membership function, membership value, Indicator function, normal imprecise number, two-dimensional imprecise number, three-dimensional imprecise number
Abstract
Discuss the real line fuzzy concept into multi- dimensional based on the reference function so as to get new imprecise numbers called the two-dimensional and three-dimensional imprecise numbers and their complements. Two and three dimensional imprecise numbers are obtained in the form of Cartesian product of fuzzy numbers. To study their character some necessary definitions like partial presence, construction of membership function, membership value ,Indicator function etc. of two and three-dimensional imprecise numbers are defined with own notation. As per as possible, try to show all the properties of classical set theory that can be hold good in the present imprecise numbers with some examples. Set Operations are defined by maximum and minimum operators just like defined in the real line imprecise numbers. Further bring out a few graphical examples to verify the intersection and union of two and three dimensional imprecise numbers are the empty and the universal set respectively. Basically Intersection and union are the operators to obtain their properties.
Cite This Paper
Sahalad Borgoyary, "An Introduction of Two and Three Dimensional Imprecise Numbers", IJIEEB, vol.7, no.5, pp.27-38, 2015. DOI:10.5815/ijieeb.2015.05.05
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