INFORMATION CHANGE THE WORLD

### International Journal of Information Engineering and Electronic Business(IJIEEB)

ISSN: 2074-9023 (Print), ISSN: 2074-9031 (Online)

IJIEEB Vol.7, No.5, Sep. 2015

#### An Introduction of Two and Three Dimensional Imprecise Numbers

Full Text (PDF, 709KB), PP.27-38

#### 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

#### Reference

[1]L.A. Zadeh, Fuzzy sets, Inform. And Control, 1965, 8, 338-353.

[2]C. H. Cheng, a new approach to ranking fuzzy numbers by distance method, Fuzzy Sets and systems, 95, 1998, 307-317.

[3]H.K. Baruah, Theory of fuzzy sets: Beliefs and realities, I.J. Energy Information and Communications. 2(2), (2011), 1-22.

[4]H.K. Baruah, Construction of membership Function of a Fuzzy Number, ICIC Express Letters 5(2), (2011), 545-549.

[5]H.K. Baruah, In search of the roots of fuzziness: the Measure Meaning of partial Presence, Annals of Fuzzy mathematics and informatics. 2(1), (2011), 57-68.

[6]S. K. Sardar and S.K. Majumder, On Cartesian Product of Fuzzy Completely Prime and Fuzzy Completely Semi-prime Ideal of Semi-groups, I.J. of Computational Cognition, Vol. 9, 2011.

[7]Muralikrishna P. and Chandram-ouleeswaran M., Generalisation of Cartesian product of Inttuitionistic L-Fuzzy BF-Ideals, I.J. Contemp. Maths. Sciences, Vol. 6, 2011, no.14, 671-679.

[8]H.K. Baruah, An introduction theory of imprecise Sets: The Mathematics of partial presence, J. Math. Computer Science 2(2), (2012), 110-124.

[9]A. Varghese and S. Kuriakose, Cartesian Product Over Intuitionistic Fuzzy Sets, International Journal of Fuzzy Sets, Vol.2, 2012, 21-27.

[10]M. Dhar, On Geometrical Representation of Fuzzy numbers, IJEIC, Korea, Vol.3, Issue 2, 2012, P-29-34.

[11]M. Dhar, The compliment of fuzzy numbers: An Exposition, Intelligent system and Applications, 2013, 08, 73-82.

[12]M. Dhar and H.K. Baruah, Theory of Fuzzy Sets: An Overview, I.J. Information Engineering and Electronic Business, 2013, 3, 22-33.

[13]M. Dhar, A Note on Determinant of Square Fuzzy matrix, I.J. Information Engineering and Electronic Business,2013,1,52-59.

[14]S. Broumi, F. Smarandache and M. Dhar, On Fuzzy Soft Matrix based on reference Function, I.J. Information Engineering and Electronic Business,2013,2,26-32.

[15]Priya T. and Ramachandran T., Homomorphism and Cartesian Product of Fuzzy PS-Algebra, Applied Mathematical science, Vol. 8, 2014, no. 16, 3321-3330.

[16]S. Borgoyary, A Few Applications of Imprecise Matrices, I.J. Intelligent system and Applications, 2015, 08, 9-17.