{"title":"Membership Surface and Arithmetic Operations of Imprecise Matrix","authors":"Dhruba Das","volume":108,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":760,"pagesEnd":770,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10003419","abstract":"In this paper, a method has been developed to
\r\nconstruct the membership surfaces of row and column vectors and
\r\narithmetic operations of imprecise matrix. A matrix with imprecise
\r\nelements would be called an imprecise matrix. The membership
\r\nsurface of imprecise vector has been already shown based on
\r\nRandomness-Impreciseness Consistency Principle. The Randomness-
\r\nImpreciseness Consistency Principle leads to defining a normal law
\r\nof impreciseness using two different laws of randomness. In this
\r\npaper, the author has shown row and column membership surfaces
\r\nand arithmetic operations of imprecise matrix and demonstrated with
\r\nthe help of numerical example.","references":"[1] H. K. Baruah, Set Superimposition and Its Application to the Theory of\r\nFuzzy Sets, Journal of the Assam Science Society, 25-31, 1999.\r\n[2] H. K. Baruah, In search of the root of fuzziness: The measure\r\ntheoretic meaning of partial presence, Annals of Fuzzy Mathematics and\r\nInformatics 2(1), 57-68, 2011.\r\n[3] H. K. Baruah, The Theory of Fuzzy Sets: Beliefs and\r\nRealities, International Journal of Energy, Information and\r\nCommunications,2(2),1-21, 2011. [4] H. K. Baruah, An introduction to the theory of imprecise sets: The\r\nmathematics of partial presence, J Math Comput Sci 2(2), 110-124, 2012.\r\n[5] G. de Barra, Measure Theory and Integration, New Delhi: Wiley Eastern\r\nLimited, 1987.\r\n[6] H. K. Baruah, D. Das, Imprecise Vector, Lambert Academic Publishing,\r\nGermany, 2014.\r\n[7] D. Das, H. K. Baruah, Construction of the Membership Surface of\r\nImprecise Vector, Springer Plus, 2014, 3:722.\r\n[8] D. Das, H. K. Baruah, Theory of Imprecise Sets: Imprecise Matrix,\r\nNational Academy Science Letters (Accepted), 2015.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 108, 2015"}