SIFAT-SIFAT OPERASI FUZZY MATRIX
Keywords:
fuzzy matrix, operasi aritmatika, operasi transposAbstract
Fuzzy matrix adalah suatu matriks dimana elemen-elemennya terdiri dari bilangan
fuzzy pada interval , -dinotasikan dengan ̃ [ ] { , -
}. Seperti pada matriks real, fuzzy matrix juga mempunyai operasi arit-
matika maupun operasi transpos. Operasi penjumlahan, pengurangan, perkalian dan
transpos fuzzy matrix berturut-turut didefinisikan dengan: ̃ ̃ ̃ ̃
( ), ̃ ̃ ( ( )) dan ( ̃) ( ).
Sebagaimana matriks real, fuzzy matrix juga memiliki sifat-sifat atau operasi-operasi
tertentu, maka dalam artikel ini akan dibahas pembuktikan sifat-sifat operasi arit- matika dan operasi transpos yang berlaku pada fuzzy matrix.
References
Chen, Guanrong. 2001.Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems. University of Houston Houston. USA: CRC Press.
Ibrahim, Ahmad M. 2004. Fuzzy Logic: for Embedded Systems Applications. USA : Elsevier Science.
Kalra, Nidhi. 2010. Study Of Fuzzy, Super and Super Fuzzy Matrix Theory. Thesis diterbitkan. Punjab: Thapar University.
Kandasamy W.B.V., Smarandache F. and Amal K., 2008. “Super Fuzzy Matri- ces and Super Fuzzy Models for Social Scientists”, Ann Arbor (2008).
Kandasamy, Vasantha. 2008. Super Fuzzy Matrices And Super Fuzzy Models For Social Scientists. United States of America: Info Learn Quest.
Klir G.J., and Yuan B. 1995. Fuzzy Sets and Fuzzy Logic: Theory and Applica- tions. USA : Prentice-Hall.
Leon, Steven J. 2001. Aljabar Linear dan Aplikasinya. Jakarta: Erlangga.
Leondes, Cornelius T. 1998. Fuzzy Logic and Expert Systems Applications. USA: Academic Press.
Oscar C. and Patricia M. 2008. Type-2 Fuzzy Logic: Theory and Applications. Verlag Berlin: Springer.
Purnomo, H., Kusumadewi, S. 2004. Aplikasi Logika Fuzzy. Yogyakarta: Gra- ha Ilmu
Serre, Denis. 2002 . Matrices ; Theory and Applications. Verlag New York: Springer.
Susilo, Frans. 2006. Himpunan dan Logika Kabur serta Aplikasinya. Yogya- karta: Graha Ilmu.
Thayer, W., Silicon, V.& Tornado, A.. Fuzzy Logic: The Logic of Fuzzy Sets. www.applet-magic.com , diakses 16 Februari 2014
Thomas S., Shores. 2000. Applied linear algebra And matrix analysis. USA: May 2000 All Rights Reserved.
Timothy, J. Ross. 2010. Fuzzy logic with Engineering applications. A John Wiley and Sons, Ltd. USA: Publication. University of New Mexico.
Vasantha Kandasamy, W.B., and Indra, V. 2000. Applications of Fuzzy Cogni- tive Maps to Determine the Maximum Utility of a Route, J. of Fuzzy Maths, publ. by the Int. fuzzy Mat. Inst., 8 (2000) 65-77.
Vasantha, Kandasamy, W.B. 2008. Set linear algebra And set fuzzy linear al- gebra. USA: Ann Arbor.
Vasantha, Kandasamy. 2007. Elementary Fuzzy Matrix Theory and Fuzzy Models for Social Scientists. USA: Automaton.
Zadeh, L.A. 1971. Similarity Relations and Fuzzy Orderings, Inform. Sci., 3 (1971) 177-200
Zadeh, L.A., 1965. Fuzzy Sets, Inform. and control, 8, 338-353.
