Abstract
This paper aims to discuss the matrix algebra over interval max-plus algebra (interval matrix) and a method tosimplify the computation of the operation of them. This matrix algebra is an extension of matrix algebra over max-plus algebra and can be used to discuss the matrix algebra over fuzzy number max-plus algebra via its alpha-cut.The finding shows that the set of all interval matrices together with the max-plus scalar multiplication operationand max-plus addition is a semimodule. The set of all square matrices over max-plus algebra together with aninterval of max-plus addition operation and max-plus multiplication operation is a semiring idempotent. As reasoningfor the interval matrix operations can be performed through the corresponding matrix interval, because thatsemimodule set of all interval matrices is isomorphic with semimodule the set of corresponding interval matrix,and the semiring set of all square interval matrices is isomorphic with semiring the set of the correspondingsquare interval matrix.
Highlights
Pemodelan dan analisa suatu jaringan dengan pendekatan aljabar max-plus dapat memberikan hasil analitis dan lebih mudah pada komputasinya, Dalam Bacelli et al, (2001), Rudhito, (2004); dan Krivulin, (2001)
This paper aims to discuss the matrix algebra over interval max-plus algebra (interval matrix) and a method to simplify the computation of the operation of them
Proceedings of the 13th UK Performance Engineering Workshop, Ilkley, UK, Edinburgh University Press, July 1997
Summary
Operasi dan perkalian skalar konsisten terhadap urutan dalam semimodul atas R . Dalam bagian ini dibahas konsep dasar aljabar max-plus interval. Dapat ditunjukkan bahwa (I(R) , , ) merupakan semiring idempoten dengan elemen netral = [ , ]. Operasi dan pada I(R)max di atas dapat diperluas untuk operasi-operasi matriks dalam. Diketahui m p max p n max Didefinisikan operasi dengan A p B adalah matriks yang unsur ke-ij-nya: (A B)ij = Aik Bkj untuk i. Berikut diberikan beberapa contoh perhitungan operasi-operasi dalam matriks interval. Sejalan dengan Teorema 2.1.11 dalam Rudhito (2003) diperoleh diperluasannya untuk versi matriks interval dalam Teorema berikut. Pernyataan-pernyataan berikut berlaku untuk sebarang skalar interval dan , dan sebarang matriks interval A , B dan C asalkan operasi yang dimaksud terdefinisi.
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