Fuzzy eigen value and its application in back-cross breeding modeling *Ema Carnia, Herlina E. Napitupulu & Asep K. Supriatna
Department of Mathematics, Padjadjaran University, Jl. Raya Bandung-Sumedang Km 21, Jatinangor 45363, Indonesia
Abstract
Abstract. Fuzzy concepts, such as Fuzzy Set, Fuzzy Number, and Fuzzy Logic have gained a lot of attention nowadays. Numerous applications are abound regarding the concepts in diverse area. On the other hand, classical concepts, such as Eigen Value, also play important roles in many applications. In this paper, we present a discussion encompassing these concepts simultaneously, i.e. the fuzzy version of eigen values of a matrix. Two approaches on how to introduce fuzziness into classical mathematics are discussed, i.e. the one that assumes that the fuzziness of input component directly affect the output in a computation with the same fuzzy membership and the other one that assume that the fuzziness involves in the computational process. Here we use the triangular fuzzy number and the result is applied to modeling a real phenomenon in back-cross breeding problem. The result shows that fuzzy eigen values are in agreement with the clasiccal eigen values of a matrix with crisp value components.
Keywords: Eigen value problem, fuzzy number, triangular fuzzy number, alpha-cut
