On the power sequence of a fuzzy interval matrix with max-min operation (original) (raw)

An n × n interval matrix A = [A, A] is called to be a fuzzy interval matrix if 0 ≤ A i j ≤ A i j ≤ 1 for all 1 ≤ i, j ≤ n. In this paper, we proposed the notion of max-min algebra of fuzzy interval matrices. We show that the max-min powers of a fuzzy interval matrix either converge or oscillate with a finite period. Conditions for limiting behavior of powers of a fuzzy interval matrix are established. Some properties of fuzzy interval matrices in max-min algebra are derived. Necessary and sufficient conditions for the powers of a fuzzy interval matrices in max-min algebra to be nilpotent are proposed as well. Keywords Interval matrix • Max-min algebra • Convergence • Nilpotence 1 Introduction Interval systems have been proposed in many different areas in the literature (see, e.g., Abdullah and Najib 2016; Allahviranloo and Ghanbari 2012; Dong et al. 2015). The properties of interval matrix have been extensively studied (see, e.g.,