TY - JOUR

T1 - Q-VFCA

T2 - Q-state vector-valued fuzzy cellular automata

AU - Nishida, Yuki

AU - Watanabe, Sennosuke

AU - Fukuda, Akiko

AU - Watanabe, Yoshihide

N1 - Publisher Copyright:
Copyright © 2020, The Authors. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/2/7

Y1 - 2020/2/7

N2 - Elementary fuzzy Cellular Automata (CA) are known as continuous counterpart of elementary CA, which are 2-state CA, via the polynomial representation of local rules. In this paper, we first develop a new fuzzification methodology for q-state CA. It is based on the vector representation of q-state CA, that is, the q-states are assigned to the standard basis vectors of the qdimensional real space and the local rule can be expressed by a tuple of q polynomials. Then, the q-state vector-valued fuzzy CA are defined by expanding the set of the states to the convex hull of the standard basis vectors in the q-dimensional real space. The vector representation of states enables us to enumerate the number-conserving rules of 3-state vector-valued fuzzy CA in a systematic way.37B15, 68Q80

AB - Elementary fuzzy Cellular Automata (CA) are known as continuous counterpart of elementary CA, which are 2-state CA, via the polynomial representation of local rules. In this paper, we first develop a new fuzzification methodology for q-state CA. It is based on the vector representation of q-state CA, that is, the q-states are assigned to the standard basis vectors of the qdimensional real space and the local rule can be expressed by a tuple of q polynomials. Then, the q-state vector-valued fuzzy CA are defined by expanding the set of the states to the convex hull of the standard basis vectors in the q-dimensional real space. The vector representation of states enables us to enumerate the number-conserving rules of 3-state vector-valued fuzzy CA in a systematic way.37B15, 68Q80

KW - Cellular automata

KW - Conservation law

KW - Fuzzy cellular automata

KW - Number-conserving rule

KW - Periodic boundary condition

KW - Vector-valued cellular automata

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M3 - Article

AN - SCOPUS:85093435003

JO - Unknown Journal

JF - Unknown Journal

ER -