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

PY - 2020

Y1 - 2020

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 q-dimensional 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 numberconserving rules of 3-state vector-valued fuzzy CA in a systematic way.

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 q-dimensional 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 numberconserving rules of 3-state vector-valued fuzzy CA in a systematic way.

KW - Cellular automata

KW - Conservation law

KW - Fuzzy cellular automata

KW - Number-conserving rule

KW - Periodic boundary condition

KW - Vector-valued cellular automata

UR - http://www.scopus.com/inward/record.url?scp=85086138376&partnerID=8YFLogxK

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M3 - Article

AN - SCOPUS:85086138376

VL - 15

SP - 207

EP - 222

JO - Journal of Cellular Automata

JF - Journal of Cellular Automata

SN - 1557-5969

IS - 3

ER -