Rough soft n-ary semigroups based on a novel congruence relation and corresponding decision making

摘要

In this paper, we consider the t-level relation of mu by U(mu, t) = {(x, y) is an element of S x S vertical bar(mu(x) boolean AND mu(y)) boolean OR Id(S) (x, y) >= t} of an n-ary semigroup S, which is a congruence relation on S if mu is a fuzzy ideal of S. Based on this novel idea, some basic operations of the lower and upper rough approximations of a soft set are discussed. Furthermore, we propose rough soft n-ary semigroups (ideals, prime ideals) based on a congruence relation in n-ary semigroups. Finally, two kinds of decision making methods for rough soft sets on n-ary semigroups are investigated.