On two novel types of three-way decisions in three-way decision spaces

In order to explore a unified theory of three-way decisions proposed by Yao, Hu introduced three-way decision spaces through an axiomatic method, established the corresponding three-way decisions, and proposed two open problems on the changes of decision parameters in definition of three-way decisions. For answering these two questions, this paper firstly discusses the parameter changes in the assumptions from 0 <= beta < alpha <= 1 to 0 <= beta <= alpha <= 1 and inequality E(A)(x) <= beta in the rejection region is replaced by E(A)(x) < beta. Under the circumstance, this paper introduces new type of three-way decisions in three-way decision spaces and discusses properties of the three-way decisions, lower and upper approximations induced by three-way decisions, aggregation three-way decisions over multiple three-way decision spaces and dynamic three-way decisions on three-way decision spaces. Then this paper discusses another question on refusal decision region when the uncertain region is defined by using inequality beta < E(A)(x) < alpha and gives one example to illustrate the similarity and difference among these three-way decisions based on three-way decision spaces. (C) 2016 Elsevier Inc. All rights reserved.