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

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Highlights

  • Two new types of 3WD through considering changes of parameter.

  • Refusal decision region of 3WD over three-way decision spaces.

  • The optimistic and pessimistic 3WD over multiple three-way decision spaces.

  • The aggregation 3WD over multiple three-way decision spaces.

  • Dynamic 3WD over multiple three-way decision spaces.

Abstract

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 0β<α1 to 0βα1 and inequality E(A)(x)β in the rejection region is replaced by E(A)(x)<β. 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 β<E(A)(x)<α and gives one example to illustrate the similarity and difference among these three-way decisions based on three-way decision spaces.

Keywords

Partially ordered sets
Fuzzy sets
Interval-valued fuzzy sets
Rough sets
Three-way decision spaces
Three-way decisions

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This paper is part of the virtual special issue on tri-partition, edited by Davide Ciucci and Yiyu Yao.