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

Bao Qing Hu, Heung Wong, Ka fai Cedric Yiu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

47 Citations (Scopus)


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≤β<α≤1 to 0≤β≤α≤1 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.
Original languageEnglish
Pages (from-to)285-306
Number of pages22
JournalInternational Journal of Approximate Reasoning
Publication statusPublished - 1 Mar 2017


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

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Artificial Intelligence
  • Applied Mathematics


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