Three-way decision spaces based on partially ordered sets and three-way decisions based on hesitant fuzzy sets

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• 作者：Bao Qing Hu^a ; ^b ; ^{bqhu@whu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; ^{bqhujjhe@hotmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Partially ordered sets ; Fuzzy sets ; Hesitant fuzzy sets ; Rough sets ; Three-way decision spaces ; Three-way decisions
• 刊名：Knowledge-Based Systems
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：91
• 期：Complete
• 页码：16-31
• 全文大小：578 K

文摘

Three-way decisions on three-way decision spaces are based on fuzzy lattices, i.e. complete distributive lattices with involutive negators. However, now some popular structures, such as hesitant fuzzy sets and type-2 fuzzy sets, do not constitute fuzzy lattices. It limits applications of the theory of three-way decision spaces. So this paper attempts to generalize measurement on decision conclusion in three-way decision spaces from fuzzy lattices to partially ordered sets. First three-way decision spaces and three-way decisions are discussed based on general partially ordered sets. Then this paper points out that the collection of non-empty subset of [0, 1] and the family of hesitant fuzzy sets are both partially ordered sets. Finally this paper systematically discusses three-way decision spaces and three-way decisions based on hesitant fuzzy sets and interval-valued hesitant fuzzy sets and obtains many useful decision evaluation functions.