New Operations of Totally Dependent-Neutrosophic Sets and Totally Dependent-Neutrosophic Soft Sets

作者：Xiaohong Zhang, Chunxin Bo, Florentín Smarandache, Choonkil Park · 发表于：Symmetry · 年份：2018 · DOI：10.3390/sym10060187 · 被引用次数：55 · 研究领域：Fuzzy and Soft Set Theory、Advanced Algebra and Logic、Multi-Criteria Decision Making

The purpose of the paper is to study new algebraic operations and fundamental properties of totally dependent-neutrosophic sets and totally dependent-neutrosophic soft sets. First, the in-coordination relationships among the original inclusion relations of totally dependent-neutrosophic sets (called type-1 and typ-2 inclusion relations in this paper) and union (intersection) operations are analyzed, and then type-3 inclusion relation of totally dependent-neutrosophic sets and corresponding type-3 union, type-3 intersection, and complement operations are introduced. Second, the following theorem is proved: all totally dependent-neutrosophic sets (based on a certain universe) determined a generalized De Morgan algebra with respect to type-3 union, type-3 intersection, and complement operations. Third, the relationships among the type-3 order relation, score function, and accuracy function of totally dependent-neutrosophic sets are discussed. Finally, some new operations and properties of totally dependent-neutrosophic soft sets are investigated, and another generalized De Morgan algebra induced by totally dependent-neutrosophic soft sets is obtained.