Complement (music)

Phenotype

Aerospace engineering

Pure mathematics

Soft set

Mathematics

Intersection (aeronautics)

Evolutionary biology

Biology

Gene

Data mining

Algebraic operation

Algebra over a field

Engineering

Mathematical analysis

Function (biology)

Algebraic structure

Artificial intelligence

Relation (database)

Chemistry

Complementation

Ecology

Type (biology)

Computer science

Biochemistry

Fuzzy logic

Algebraic number

Symmetry

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.

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