Keyword-Based Knowledge Graph Exploration Based on Quadratic Group Steiner Trees

Exploring complex structured knowledge graphs (KGs) is challenging for non-experts as it requires knowledge of query languages and the underlying structure of the KGs. Keyword-based exploration is a convenient paradigm, and computing a group Steiner tree (GST) as an answer is a popular implementation. Recent studies suggested improving the cohesiveness of an answer where entities have small semantic distances from each other. However, how to efficiently compute such an answer is open. In this paper, to model cohesiveness in a generalized way, the quadratic group Steiner tree problem (QGSTP) is formulated where the cost function extends GST with quadratic terms representing semantic distances. For QGSTP we design a branch-and-bound best-first (B3F) algorithm where we exploit combinatorial methods to estimate lower bounds for costs. This exact algorithm shows practical performance on medium-sized KGs.

Union of Fuzzy Sub - Quadradic Groups Fuzzy Sub - Pendant Groups and Fuzzy Sub - N Groups

In this paper, union of Fuzzy subsets, Fuzzy sub – Quadratic group, fuzzy sub - Pendant group and Fuzzy sub–N groups are discussed. Moreover, some properties and theorems based on these have been derived and derive the definitions of Union of Fuzzy sub – Quadratic group, definitions of Union of fuzzy sub- Pendant group and soon definitions of Union of Fuzzy sub–N groups, and derive the definitions of Fuzzy Quadratic group, definitions of fuzzy Pendant group and soon definitions of Fuzzy N group and definition of Quadratic group, definitions of Pendant group and soon definitions of N group.

Algebraic Structure of Union of Fuzzy (Anti-Fuzzy) Normal Sub - Groups Fuzzy (Anti-Fuzzy) Normal Sub ch Bigroups And Soon Fuzzy (Anti-Fuzzy) Normal Sub - N Groups

In this paper, union of Fuzzy subsets, definition of Fuzzy normal subgroup, definition of Fuzzy normal sub bi-group, definition of Fuzzy normal sub tri-group, definition of Fuzzy normal sub – Quadratic group, definition of fuzzy normal sub- Pentant group and definition of Fuzzy normal sub–N groups are derived. Moreover, some properties and theorems of union in fuzzy normal based on these have been derived.