On set star-Lindelöf spaces

[EN] A space X is said to be set star-Lindelöf if for each nonempty subset A of X and each collection U of open sets in X such that A ⊆ SU, there is a countable subset V of U such that A ⊆ St(SV, U). The class of set star-Lindelöf spaces lie between the class of Lindel¨of spaces and the class of star-Lindelöf spaces. In this paper, we investigate the relationship between set star-Lindelöf spaces and other related spaces by providing some suitable examples and study the topological properties of set starLindelöf spaces.Singh, S. (2022). On set star-Lindelöf spaces. Applied General Topology. 23(2):315-323. https://doi.org/10.4995/agt.2022.1702131532323

Remarks on monotonically star compact spaces

summary:A space $X$ is said to be monotonically star compact if one assigns to each open cover $\mathcal {U}$ a subspace $s(\mathcal {U}) \subseteq X$, called a kernel, such that $s(\mathcal {U})$ is a compact subset of $X$ and ${\rm St}(s(\mathcal {U}),\mathcal {U})=X$, and if $\mathcal {V}$ refines $\mathcal {U}$ then $s(\mathcal {U}) \subseteq s(\mathcal {V})$, where ${\rm St}(s(\mathcal {U}),\mathcal {U})= \bigcup \{U \in \nobreak \mathcal {U}\colon U \cap s(\mathcal {U}) \not = \emptyset \}$. We prove the following statements: \item {(1)} The inverse image of a monotonically star compact space under the open perfect map is monotonically star compact. \item {(2)} The product of a monotonically star compact space and a compact space is monotonically star compact. \item {(3)} If $X$ is monotonically star compact space with $e(X) < \omega$, then $A(X)$ is monotonically star compact, where $A(X)$ is the Alexandorff duplicate of space $X$. \endgraf The above statement (2) gives an answer to the question of Song (2015)

Implementation of an efficient Fuzzy Logic based Information Retrieval System

This paper exemplifies the implementation of an efficient Information Retrieval (IR) System to compute the similarity between a dataset and a query using Fuzzy Logic. TREC dataset has been used for the same purpose. The dataset is parsed to generate keywords index which is used for the similarity comparison with the user query. Each query is assigned a score value based on its fuzzy similarity with the index keywords. The relevant documents are retrieved based on the score value. The performance and accuracy of the proposed fuzzy similarity model is compared with Cosine similarity model using Precision-Recall curves. The results prove the dominance of Fuzzy Similarity based IR system.Comment: arXiv admin note: substantial text overlap with http://ntz-develop.blogspot.in/ , http://www.micsymposium.org/mics2012/submissions/mics2012_submission_8.pdf , http://www.slideshare.net/JeffreyStricklandPhD/predictive-modeling-and-analytics-selectchapters-41304405 by other author