General Topology-I

An improvement of rough sets’ accuracy measure using containment neighborhoods with a medical application

In this paper, we generalize three types of rough set models based on j-neighborhood space (i.e, type 1 j-neighborhood rough set, type 2 j-neighborhood rough set, and type 3 j-neighborhood rough set), and investigate some of their basic properties. Also, we present another three types of rough set models based on j-adhesion neighborhood space (i.e, type 4 j-adhesion neighborhood rough set, type 5 j-adhesion neighborhood rough set, and type 6 j-adhesion neighborhood rough set). The fundamental properties of approximation operators based on j-adhesion neighborhood space are established. The relationship between the properties of these types is explained. Finally, according to j-adhesion neighborhood space, we give a comparison between the Yao’s approach and our approach.

Comparison of six types of rough approximations based on j-neighborhood space and j-adhesion neighborhood space

In this paper, with the aid of fuzzy soft $$\beta $$
 -neighborhoods, we introduce fuzzy soft covering-based multi-granulation fuzzy rough set models. We examine some of the relevant properties of fuzzy soft covering based on optimistic, pessimistic, and variable precision multi-granulation fuzzy rough set models. Then, we give fuzzy soft coverings based on $$\psi $$
 -optimistic and $${\mathscr {D}}$$
 -optimistic (
 $$\psi $$
 -pessimistic and $${\mathscr {D}}$$
 -pessimistic) multi-granulation fuzzy rough sets from fuzzy soft measures. It also discusses the interactions between these forms of fuzzy soft coverings based on multi-granulation fuzzy rough sets. Eventually, we apply the proposed models for solving MAGDM problems. The effectiveness and feasibility of our approach are noted from the introduced comparisons between our method and some methods given in the previous studies.

Fuzzy soft covering-based multi-granulation fuzzy rough sets and their applications

Neighborhood systems are used to approximate graphs as finite topological structures. Throughout this article, we construct new types of eight neighborhoods for vertices of an arbitrary graph, say, j-adhesion neighborhoods. Both notions of Allam et al. and Yao will be extended via j-adhesion neighborhoods. We investigate new types of j-lower approximations and j-upper approximations for any subgraph of a given graph. Then, the accuracy of these approximations will be calculated. Moreover, a comparison between accuracy measures and boundary regions for different kinds of approximations will be discussed. To generate j-adhesion neighborhoods and rough sets on graphs, some algorithms will be introduced. Finally, a sample of a chemical example for Walczak will be introduced to illustrate our proposed methods.

/pdf/rough-approximation-models-via-graphs-based-on-neighborhood-4t3ftb4tc6.pdf

Rough approximation models via graphs based on neighborhood systems

It is known that mathematical statics, mathematical modeling, and differential equations are used to give an in-depth understanding of many medical problems. On the edge of the information revolution, minimal structures show some qualitative properties issues that are difficult to deal with it, such as quality of education, nutrition, etc. The aim of this paper is to discuss two medical applications and show that a minimal structure space is suitable for analyzing several real-life problems. Then, the accuracy of the decision-making and attributes reduction of the medical information system are explained and obtained. Furthermore, we introduce a comparison between our approach and Pawlak’s approach to find accuracy for decision-making. Finally, the accuracy of decision-making via a variable precision model is improved.

Medical applications via minimal topological structure

One of the considerable subjects in mathematics is the study of topology. Deducing topology from arbitrary binary relations has enticed the attention of many researchers. So, we devote this article...

/pdf/various-topologies-generated-from-ej-neighbourhoods-via-3d6xr5zhdk.pdf

, Various topologies generated from Ej-neighbourhoods via ideals

An intuitionistic fuzzy set is one of the efficient generalizations of a fuzzy set for dealing with vagueness/uncertainties in information. Under this environment, in this manuscript, we familiarize a new type of extensions of fuzzy sets called square-root fuzzy sets (briefly, SR-Fuzzy sets) and contrast SR-Fuzzy sets with intuitionistic fuzzy sets and Pythagorean fuzzy sets. We discover the essential set of operations for the SR-Fuzzy sets along with their several properties. In addition, we define a score function for the ranking of SR-Fuzzy sets. To study multiattribute decision-making problems, we introduce four new weighted aggregated operators, namely, SR-Fuzzy weighted average (SR-FWA) operator, SR-Fuzzy weighted geometric (SR-FWG) operator, SR-Fuzzy weighted power average (SR-FWPA) operator, and SR-Fuzzy weighted power geometric (SR-FWPG) operator over SR-Fuzzy sets. We apply these operators to select the top-rank university and show how we can choose the best option by comparing the aggregate outputs through score values.

https://downloads.hindawi.com/journals/jfs/2022/3653225.pdf

SR-Fuzzy Sets and Their Weighted Aggregated Operators in Application to Decision-Making

As daily problems involve a great deal of data and ambiguity, it has become vital to build new mathematical ways to cope with them, and soft set theory is the greatest tool for doing so. As a result, we study methods of generating soft topologies through several soft set operators. A soft topology is known to be determined by the system of special soft sets, which are called soft open (dually soft closed) sets. The relationship between specific types of soft topologies and their classical topologies (known as parametric topologies) is linked to the idea of symmetry. Under this symmetry, we can study the behaviors and properties of classical topological concepts via soft settings and vice versa. In this paper, we show that soft topological spaces can be characterized by soft closure, soft interior, soft boundary, soft exterior, soft derived set, or co-derived set operators. All of the soft topologies that result from such operators are equivalent, as well as being identical to their classical counterparts under enriched (extended) conditions. Moreover, some of the soft topologies are the systems of all fixed points of specific soft operators. Multiple examples are presented to show the implementation of these operators. Some of the examples show that, by removing any axiom, we will miss the uniqueness of the resulting soft topology.

/pdf/generating-soft-topologies-via-soft-set-operators-2ro7z43n.pdf

A. A. Azzam

Papers

Comparison of six types of rough approximations based on j-neighborhood space and j-adhesion neighborhood space

Medical applications via minimal topological structure

, Various topologies generated from Ej-neighbourhoods via ideals

SR-Fuzzy Sets and Their Weighted Aggregated Operators in Application to Decision-Making

Generating Soft Topologies via Soft Set Operators