scholarly journals Diabetes Disease Analysis Using Rough Soft Set

2018 ◽  
Vol 7 (4.10) ◽  
pp. 316
Author(s):  
M. Manimaran ◽  
B. Praba ◽  
G. Deepa ◽  
V. M. Chandrasekaran ◽  
Krishnamoorthy Venkatesan
Keyword(s):  
Diabetes Mellitus ◽  
Set Theory ◽  
Rough Set ◽  
Soft Set ◽  
Age Group ◽  
Health Issues ◽  
Soft Decision ◽  
High Blood Glucose ◽  
Special Cases ◽  
Disease Analysis

Diabetes is a noteworthy medical issue in both modern and creating nations, and its frequency is rising apparently. It is a metabolic disease in which the person who has been affected will have high blood glucose or high blood sugar. It is mainly because of inadequate production of insulin or the body’s cells do not respond to insulin. In some special cases it may be due to both the reasons. This disease causes a lot of health issues in humans’ life. Rough set and soft set theory plays a major role for dealing with uncertainty and it has been applied in many fields. In this paper we aim at finding the age group of people in which maximum diabetes mellitus occurs using the concept of rough soft set and rough soft decision set.  

On soft set-valued maps and integral inclusions

2021 ◽  
pp. 1-15
Author(s):  
Monairah Alansari ◽  
Shehu Shagari Mohammed ◽  
Akbar Azam
Keyword(s):  
Fixed Point ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Fixed Point Theorems ◽  
Soft Set ◽  
Mathematical Tool ◽  
Multivalued Maps ◽  
Soft Sets ◽  
Special Cases ◽  
New Development

As an improvement of fuzzy set theory, the notion of soft set was initiated as a general mathematical tool for handling phenomena with nonstatistical uncertainties. Recently, a novel idea of set-valued maps whose range set lies in a family of soft sets was inaugurated as a significant refinement of fuzzy mappings and classical multifunctions as well as their corresponding fixed point theorems. Following this new development, in this paper, the concepts of e-continuity and E-continuity of soft set-valued maps and αe-admissibility for a pair of such maps are introduced. Thereafter, we present some generalized quasi-contractions and prove the existence of e-soft fixed points of a pair of the newly defined non-crisp multivalued maps. The hypotheses and usability of these results are supported by nontrivial examples and applications to a system of integral inclusions. The established concepts herein complement several fixed point theorems in the framework of point-to-set-valued maps in the comparable literature. A few of these special cases of our results are highlighted and discussed.

scholarly journals Some More Results on IF Soft Rough Approximation Space

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Sharmistha Bhattacharya (Halder) ◽  
Bijan Davvaz
Keyword(s):  
Data Mining ◽  
Decision Making ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Soft Set ◽  
Approximation Space ◽  
Rough Approximation ◽  
Frame Work ◽  
Set Approximation

Fuzzy sets, rough sets, and later on IF sets became useful mathematical tools for solving various decision making problems and data mining problems. Molodtsov introduced another concept soft set theory as a general frame work for reasoning about vague concepts. Since most of the data collected are either linguistic variable or consist of vague concepts so IF set and soft set help a lot in data mining problem. The aim of this paper is to introduce the concept of IF soft lower rough approximation and IF upper rough set approximation. Also, some properties of this set are studied, and also some problems of decision making are cited where this concept may help. Further research will be needed to apply this concept fully in the decision making and data mining problems.

scholarly journals A Soft Interval Based Decision Making Method and Its Computer Application

2021 ◽  
Vol 46 (3) ◽  
pp. 273-296
Author(s):  
Gözde Yaylalı ◽  
Nazan Çakmak Polat ◽  
Bekir Tanay
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Soft Set ◽  
Computer Application ◽  
Complex Data ◽  
Soft Sets ◽  
Mathematical Algorithm ◽  
Huge Data ◽  
Special Cases ◽  
General Method

Abstract In today’s society, decision making is becoming more important and complicated with increasing and complex data. Decision making by using soft set theory, herein, we firstly report the comparison of soft intervals (SI) as the generalization of interval soft sets (ISS). The results showed that SIs are more effective and more general than the ISSs, for solving decision making problems due to allowing the ranking of parameters. Tabular form of SIs were used to construct a mathematical algorithm to make a decision for problems that involves uncertainties. Since these kinds of problems have huge data, constructing new and effective methods solving these problems and transforming them into the machine learning methods is very important. An important advance of our presented method is being a more general method than the Decision-Making methods based on special situations of soft set theory. The presented method in this study can be used for all of them, while the others can only work in special cases. The structures obtained from the results of soft intervals were subjected to test with examples. The designed algorithm was written in recently used functional programing language C# and applied to the problems that have been published in earlier studies. This is a pioneering study, where this type of mathematical algorithm was converted into a code and applied successfully.

SAR

2011 ◽  
Vol 1 (4) ◽  
pp. 38-52
Author(s):  
Rabiei Mamat ◽  
Tutut Herawan ◽  
Mustafa Mat Deris
Keyword(s):  
Decision Making ◽  
Information System ◽  
Set Theory ◽  
Rough Set ◽  
Soft Set ◽  
Decision Makers ◽  
Benchmark Datasets

Soft-set theory proposed by Molodstov is a general mathematic tool for dealing with uncertainty. Recently, several algorithms have been proposed for decision making using soft-set theory. However, these algorithms still concern on Boolean-valued information system. In this paper, Support Attribute Representative (SAR), a soft-set based technique for decision making in categorical-valued information system is proposed. The proposed technique has been tested on three datasets to select the best partitioning attribute. Furthermore, two UCI benchmark datasets are used to elaborate the performance of the proposed technique in term of executing time. On these two datasets, it is shown that SAR outperforms three rough set-based techniques TR, MMR, and MDA up to 95% and 50%, respectively. The results of this research will provide useful information for decision makers to handle categorical datasets.

The Position of Rough Set in Soft Set

2012 ◽  
Vol 3 (3) ◽  
pp. 33-48
Author(s):  
Tutut Herawan
Keyword(s):  
Topological Space ◽  
Set Theory ◽  
Rough Set ◽  
Equivalence Relation ◽  
Rough Set Theory ◽  
Soft Set ◽  
General Topology ◽  
Discrete Topology ◽  
Special Case

In this paper, the author presents the concept of topological space that must be used to show a relation between rough set and soft set. There are two main results presented; firstly, a construction of a quasi-discrete topology using indiscernibility (equivalence) relation in rough set theory is described. Secondly, the paper describes that a “general” topology is a special case of soft set. Hence, it is concluded that every rough set can be considered as a soft set.

A Theoretical Formulation of Object-Oriented Rough Set Models

2006 ◽  
Vol 10 (5) ◽  
pp. 612-620 ◽  
Author(s):  
Yasuo Kudo ◽  
◽  
Tetsuya Murai ◽  
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Object Oriented ◽  
Theoretical Formulation ◽  
Structural Hierarchy ◽  
Special Cases ◽  
Abstract Data ◽  
Lower And Upper Approximations

We introduce object-oriented paradigm into rough set theory. First, we provide concepts of class, object, and name, respectively. Class structures represent abstract data forms, and abstract structural hierarchy based on is-a relationship and has-a relationship. Object structures illustrate many kinds of objects and actual dependence among objects by is-a relationship and has-a relationship. Name structures provide concrete design of objects, and connect class structures and object structures consistently. Next, combining class, name and object structures, we propose object-oriented information systems, which include “traditional” information systems as special cases. Moreover, we introduce indiscernibility relations on the set of objects, lower and upper approximations, and object-oriented rough sets in the object-oriented information systems.

scholarly journals Soft Rough Approximation Operators and Related Results

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Zhaowen Li ◽  
Bin Qin ◽  
Zhangyong Cai
Keyword(s):  
Topological Space ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Soft Set ◽  
Soft Sets ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Generalized Rough Set ◽  
Special Case

Soft set theory is a newly emerging tool to deal with uncertain problems. Based on soft sets, soft rough approximation operators are introduced, and soft rough sets are defined by using soft rough approximation operators. Soft rough sets, which could provide a better approximation than rough sets do, can be seen as a generalized rough set model. This paper is devoted to investigating soft rough approximation operations and relationships among soft sets, soft rough sets, and topologies. We consider four pairs of soft rough approximation operators and give their properties. Four sorts of soft rough sets are investigated, and their related properties are given. We show that Pawlak's rough set model can be viewed as a special case of soft rough sets, obtain the structure of soft rough sets, give the structure of topologies induced by a soft set, and reveal that every topological space on the initial universe is a soft approximating space.

scholarly journals Soft covering based rough graphs and corresponding decision making

2019 ◽  
Vol 17 (1) ◽  
pp. 423-438
Author(s):  
Choonkil Park ◽  
Nasir Shah ◽  
Noor Rehman ◽  
Abbas Ali ◽  
Muhammad Irfan Ali ◽  
...  
Keyword(s):  
Decision Making ◽  
Graph Theory ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Soft Set ◽  
Basic Properties

Abstract Soft set theory and rough set theory are two new tools to discuss uncertainty. Graph theory is a nice way to depict certain information. Particularly soft graphs serve the purpose beautifully. In order to discuss uncertainty in soft graphs, some new types of graphs called soft covering based rough graphs are introduced. Several basic properties of these newly defined graphs are explored. Applications of soft covering based rough graphs in decision making can be very fruitful. In this regard an algorithm has been proposed.

scholarly journals Multicriteria Decision Making Method Based on the Higher Order Hesitant Fuzzy Soft Set

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
B. Farhadinia
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Multicriteria Decision Making ◽  
Higher Order ◽  
Soft Set ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Fuzzy Soft Set ◽  
Multicriteria Decision ◽  
Special Cases

The main goal of this contribution is to introduce the concept of higher order hesitant fuzzy soft set as an extension of fuzzy soft set that encompasses most of the existing extensions of fuzzy soft set as special cases. Furthermore, this new concept provides us with a method for dealing with multicriteria fuzzy decision making problems which are difficult to explain in other existing extensions of fuzzy soft set theory, especially when problems involve parameters with different-dimensional levels.

On Connections of Soft Set Theory with Existing Mathematics of Uncertainties: A Short Discussion for Non-Mathematicians with Respect to Soft Set Theory

2018 ◽  
Vol 14 (01) ◽  
pp. 1-9 ◽  
Author(s):  
Santanu Acharjee
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Rough Set Theory ◽  
Mathematical Structure ◽  
Soft Set ◽  
Hybrid Structures ◽  
Hesitant Fuzzy Set ◽  
Short Discussion

This paper focuses on two very important questions: “what is the future of a hybrid mathematical structure of soft set in science and social science?” and “why should we take care to use hybrid structures of soft set?”. At present, these are the most fundamental questions; which encircle a few prominent areas of mathematics of uncertainties viz. fuzzy set theory, rough set theory, vague set theory, hesitant fuzzy set theory, IVFS theory, IT2FS theory, etc. In this paper, we review connections of soft set theory and hybrid structures in a non-technical manner; so that it may be helpful for a non-mathematician to think carefully to apply hybrid structures in his research areas. Moreover, we must express that we do not have any intention to nullify contributions of fuzzy set theory or rough set theory, etc. to mankind; but our main intention is to show that we must be careful to develop any new hybrid structure with soft set. Here, we have a short discussion on needs of artificial psychology and artificial philosophy to enrich artificial intelligence.

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