scholarly journals Some Topological Approaches for Generalized Rough Sets and Their Decision-Making Applications

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 95
Author(s):  
Radwan Abu-Gdairi ◽  
Mostafa A. El-Gayar ◽  
Tareq M. Al-shami ◽  
Ashraf S. Nawar ◽  
Mostafa K. El-Bably
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Real Life ◽  
Life Problems ◽  
Rough Approximation ◽  
Affirmative Solution ◽  
The Relationship ◽  
Topological Models ◽  
Day By Day ◽  
Generalized Rough Sets

The rough set principle was proposed as a methodology to cope with vagueness or uncertainty of data in the information systems. Day by day, this theory has proven its efficiency in handling and modeling many real-life problems. To contribute to this area, we present new topological approaches as a generalization of Pawlak’s theory by using j-adhesion neighborhoods and elucidate the relationship between them and some other types of approximations with the aid of examples. Topologically, we give another generalized rough approximation using near open sets. Also, we generate generalized approximations created from the topological models of j-adhesion approximations. Eventually, we compare the approaches given herein with previous ones to obtain a more affirmative solution for decision-making problems.

scholarly journals Two Different Views for Generalized Rough Sets with Applications

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2275
Author(s):  
Radwan Abu-Gdairi ◽  
Mostafa A. El-Gayar ◽  
Mostafa K. El-Bably ◽  
Kamel K. Fleifel
Keyword(s):  
Decision Making ◽  
Information System ◽  
Rough Set ◽  
Rough Sets ◽  
Real Life ◽  
Binary Relations ◽  
Medical Field ◽  
Good Decision ◽  
Heart Attacks ◽  
Generalized Rough Sets

Rough set philosophy is a significant methodology in the knowledge discovery of databases. In the present paper, we suggest new sorts of rough set approximations using a multi-knowledge base; that is, a family of the finite number of general binary relations via different methods. The proposed methods depend basically on a new neighborhood (called basic-neighborhood). Generalized rough approximations (so-called, basic-approximations) represent a generalization to Pawlak’s rough sets and some of their extensions as confirming in the present paper. We prove that the accuracy of the suggested approximations is the best. Many comparisons between these approaches and the previous methods are introduced. The main goal of the suggested techniques was to study the multi-information systems in order to extend the application field of rough set models. Thus, two important real-life applications are discussed to illustrate the importance of these methods. We applied the introduced approximations in a set-valued ordered information system in order to be accurate tools for decision-making. To illustrate our methods, we applied them to find the key foods that are healthy in nutrition modeling, as well as in the medical field to make a good decision regarding the heart attacks problem.

scholarly journals ACO with Intuitionistic Fuzzy Pheromone Updating Applied on Multiple-Constraint Knapsack Problem

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1456
Author(s):  
Stefka Fidanova ◽  
Krassimir Todorov Atanassov
Keyword(s):  
Decision Making ◽  
Knapsack Problem ◽  
Propositional Logic ◽  
Optimization Problems ◽  
Real Life ◽  
Combinatorial Optimization Problems ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Multiple Constraint

Some of industrial and real life problems are difficult to be solved by traditional methods, because they need exponential number of calculations. As an example, we can mention decision-making problems. They can be defined as optimization problems. Ant Colony Optimization (ACO) is between the best methods, that solves combinatorial optimization problems. The method mimics behavior of the ants in the nature, when they look for a food. One of the algorithm parameters is called pheromone, and it is updated every iteration according quality of the achieved solutions. The intuitionistic fuzzy (propositional) logic was introduced as an extension of Zadeh’s fuzzy logic. In it, each proposition is estimated by two values: degree of validity and degree of non-validity. In this paper, we propose two variants of intuitionistic fuzzy pheromone updating. We apply our ideas on Multiple-Constraint Knapsack Problem (MKP) and compare achieved results with traditional ACO.

scholarly journals Calculators as Facilitators of Understanding Computational and Mathematical Contexts

2019 ◽  
Vol 1 (1) ◽  
pp. 177-183
Author(s):  
Jan Guncaga ◽  
Lilla Korenova ◽  
Jozef Hvorecky
Keyword(s):  
Soft Skills ◽  
Real Life ◽  
Theoretical Background ◽  
Learning Processes ◽  
Complex Phenomenon ◽  
Learning To Learn ◽  
Life Problems ◽  
The Subject ◽  
The Relationship

AbstractLearning is a complex phenomenon. Contemporary theories of education underline active participation of learners in their learning processes. One of the key arguments supporting this approach is the learner’s simultaneous and unconscious development of their ability of “learning to learn”. This ability belongs to the soft skills highly valued by employers today.For Mathematics Education, it means that teachers have to go beyond making calculations and memorizing formulas. We have to teach the subject in its social context. When the students start understanding the relationship between real-life problems and the role of numbers and formulas for their solutions, their learning becomes a part of their tacit knowledge. Below we explain the theoretical background of our approach and provide examples of such activities.

Introduction and Historical Background

2019 ◽  
pp. 1-26
Keyword(s):  
Decision Making ◽  
Historical Development ◽  
Real Life ◽  
Literature Survey ◽  
Historical Background ◽  
Simultaneous Occurrence ◽  
Special Interests ◽  
Life Problems ◽  
Complex Decision Making ◽  
Complex Decision

This chapter describes the evolution of different multi-objective decision-making (MODM) models with their historical backgrounds. Starting from MODM models in deterministic environments along with various solution techniques, the chapter presents how different kinds of uncertainties may be associated with such decision-making models. Among several types of uncertainties, it has been found that probabilistic and possibilistic uncertainties are of special interests. A brief literature survey on different existing methods to solve those types of uncertainties, independently, is discussed and focuses on the need of considering simultaneous occurrence of those types of uncertainties in MODM contexts. Finally, a bibliographic survey on several approaches for MODM under hybrid fuzzy environments has been presented. Through this chapter the readers can be able to get some concepts about the historical development of MODM models in hybrid fuzzy environments and their importance in solving various real-life problems in the current complex decision-making arena.

scholarly journals A Novel Hybrid Fuzzy Grey TOPSIS Method: Supplier Evaluation of a Collaborative Manufacturing Enterprise

2019 ◽  
Vol 9 (18) ◽  
pp. 3770 ◽  
Author(s):  
Yixiong Feng ◽  
Zhifeng Zhang ◽  
Guangdong Tian ◽  
Amir Mohammad Fathollahi-Fard ◽  
Nannan Hao ◽  
...  
Keyword(s):  
Decision Making ◽  
Comprehensive Evaluation ◽  
Real Life ◽  
Fuzzy Topsis ◽  
Supplier Evaluation ◽  
Manufacturing Enterprise ◽  
Collaborative Manufacturing ◽  
Life Problems ◽  
Order Preference ◽  
The Difference

Recently, there is of significant interest in developing multi-criteria decision making (MCDM) techniques with large applications for real-life problems. Making a reasonable and accurate decision on MCDM problems can help develop enterprises better. The existing MCDM methods, such as the grey comprehensive evaluation (GCE) method and the technique for order preference by similarity to an ideal solution (TOPSIS), have their one-sidedness and shortcomings. They neither consider the difference of shape and the distance of the evaluation sequence of alternatives simultaneously nor deal with the interaction that universally exists among criteria. Furthermore, some enterprises cannot consult the best professional expert, which leads to inappropriate decisions. These reasons motivate us to contribute a novel hybrid MCDM technique called the grey fuzzy TOPSIS (FGT). It applies fuzzy measures and fuzzy integral to express and integrate the interaction among criteria, respectively. Fuzzy numbers are employed to help the experts to make more reasonable and accurate evaluations. The GCE method and the TOPSIS are combined to improve their one-sidedness. A case study of supplier evaluation of a collaborative manufacturing enterprise verifies the effectiveness of the hybrid method. The evaluation result of different methods shows that the proposed approach overcomes the shortcomings of GCE and TOPSIS. The proposed hybrid decision-making model provides a more accurate and reliable method for evaluating the fuzzy system MCDM problems with interaction criteria.

scholarly journals An Integrated Decision-Making Method Based on Neutrosophic Numbers for Investigating Factors of Coastal Erosion

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 328 ◽  
Author(s):  
Azzah Awang ◽  
Nur Aizam ◽  
Lazim Abdullah
Keyword(s):  
Decision Making ◽  
Coastal Erosion ◽  
Real Life ◽  
Analytic Network Process ◽  
Peninsular Malaysia ◽  
Coastal Development ◽  
Weighted Averaging ◽  
Life Problems ◽  
Network Process ◽  
Integrated Decision Making

The recent boom of various integrated decision-making methods has attracted many researchers to the field. The recent integrated Analytic Network Process and Decision Making Trial and Evaluation Laboratory (ANP–DEMATEL) methods were developed based on crisp numbers and fuzzy numbers. However, these numbers are incapable of dealing with the indeterminant and inconsistent information that exists in real-life problems. This paper proposes improvements to the integrated ANP–DEMATEL method by bringing together the neutrosophic numbers, the ANP method, and the DEMATEL method, which are later abbreviated to NS-DANP. The proposed NS-DANP method can handle the indeterminacy elements in the decision-making environment, as the single-valued neutrosophic numbers are used in the decision analysis. This proposed NS-DANP modification method includes linguistic variables representing the single-valued neutrosophic numbers (SVNNs), and also introduces the single-valued neutrosophic weighted averaging (SVNWA) aggregation operator to aggregate the decision makers’ judgments instead of the typical averaging method. The applicability of the proposed method is illustrated by a case study of the coastal erosion problem along the Peninsular Malaysia coastline, where 12 factors were considered. Three experts of coastal erosion from different organizations were invited to elicit their linguistic judgments on the cause–effect of the coastal erosion. The seven-step decision approach was developed to acquire the weightage of each coastal erosion factor. The outcome of this study reveals that coastal development is the riskiest factor toward coastal erosion. The weight of factors and the cause–effect diagram could be very helpful for government and stakeholders to project a better mitigation plan for the coastal erosion problem. Comparative analysis is also provided to check the feasibility of the proposed method.

scholarly journals Fuzzy Analytic Hierarchy Process-Based Multi-Criteria Decision Making for Universities Ranking

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1351
Author(s):  
Rashad Aliyev ◽  
Hasan Temizkan ◽  
Rafig Aliyev
Keyword(s):  
Decision Making ◽  
Analytic Hierarchy Process ◽  
Performance Indicator ◽  
Real Life ◽  
Fuzzy Analytic Hierarchy Process ◽  
Multi Criteria Decision Making ◽  
Analytic Hierarchy ◽  
Life Problems ◽  
Types Of Information ◽  
Hierarchy Process

High competition between universities has been increasing over the years, and stimulates higher education institutions to attain higher positions in the ranking list. Ranking is an important performance indicator of university status evaluation, and therefore plays an essential role in students’ university selection. The ranking of universities has been carried out using different techniques. Main goal of decision processes in real-life problems is to deal with the symmetry or asymmetry of different types of information. We consider that multi-criteria decision making (MCDM) is well applicable to symmetric information modelling. Analytic hierarchy process (AHP) is a well-known technique of MCDM discipline, and is based on pairwise comparisons of criteria/alternatives for alternatives’ evaluation. Unfortunately, the classical AHP method is unable to deal with imprecise, vague, and subjective information used for the decision making process in complex problems. So, introducing a more advanced tool for decision making under such circumstances is inevitable. In this paper, fuzzy analytic hierarchy process (FAHP) is applied for the comparison and ranking of performances of five UK universities, according to four criteria. The criteria used for the evaluation of universities’ performances are teaching, research, citations, and international outlook. It is proven that applying FAHP approach makes the system consistent, and by the calculation of coefficient of variation for all alternatives, it becomes possible to rank them in prioritized order.

The Role of Smart Technologies to Support Citizen Engagement and Decision Making

2018 ◽  
Vol 14 (4) ◽  
pp. 1-17 ◽  
Author(s):  
Gabriela Viale Pereira ◽  
Gregor Eibl ◽  
Constantinos Stylianou ◽  
Gilberto Martínez ◽  
Haris Neophytou ◽  
...  
Keyword(s):  
Decision Making ◽  
Social Media ◽  
Real Life ◽  
Digital Technologies ◽  
Fuzzy Cognitive Maps ◽  
Data Driven ◽  
Social Media Data ◽  
Life Problems ◽  
Smart Technologies ◽  
Media Data

Smart government relies both on the application of digital technologies to enable citizen's participation in order to achieve a high level of citizen centricity and on data-driven decision making in order to improve the quality of life of citizens. Data-driven decisions in turn depend on accessible and reliable datasets, which open government and social media data are likely to promise. The SmartGov project uses digital technologies by integrating open and social media data in Fuzzy Cognitive Maps to model real life problems and simulate different scenarios leading to better decision making. This research performed a multiple-case analysis in two pilot cities. Both municipalities use the technologies to find the best routes: Limassol to improve the garbage collection and Quart de Poblet to improve the walking routes of chaperones guiding children to school. The article proposes a generic framework for Smart City Governance focusing on the inputs and outcomes of this process in the use of technologies for policy making built based on the analysis of the SmartGov.

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 Intuitionistic Fuzzy Soft Rough Set and Its Application in Decision Making

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Haidong Zhang ◽  
Lan Shu ◽  
Shilong Liao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Mathematical Tool ◽  
Intuitionistic Fuzzy ◽  
Rough Approximation ◽  
Soft Rough Set

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. In this paper, we present concepts of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets, and investigate some properties of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets in detail. Furthermore, classical representations of intuitionistic fuzzy soft rough approximation operators are presented. Finally, we develop an approach to intuitionistic fuzzy soft rough sets based on decision making and a numerical example is provided to illustrate the developed approach.

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