scholarly journals Multi-Granulation Neutrosophic Rough Sets on a Single Domain and Dual Domains with Applications

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 296 ◽  
Author(s):  
Chunxin Bo ◽  
Xiaohong Zhang ◽  
Songtao Shao ◽  
Florentin Smarandache
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Rough Set ◽  
Group Decision Making ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Group Decision ◽  
Single Domain ◽  
Particle Structure ◽  
Interesting Direction

It is an interesting direction to study rough sets from a multi-granularity perspective. In rough set theory, the multi-particle structure was represented by a binary relation. This paper considers a new neutrosophic rough set model, multi-granulation neutrosophic rough set (MGNRS). First, the concept of MGNRS on a single domain and dual domains was proposed. Then, their properties and operators were considered. We obtained that MGNRS on dual domains will degenerate into MGNRS on a single domain when the two domains are the same. Finally, a kind of special multi-criteria group decision making (MCGDM) problem was solved based on MGNRS on dual domains, and an example was given to show its feasibility.

(α, β)-Multi-granulation bipolar fuzzified rough sets and their applications to multi criteria group decision making

2021 ◽  
pp. 1-36
Author(s):  
Rizwan Gul ◽  
Muhammad Shabir
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Rough Set ◽  
Group Decision Making ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Group Decision ◽  
Research Direction ◽  
New Approach ◽  
Accuracy Of Approximation

Pawlak’s rough set theory based on single granulation has been extended to multi-granulation rough set structure in recent years. Multi-granulation rough set theory has become a flouring research direction in rough set theory. In this paper, we propose the notion of (α, β)-multi-granulation bipolar fuzzified rough set ((α, β)-MGBFRSs). For this purpose, a collection of bipolar fuzzy tolerance relations has been used. In the framework of multi-granulation, we proposed two types of (α, β)-multi-granulation bipolar fuzzified rough sets model. One is called the optimistic (α, β)-multi-granulation bipolar fuzzified rough sets ((α, β) o-MGBFRSs) and the other is called the pessimistic (α, β)-multi-granulation bipolar fuzzified rough sets ((α, β) p-MGBFRSs). Subsequently, a number of important structural properties and results of proposed models are investigated in detail. The relationships among the (α, β)-MGBFRSs, (α, β) o-MGBFRSs and (α, β) p-MGBFRSs are also established. In order to illustrate our proposed models, some examples are considered, which are helpful for applying this theory in practical issues. Moreover, several important measures associated with (α, β)-multi-granulation bipolar fuzzified rough set like the measure of accuracy, the measure of precision, and accuracy of approximation are presented. Finally, we construct a new approach to multi-criteria group decision-making method based on (α, β)-MGBFRSs, and the validity of this technique is illustrated by a practical application. Compared with the existing results, we also expound its advantages.

scholarly journals Two Types of Intuitionistic Fuzzy Covering Rough Sets and an Application to Multiple Criteria Group Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 462 ◽  
Author(s):  
Jingqian Wang ◽  
Xiaohong Zhang
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Group Decision Making ◽  
Rough Sets ◽  
Group Decision ◽  
Multiple Criteria ◽  
Approximation Spaces ◽  
Intuitionistic Fuzzy ◽  
Definition Of ◽  
Covering Rough Set

Intuitionistic fuzzy rough sets are constructed by combining intuitionistic fuzzy sets with rough sets. Recently, Huang et al. proposed the definition of an intuitionistic fuzzy (IF) β -covering and an IF covering rough set model. In this paper, some properties of IF β -covering approximation spaces and the IF covering rough set model are investigated further. Moreover, we present a novel methodology to the problem of multiple criteria group decision making. Firstly, some new notions and properties of IF β -covering approximation spaces are proposed. Secondly, we study the characterizations of Huang et al.’s IF covering rough set model and present a new IF covering rough set model for crisp sets in an IF environment. The relationships between these two IF covering rough set models and some other rough set models are investigated. Finally, based on the IF covering rough set model, Huang et al. also defined an optimistic multi-granulation IF rough set model. We present a novel method to multiple criteria group decision making problems under the optimistic multi-granulation IF rough set model.

scholarly journals A Novel Group Decision-Making Approach for Hesitant Fuzzy Linguistic Term Sets and Its Application to VIKOR

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Xiuli Geng ◽  
Yunting Jin ◽  
Yongzheng Zhang
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Group Decision Making ◽  
Rough Set Theory ◽  
Group Decision ◽  
Vikor Method ◽  
Context Free Grammar ◽  
Linguistic Term ◽  
Fuzzy Linguistic ◽  
Context Free

This paper develops a novel group decision-making (GDM) approach for solving multiple-criteria group decision-making (MCGDM) problems with uncertainty. The hesitant fuzzy linguistic term sets (HFLTSs) are applied to elicit the decision makers’ linguistic preferences due to their distinguished efficiency and flexibility in representing uncertainty. However, the existing context-free grammar for linguistic description cannot allow generating the linguistic expressions completely free to limit the richness of HFLTSs, and the related methods for dealing with HFLTSs also have limitations in aggregating HFLTSs with different lengths and types. Therefore, this paper proposes extended context-free grammar and a novel GDM approach for HFLTSs, considering the advantages of the rough set theory and OWA operators. The rough set theory can manage the uncertainty existing in the fuzzy representation and deal with HFLTSs represented by the 2-tuple fuzzy linguistic model to get rough number sets. The OWA operator can aggregate these sets with different numbers of elements into an interval simply and objectively. Then, an extended VIKOR method based on the proposed GDM approach for HFLTSs is presented to solve the MCGDM problems. Finally, two examples are given to illustrate the applicability and validity of the developed GDM approach and the hesitant VIKOR method through sensitivity and comparison analysis with other existing approaches.

scholarly journals Decision-Making Method based on Mixed Integer Linear Programming and Rough Set: A Case Study of Diesel Engine Quality and Assembly Clearance Data

2019 ◽  
Vol 11 (3) ◽  
pp. 620 ◽  
Author(s):  
Wenbing Chang ◽  
Xinglong Yuan ◽  
Yalong Wu ◽  
Shenghan Zhou ◽  
Jingsong Lei ◽  
...  
Keyword(s):  
Decision Making ◽  
Linear Programming ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Mixed Integer Linear Programming ◽  
Rough Set Theory ◽  
Mixed Integer ◽  
Quality Level ◽  
Proposed Model

The purpose of this paper is to establish a decision-making system for assembly clearance parameters and machine quality level by analyzing the data of assembly clearance parameters of diesel engine. Accordingly, we present an extension of the rough set theory based on mixed-integer linear programming (MILP) for rough set-based classification (MILP-FRST). Traditional rough set theory has two shortcomings. First, it is sensitive to noise data, resulting in a low accuracy of decision systems based on rough sets. Second, in the classification problem based on rough sets, the attributes cannot be automatically determined. MILP-FRST has the advantages of MILP in resisting noisy data and has the ability to select attributes flexibly and automatically. In order to prove the validity and advantages of the proposed model, we used the machine quality data and assembly clearance data of 29 diesel engines of a certain type to validate the proposed model. Experiments show that the proposed decision-making method based on MILP-FRST model can accurately determine the quality level of the whole machine according to the assembly clearance parameters.

Investment Risk Assessment of Hydraulic Engineering Based on Rough Set Theory

2014 ◽  
Vol 584-586 ◽  
pp. 2640-2643
Author(s):  
Zhi Ding Chen ◽  
Hai Man Gao ◽  
Qi Guo
Keyword(s):  
Risk Assessment ◽  
Decision Making ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Hydraulic Engineering ◽  
New Method ◽  
Decision Table ◽  
Investment Risk

The rough set theory is a new method for analyzing and dealing with data. By using this theory, we proposed a risk assessment algorithm based on rough set theory, which was described in detail in this paper. the decision table can be simplified and redundant attributes can be got rid of A method of inference based on the knowledge of rough sets and an example to show how to acquire the rules of new decision making, thus filling the method with a practical and publicizing value are given.

Uncertainty and Vagueness Concepts in Decision Making

2011 ◽  
pp. 901-909
Author(s):  
Georg Peters
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
17Th Century ◽  
Basic Principles ◽  
In The Beginning

One of the main challenges in decision making is how to deal with uncertainty and vagueness. The classic uncertainty concept is probability, which goes back to the 17th century. Possible candidates for the title of father of probability are Bernoulli, Laplace, and Pascal. Some 40 years ago, Zadeh (1965) introduced the concept of fuzziness, which is sometimes interpreted as one form of probability. However, we will show that the terms fuzzy and probability are complementary. Recently, in the beginning of the ’80s, Pawlak (1982) suggested rough sets to manage uncertainties. The objective of this article is to give a basic introduction into probability, fuzzy set, and rough set theory and show their potential in dealing with uncertainty and vagueness. The article is structured as follows. In the next three sections we will discuss the basic principles of probability, fuzzy sets, and rough sets, and their relationship with each other. The article concludes with a short summary.

scholarly journals An application of multicriteria group decision making by soft covering based rough sets

Filomat ◽  
2015 ◽  
Vol 29 (1) ◽  
pp. 209-219 ◽  
Author(s):  
Şaziye Yüksel ◽  
Naime Tozlu ◽  
Tuğba Dizman
Keyword(s):  
Prostate Cancer ◽  
Decision Making ◽  
Cancer Risk ◽  
Rough Set ◽  
Group Decision Making ◽  
Rough Sets ◽  
Group Decision ◽  
Prostate Cancer Risk ◽  
Multicriteria Group Decision Making

In this work we define soft covering based rough set and present its related properties. Also we present an example in medicine which aims to find the patients with high prostate cancer risk. Our datas are 56 patients from Selcuk University Meram Medicine Faculty.

Analysing diabetes using rough sets

2020 ◽  
pp. 533-538
Author(s):  
S. Arjun Raj ◽  
M. Vigneshwaran
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
International Diabetes Federation ◽  
Published Data ◽  
Lower And Upper Approximations

In this article we use the rough set theory to generate the set of decision concepts in order to solve a medical problem.Based on officially published data by International Diabetes Federation (IDF), rough sets have been used to diagnose Diabetes.The lower and upper approximations of decision concepts and their boundary regions have been formulated here.

A User-Centered Medical Device Design Decision Making Approach Using Hybrid Rough Cooperative Game Model

2021 ◽  
Author(s):  
Liting Jing ◽  
Junfeng Ma
Keyword(s):  
Decision Making ◽  
Medical Device ◽  
Set Theory ◽  
Cooperative Game ◽  
Rough Set ◽  
Rough Set Theory ◽  
Design Decision ◽  
Device Design ◽  
Medical Device Design ◽  
User Centered

Abstract With the advancement of new technologies and diverse customer-centered design requirements, the medical device design decision making becomes challenge. Incorporating multiple stakeholders’ requirements into the medical device design will significantly affect the market competitiveness and performance. The classic design decision making approaches mainly focused on design criteria priority determination and conceptual schemes evaluation, which lack the capacity of reflecting the interdependence of interest among stakeholders and capturing the ambiguous influence on the overall design expectations, leading to the unreliable decision making results. In order to relax these constraints in the medical device design, this paper incorporates rough set theory with cooperative game theory model to develop a novel user-centered design decision making framework. The proposed approach is composed of three components: 1) end/professional user needs identification and classification, 2) evaluation criteria correlation diagram and scheme value matrix establishment using rough set theory; and 3) fuzzy coalition utility model development to obtain optimal desirability considering users’ conflict interests. We used a blood pressure meter case study to demonstrate and validate the proposed approach. Compared with the traditional Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) approach, the proposed approach is more robust.

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