scholarly journals Three-Way Decisions Making Using Covering Based Fractional Orthotriple Fuzzy Rough Set Model

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1121 ◽  
Author(s):  
Shougi S. Abosuliman ◽  
Saleem Abdullah ◽  
Muhammad Qiyas
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Rough Sets ◽  
Fuzzy Numbers ◽  
Loss Functions ◽  
Multi Criteria Decision Making ◽  
Expected Loss ◽  
Fuzzy Rough Set ◽  
Decision Method ◽  
Proposed Model

On the basis of decision-theoretical rough sets (DTRSs), the three-way decisions give new model of decision approach for deal with the problem of decision. This proposed model of decision method is based on the loss function of DTRSs. First, the concept of fractional orthotriple fuzzy β -covering (FOF β -covering) and fractional orthotriple fuzzy β -neighborhood (FOF β -neighborhood) was introduced. We combined loss feature of DTRSs with covering-based fractional orthotriple fuzzy rough sets (CFOFSs) under the fractional orthotriple fuzzy condition. Secondly, we proposed a new FOF-covering decision-theoretical rough sets model (FOFCDTRSs) and developed related properties. Then, based on the grade of positive, neutral and negative membership of fractional orthotriple fuzzy numbers (FOFNs), five methods are established for addressing the expected loss expressed in the form of FOFNs and the corresponding three-way decisions are also derived. Based on this, we presented a FOFCDTRS-based algorithm for multi-criteria decision making (MCDM). Then, an example verifies the feasibility of the five methods for solving the MCDM problem. Finally, by comparing the results of the decisions of five methods with different loss functions.

scholarly journals Overlap Functions Based (Multi-Granulation) Fuzzy Rough Sets and Their Applications in MCDM

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1779
Author(s):  
Xiaofeng Wen ◽  
Xiaohong Zhang
Keyword(s):  
Decision Making ◽  
Theoretical Analysis ◽  
Rough Set ◽  
Rough Sets ◽  
Group Decision ◽  
Decision Makers ◽  
Multi Criteria Decision Making ◽  
Fuzzy Rough Sets ◽  
Fuzzy Rough Set ◽  
New Class

Through a combination of overlap functions (which have symmetry and continuity) and a fuzzy β-covering fuzzy rough set (FCFRS), a new class of FCFRS models is established, and the basic properties of the new fuzzy β-neighborhood lower and upper approximate operators are analyzed and studied. Then the model is extended to the case of multi-granulation, and the properties of a multi-granulation optimistic fuzzy rough set are mainly investigated. By theoretical analysis for the fuzzy covering (multi-granulation) fuzzy rough sets, the solutions to problems in multi-criteria decision-making (MCDM) and multi-criteria group decision-making (MCGDM) problem methods are built, respectively. To fully illustrate these methodologies, effective examples are developed. By comparing the method proposed in this paper with the existing methods, we find that the method proposed is more suitable for solving decision making problems than the traditional methods, while the results obtained are more helpful to decision makers.

Three-way decisions with decision-theoretic rough sets based on covering-based q-rung orthopair fuzzy rough set model

2021 ◽  
pp. 1-21
Author(s):  
Fang Liu ◽  
Yi Liu ◽  
Saleem Abdullah
Keyword(s):  
Rough Set ◽  
Loss Function ◽  
Rough Sets ◽  
Fuzzy Numbers ◽  
Fuzzy Rough Set ◽  
Decision Method ◽  
Fuzzy Environment ◽  
Multi Attribute Decision Making ◽  
The Stability ◽  
Function Matrix

Based on decision theory rough sets (DTRSs), three-way decisions (TWDs) provide a risk decision method for solving multi-attribute decision making (MADM) problems. The loss function matrix of DTRS is the basis of this method. In order to better solve the uncertainty and ambiguity of the decision problem, we introduce the q-rung orthopair fuzzy numbers (q-ROFNs) into the loss function. Firstly, we introduce concepts of q-rung orthopair fuzzy β-covering (q-ROF β-covering) and q-rung orthopair fuzzy β-neighborhood (q-ROF β-neighborhood). We combine covering-based q-rung orthopair fuzzy rough set (Cq-ROFRS) with the loss function matrix of DTRS in the q-rung orthopair fuzzy environment. Secondly, we propose a new model of q-ROF β-covering DTRSs (q-ROFCDTRSs) and elaborate its relevant properties. Then, by using membership and non-membership degrees of q-ROFNs, five methods for solving expected losses based on q-ROFNs are given and corresponding TWDs are also derived. On this basis, we present an algorithm based on q-ROFCDTRSs for MADM. Then, the feasibility of these five methods in solving the MADM problems is verified by an example. Finally, the sensitivity of each parameter and the stability and effectiveness of these five methods are compared and analyzed.

scholarly journals Some New Covering-Based Multigranulation Fuzzy Rough Sets and Corresponding Application in Multicriteria Decision Making

2021 ◽  
Vol 2021 ◽  
pp. 1-25
Author(s):  
Zaibin Chang ◽  
Lingling Mao
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Rough Sets ◽  
Large Scale ◽  
Rough Set Theory ◽  
Multicriteria Decision Making ◽  
Matrix Representations ◽  
Fuzzy Rough Set ◽  
Multicriteria Decision ◽  
Multigranulation Rough Set

Multigranulation rough set theory is an important tool to deal with the problem of multicriteria information system. The notion of fuzzy β -neighborhood has been used to construct some covering-based multigranulation fuzzy rough set (CMFRS) models through multigranulation fuzzy measure. But the β -neighborhood has not been used in these models, which can be seen as the bridge of fuzzy covering-based rough sets and covering-based rough sets. In this paper, the new concept of multigranulation fuzzy neighborhood measure and some types of covering-based multigranulation fuzzy rough set (CMFRS) models based on it are proposed. They can be seen as the further combination of fuzzy sets: covering-based rough sets and multigranulation rough sets. Moreover, they are used to solve the problem of multicriteria decision making. Firstly, the definition of multigranulation fuzzy neighborhood measure is given based on the concept of β -neighborhood. Moreover, four types of CMFRS models are constructed, as well as their characteristics and relationships. Then, novel matrix representations of them are investigated, which can satisfy the need of knowledge discovery from large-scale covering information systems. The matrix representations can be more easily implemented than set representations by computers. Finally, we apply them to manage the problem of multicriteria group decision making (MCGDM) and compare them with other methods.

Multi-Criteria Decision Making in Marketing by Using Fuzzy Rough Set

2017 ◽  
pp. 100-118 ◽  
Author(s):  
Tapan Kumar Das
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Good Choice ◽  
Multi Criteria Decision Making ◽  
Fuzzy Rough Set ◽  
Considerable Uncertainty ◽  
Intuitionistic Fuzzy ◽  
Intelligent Technique ◽  
Operating Environments ◽  
Business Dynamics

Most of the marketing problems are complex and unstructured due to the business dynamics and considerable uncertainty involved in the operating environments. Hence decision making in marketing involves evaluation of several parameters and thus multi criteria decision makings are a good choice in most of the decision-making tasks like supplier selection; market places selection; target marketing; etc. This chapter begins with a brief introduction of the theory of rough set which is an intelligent technique for handling uncertainty aspect in the data. However, the notions of fuzzy rough set and intuitionistic fuzzy rough (IFR) sets are defined, and its properties are studied. Thereafter rough set on two universal sets has been studied. In addition, intuitionistic fuzzy rough set on two universal sets has been extensively studied. Furthermore, this chapter shows that intuitionistic fuzzy rough set can be successfully practiced in decision making problems.

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.

Novel multi-criteria decision-making methods with soft rough q-rung orthopair fuzzy sets and q-rung orthopair fuzzy soft rough sets

2021 ◽  
pp. 1-19
Author(s):  
Muhammad Riaz ◽  
Nawazish Ali ◽  
Bijan Davvaz ◽  
Muhammad Aslam
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Rough Sets ◽  
Smart Phone ◽  
Optimal Decision ◽  
Multi Criteria Decision Making ◽  
Public Parks ◽  
Decision Attributes ◽  
Develop Algorithm ◽  
Soft Rough Set

The aim of this paper is to introduce the concepts of soft rough q-rung orthopair fuzzy set (SRqROFS) and q-rung orthopair fuzzy soft rough set (qROPFSRS) based on soft rough set and fuzzy soft relation, respectively. We define some fundamental operations on both SRqROFS and qROPFSRS and discuss some key properties of these models by using upper and lower approximation operators. The suggested models are superior than existing soft rough sets, intuitionistic fuzzy soft rough sets and Pythagorean fuzzy soft rough sets. These models are more efficient to deal with vagueness in multi-criteria decision-making (MCDM) problems. We develop Algorithm i (i = 1, 2, 3, 4, 5) for the construction of SRqROFS, construction of qROFSRS, selection of a smart phone, ranking of beautiful public parks, and ranking of government challenges, respectively. The notions of upper reduct and lower reduct based on the upper approximations and lower approximations by variation of the decision attributes are also proposed. The applications of the proposed MCDM methods are demonstrated by respective numerical examples. The idea of core is used to find a unanimous optimal decision which is obtained by taking the intersection of all lower reducts and upper reducts.

Logarithmic Entropy Measures for Fuzzy Rough Set and their Application in Decision Making Problem

2020 ◽  
Vol 9 (2) ◽  
pp. 80-97
Author(s):  
Omdutt Sharma ◽  
Priti Gupta
Keyword(s):  
Decision Making ◽  
Information Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Critical Problem ◽  
Fuzzy Rough Set ◽  
Probabilistic Measure ◽  
Entropy Measures ◽  
Decision Making Problem ◽  
Probabilistic Entropy

Decision-making is a critical problem in various circumstances where some vagueness and ambiguity is found in information. To handle these types of problems, entropy is an important measure of information theory which is exploited to evaluate the uncertain degree of any data. There are two methodologies to determine the entropy, one is probabilistic in nature and other is non-probabilistic. It is shown that for every probabilistic measure there is a corresponding non-probabilistic measure. In this article, some logarithmic non-probabilistic entropy measures have been proposed for the fuzzy rough set corresponding to existing probabilistic entropy measures. The proposed measures are employed in a decision-making problem, which is related to the agriculture. Finally, these proposed measures are compared with the existing trigonometric entropy measures for fuzzy rough sets.

Multi Criteria Decision Making Techniques for Asset Selection

2019 ◽  
Vol 13 ◽  
Author(s):  
Shraddha Harode ◽  
Manoj Jha ◽  
Namita Srivastava
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Stock Exchange ◽  
Medical Engineering ◽  
Performance Measure ◽  
Soft Set ◽  
Multi Criteria Decision Making ◽  
Fuzzy Rough Set ◽  
Financial Trading ◽  
Level Soft Set

: A majority of the problems faced by many sophisticated fields, such as, Medical, Engineering, Environment, Social, Financial Mathematics and Economics, are due to uncertainty and ambiguity. Decision-making methods play a crucial role in solving these problems by getting the optimal portfolio. The Fuzzy Soft Set (FSS) is one such decision-making method, which is easily solvable. In this article, an appropriate selection of assets is introduced in financial trading, with the help of different multi-criteria decision-making approaches, such as, Level Soft Set (LSS), Mean Potentiality Approach (MPA), Non-Fuzzy Set and Soft Hesitant Fuzzy Rough Set (SHFRS). Following comparison of the Performance Measure, it was found that the Soft Hesitant Fuzzy Rough Set was capable of constructing a portfolio of assets according to the investor’s preference. In addition to this assessment of the investment, the Firefly Optimization algorithm was used to obtain the proportion of assets in the portfolio. Furthermore, the Bombay Stock Exchange, India (BSE) data was used to check the effectiveness and performance of the Soft Hesitant Fuzzy Rough set algorithm, to note its effectiveness, based on the performance.

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