A three-way decision method based on fuzzy rough set models under incomplete environments

2021 ◽  
Author(s):  
Jin Ye ◽  
Jianming Zhan ◽  
Bingzhen Sun
Keyword(s):  
Rough Set ◽  
Fuzzy Rough Set ◽  
Decision Method

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 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.

Bipolar fuzzy rough set model on two different universes and its application

2012 ◽  
Vol 35 ◽  
pp. 94-101 ◽  
Author(s):  
Hai-Long Yang ◽  
Sheng-Gang Li ◽  
Shouyang Wang ◽  
Jue Wang
Keyword(s):  
Rough Set ◽  
Fuzzy Rough Set

GENERALIZED FUZZY ROUGH SETS BY CONDITIONAL PROBABILITY RELATIONS

2002 ◽  
Vol 16 (07) ◽  
pp. 865-881 ◽  
Author(s):  
ROLLY INTAN ◽  
MASAO MUKAIDONO
Keyword(s):  
Conditional Probability ◽  
Rough Set ◽  
Real World ◽  
Rough Sets ◽  
Similarity Relation ◽  
Fuzzy Rough Set ◽  
Fuzzy Similarity ◽  
Fuzzy Similarity Relation ◽  
Real World Applications ◽  
The Universe

In 1982, Pawlak proposed the concept of rough sets with a practical purpose of representing indiscernibility of elements or objects in the presence of information systems. Even if it is easy to analyze, the rough set theory built on a partition induced by equivalence relation may not provide a realistic view of relationships between elements in real-world applications. Here, coverings of, or nonequivalence relations on, the universe can be considered to represent a more realistic model instead of a partition in which a generalized model of rough sets was proposed. In this paper, first a weak fuzzy similarity relation is introduced as a more realistic relation in representing the relationship between two elements of data in real-world applications. Fuzzy conditional probability relation is considered as a concrete example of the weak fuzzy similarity relation. Coverings of the universe is provided by fuzzy conditional probability relations. Generalized concepts of rough approximations and rough membership functions are proposed and defined based on coverings of the universe. Such generalization is considered as a kind of fuzzy rough set. A more generalized fuzzy rough set approximation of a given fuzzy set is proposed and discussed as an alternative to provide interval-value fuzzy sets. Their properties are examined.

Unsupervised fuzzy-rough set-based dimensionality reduction

2013 ◽  
Vol 229 ◽  
pp. 106-121 ◽  
Author(s):  
Neil Mac Parthaláin ◽  
Richard Jensen
Keyword(s):  
Dimensionality Reduction ◽  
Rough Set ◽  
Fuzzy Rough Set
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