scholarly journals Fuzzy covering-based rough set on two different universes and its application

2021 ◽  
Author(s):  
Bin Yang
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Multiple Criteria Decision Making ◽  
Multiple Criteria ◽  
Extension Principle ◽  
Upper Approximation ◽  
New Type ◽  
New Perspective ◽  
Definition Of ◽  
Two Universes

Abstract In this paper, we propose a new type of fuzzy covering-based rough set model over two different universes by using Zadeh’s extension principle. We mainly address the following issues in this paper. First, we present the definition of fuzzy β-neighborhood, which can be seen as a fuzzy mapping from a universe to the set of fuzzy sets on another universe and study its properties. Then we define a new type of fuzzy covering-based rough set model on two different universes and investigate the properties of this model. Meanwhile, we give a necessary and sufficient condition under which two fuzzy β-coverings to generate the same fuzzy covering lower approximation or the same fuzzy covering upper approximation. Moreover, matrix representations of thefuzzy covering lower and fuzzy covering upper approximation operators are investigated. Finally, we propose a new approach to a kind of multiple criteria decision making problem based on fuzzy covering-based rough set model over two universes. The proposed models not onlyenrich the theory of fuzzy covering-based rough set but also provide a new perspective for multiple criteria decision making with uncertainty.

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 Micro Family Businesses in the Czech Republic from the Perspective of Multiple Criteria Decision-Making

2021 ◽  
Vol 92 ◽  
pp. 05021
Author(s):  
Vojtěch Meier
Keyword(s):  
Decision Making ◽  
Czech Republic ◽  
Family Business ◽  
Multiple Criteria Decision Making ◽  
Family Businesses ◽  
Multiple Criteria ◽  
Legal Form ◽  
The Czech Republic ◽  
The Family ◽  
Definition Of

Research background: Family businesses are undoubtedly important in both the Czech and international economy. They also play a crucial part in globalization. They have always been providing the largest job source in the private sector all over the world. However, over all these years, there has not been a unified definition of family business, which makes the government hard to distinguish between family and non – family business. Thus, this complicated the administrative and legal process. Finally, in 2019, the definition of the family business in the Czech Republic has been specified, which has facilitated many administrative and legal processes. Simultaneously, the management of Czech family businesses is currently facing the first “post-revolutionary” transition of generations. Many family businesses are deciding whether to maintain or to change the type of business entities. Purpose of the article: This article aims to determine the most advantageous legal form of business for micro family businesses. Methods: This article uses the Saaty pair comparison method and TOPSIS method. In addition to the methods of analysis, synthesis, and comparison, the selected methods of multiple criteria decision making are used in the article. Findings & Value added: The results of the decision analysis revealed that, based on the criteria considered (legal, accounting, tax and managerial), the most optimal legal form of the family business is self-employed. Apart from the results, the research adds value to this topic for the Czech business environment, in which future scholars can compare between the Czech Republic and the other countries.

scholarly journals New Multigranulation Neutrosophic Rough Set with Applications

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 578 ◽  
Author(s):  
Chunxin Bo ◽  
Xiaohong Zhang ◽  
Songtao Shao ◽  
Florentin Smarandache
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Neutrosophic Set ◽  
Type I ◽  
Type Ii ◽  
Type Iii ◽  
Proposed Model ◽  
Definition Of ◽  
Two Universes ◽  
Special Case

After the neutrosophic set (NS) was proposed, NS was used in many uncertainty problems. The single-valued neutrosophic set (SVNS) is a special case of NS that can be used to solve real-word problems. This paper mainly studies multigranulation neutrosophic rough sets (MNRSs) and their applications in multi-attribute group decision-making. Firstly, the existing definition of neutrosophic rough set (we call it type-I neutrosophic rough set (NRSI) in this paper) is analyzed, and then the definition of type-II neutrosophic rough set (NRSII), which is similar to NRSI, is given and its properties are studied. Secondly, a type-III neutrosophic rough set (NRSIII) is proposed and its differences from NRSI and NRSII are provided. Thirdly, single granulation NRSs are extended to multigranulation NRSs, and the type-I multigranulation neutrosophic rough set (MNRSI) is studied. The type-II multigranulation neutrosophic rough set (MNRSII) and type-III multigranulation neutrosophic rough set (MNRSIII) are proposed and their different properties are outlined. We found that the three kinds of MNRSs generate tcorresponding NRSs when all the NRs are the same. Finally, MNRSIII in two universes is proposed and an algorithm for decision-making based on MNRSIII is provided. A car ranking example is studied to explain the application of the proposed model.

scholarly journals A New Grey Approach for Using SWARA and PIPRECIA Methods in a Group Decision-Making Environment

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1554
Author(s):  
Dragiša Stanujkić ◽  
Darjan Karabašević ◽  
Gabrijela Popović ◽  
Predrag S. Stanimirović ◽  
Muzafer Saračević ◽  
...  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Multiple Criteria Decision Making ◽  
Grey System Theory ◽  
Multiple Criteria ◽  
Decision Making Process ◽  
Grey System ◽  
Criteria Weights

The environment in which the decision-making process takes place is often characterized by uncertainty and vagueness and, because of that, sometimes it is very hard to express the criteria weights with crisp numbers. Therefore, the application of the Grey System Theory, i.e., grey numbers, in this case, is very convenient when it comes to determination of the criteria weights with partially known information. Besides, the criteria weights have a significant role in the multiple criteria decision-making process. Many ordinary multiple criteria decision-making methods are adapted for using grey numbers, and this is the case in this article as well. A new grey extension of the certain multiple criteria decision-making methods for the determination of the criteria weights is proposed. Therefore, the article aims to propose a new extension of the Step-wise Weight Assessment Ratio Analysis (SWARA) and PIvot Pairwise Relative Criteria Importance Assessment (PIPRECIA) methods adapted for group decision-making. In the proposed approach, attitudes of decision-makers are transformed into grey group attitudes, which allows taking advantage of the benefit that grey numbers provide over crisp numbers. The main advantage of the proposed approach in relation to the use of crisp numbers is the ability to conduct different analyses, i.e., considering different scenarios, such as pessimistic, optimistic, and so on. By varying the value of the whitening coefficient, different weights of the criteria can be obtained, and it should be emphasized that this approach gives the same weights as in the case of crisp numbers when the whitening coefficient has a value of 0.5. In addition, in this approach, the grey number was formed based on the median value of collected responses because it better maintains the deviation from the normal distribution of the collected responses. The application of the proposed approach was considered through two numerical illustrations, based on which appropriate conclusions were drawn.

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