Belief function of Pythagorean fuzzy rough approximation space and its applications

2020 ◽  
Vol 119 ◽  
pp. 58-80
Author(s):  
Shao-Pu Zhang ◽  
Pin Sun ◽  
Ju-Sheng Mi ◽  
Tao Feng
Keyword(s):  
Belief Function ◽  
Approximation Space ◽  
Rough Approximation

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 A Lattice-Theoretic Approach to Multigranulation Approximation Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xiaoli He ◽  
Yanhong She
Keyword(s):  
Distributive Lattice ◽  
Mathematical Structure ◽  
Galois Connection ◽  
Theoretic Approach ◽  
Approximation Space ◽  
Approximation Spaces ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Definable Sets

In this paper, we mainly investigate the equivalence between multigranulation approximation space and single-granulation approximation space from the lattice-theoretic viewpoint. It is proved that multigranulation approximation space is equivalent to single-granulation approximation space if and only if the pair of multigranulation rough approximation operators(Σi=1nRi¯,Σi=1nRi_)forms an order-preserving Galois connection, if and only if the collection of lower (resp., upper) definable sets forms an (resp., union) intersection structure, if and only if the collection of multigranulation upper (lower) definable sets forms a distributive lattice whenn=2, and if and only if∀X⊆U,  Σi=1nRi_(X)=∩i=1nRi_(X). The obtained results help us gain more insights into the mathematical structure of multigranulation approximation spaces.

The approximation set of a vague set in rough approximation space

2015 ◽  
Vol 300 ◽  
pp. 1-19 ◽  
Author(s):  
Qinghua Zhang ◽  
Jin Wang ◽  
Guoyin Wang ◽  
Hong Yu
Keyword(s):  
Approximation Space ◽  
Vague Set ◽  
Rough Approximation ◽  
Approximation Set

scholarly journals A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Tianyu Xue ◽  
Zhan’ao Xue ◽  
Huiru Cheng ◽  
Jie Liu ◽  
Tailong Zhu
Keyword(s):  
Rough Sets ◽  
Rough Set Theory ◽  
Binary Relations ◽  
Approximation Space ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Fuzzy Binary Relation ◽  
Novel Method ◽  
Interval Valued

Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are shown to be equivalent to the generalized interval fuzzy rough approximation operators introduced by Dubois, which are determined by any interval-valued fuzzy binary relation expressed in a generalized approximation space. Main properties of these operators are discussed under different interval-valued fuzzy binary relations, and the illustrative examples are given to demonstrate the main features of the proposed operators.

N-soft rough sets and its applications

2021 ◽  
Vol 40 (1) ◽  
pp. 565-573
Author(s):  
Di Zhang ◽  
Pi-Yu Li ◽  
Shuang An
Keyword(s):  
Decision Making ◽  
Hybrid Model ◽  
Rough Sets ◽  
Real Life ◽  
Decision Problems ◽  
Multi Criteria Decision Making ◽  
Approximation Space ◽  
Soft Sets ◽  
Approximation Operators ◽  
Rough Approximation

In this paper, we propose a new hybrid model called N-soft rough sets, which can be seen as a combination of rough sets and N-soft sets. Moreover, approximation operators and some useful properties with respect to N-soft rough approximation space are introduced. Furthermore, we propose decision making procedures for N-soft rough sets, the approximation sets are utilized to handle problems involving multi-criteria decision-making(MCDM), aiming at electing the optional objects and the possible optional objects based on their attribute set. The algorithm addresses some limitations of the extended rough sets models in dealing with inconsistent decision problems. Finally, an application of N-soft rough sets in multi-criteria decision making is illustrated with a real life example.

Uncertainty Measure Based on Evidence Theory

2013 ◽  
Vol 329 ◽  
pp. 344-348
Author(s):  
Shao Pu Zhang ◽  
Tao Feng
Keyword(s):  
Information System ◽  
Information Fusion ◽  
Rough Set Theory ◽  
Evidence Theory ◽  
Belief Function ◽  
Mass Function ◽  
Uncertainty Measure ◽  
Rough Approximation ◽  
Uncertainty Information ◽  
Uncertainty Method

Evidence theory is an effective method to deal with uncertainty information. And uncertainty measure is to reflect the uncertainty of an information system. Thus we want to merge evidence theory with uncertainty method in order to measure the roughness of a rough approximation space. This paper discusses the information fusion and uncertainty measure based on rough set theory. First, we propose a new method of information fusion based on the Bayse function, and define a pair of belief function and plausibility function using the fused mass function in an information system. Then we construct entropy for every decision class to measure the roughness of every decision class, and entropy for decision information system to measure the consistence of decision table.

Extended two-dimensional belief function based on divergence measurement

2020 ◽  
pp. 1-8
Author(s):  
Jianping Fan ◽  
Jing Wang ◽  
Meiqin Wu
Keyword(s):  
Belief Function ◽  
Distribution Functions ◽  
Divergence Measure ◽  
Uncertain Information ◽  
Belief Functions ◽  
Two Dimensional ◽  
Probability Distribution Functions ◽  
Basic Probability ◽  
The Difference ◽  
Supporting Degree

The two-dimensional belief function (TDBF = (mA, mB)) uses a pair of ordered basic probability distribution functions to describe and process uncertain information. Among them, mB includes support degree, non-support degree and reliability unmeasured degree of mA. So it is more abundant and reasonable than the traditional discount coefficient and expresses the evaluation value of experts. However, only considering that the expert’s assessment is single and one-sided, we also need to consider the influence between the belief function itself. The difference in belief function can measure the difference between two belief functions, based on which the supporting degree, non-supporting degree and unmeasured degree of reliability of the evidence are calculated. Based on the divergence measure of belief function, this paper proposes an extended two-dimensional belief function, which can solve some evidence conflict problems and is more objective and better solve a class of problems that TDBF cannot handle. Finally, numerical examples illustrate its effectiveness and rationality.

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