A Characterization for Intuitionistic Fuzzy Sets Based on the Assistant Sets Generated by S-Rough Sets

2009 ◽  
pp. 627-631 ◽  
Author(s):  
Meng-Lei Lin
Keyword(s):  
Fuzzy Sets ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy

Rough Sets and Approximate Reasoning

2014 ◽  
pp. 180-228 ◽  
Author(s):  
B. K. Tripathy
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Point Of View ◽  
Approximate Reasoning ◽  
Human Reasoning ◽  
Intuitionistic Fuzzy ◽  
Application Point ◽  
Future Work

Several models have been introduced to capture impreciseness in data. Fuzzy sets introduced by Zadeh and Rough sets introduced by Pawlak are two of the most popular such models. In addition, the notion of intuitionistic fuzzy sets introduced by Atanassov and the hybrid models obtained thereof have been very fruitful from the application point of view. The introduction of fuzzy logic and the approximate reasoning obtained through it are more realistic as they are closer to human reasoning. Equality of sets in crisp mathematics is too restricted from the application point of view. Therefore, extending these concepts, three types of approximate equalities were introduced by Novotny and Pawlak using rough sets. These notions were found to be restrictive in the sense that they again boil down to equality of sets and also the lower approximate equality is artificial. Keeping these points in view, three other types of approximate equalities were introduced by Tripathy in several papers. These approximate equalities were further generalised to cover the approximate equalities of fuzzy sets and intuitionistic fuzzy sets by him. In addition, considering the generalisations of basic rough sets like the covering-based rough sets and multigranular rough sets, the study has been carried out further. In this chapter, the authors provide a comprehensive study of all these forms of approximate equalities and illustrate their applicability through several examples. In addition, they provide some problems for future work.

scholarly journals Intuitionistic Fuzzy Soft Rough Set and Its Application in Decision Making

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Haidong Zhang ◽  
Lan Shu ◽  
Shilong Liao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Mathematical Tool ◽  
Intuitionistic Fuzzy ◽  
Rough Approximation ◽  
Soft Rough Set

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. In this paper, we present concepts of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets, and investigate some properties of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets in detail. Furthermore, classical representations of intuitionistic fuzzy soft rough approximation operators are presented. Finally, we develop an approach to intuitionistic fuzzy soft rough sets based on decision making and a numerical example is provided to illustrate the developed approach.

scholarly journals Three-Way Decisions with Interval-Valued Intuitionistic Fuzzy Decision-Theoretic Rough Sets in Group Decision-Making

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 281 ◽  
Author(s):  
Dajun Ye ◽  
Decui Liang ◽  
Pei Hu
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Rough Sets ◽  
Group Decision ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Decision ◽  
Grey Correlation ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

In this article, we demonstrate how interval-valued intuitionistic fuzzy sets (IVIFSs) can function as extended intuitionistic fuzzy sets (IFSs) using the interval-valued intuitionistic fuzzy numbers (IVIFNs) instead of precision numbers to describe the degree of membership and non-membership, which are more flexible and practical in dealing with ambiguity and uncertainty. By introducing IVIFSs into three-way decisions, we provide a new description of the loss function. Thus, we firstly propose a model of interval-valued intuitionistic fuzzy decision-theoretic rough sets (IVIFDTRSs). According to the basic framework of IVIFDTRSs, we design a strategy to address the IVIFNs and deduce three-way decisions. Then, we successfully extend the results of IVIFDTRSs from single-person decision-making to group decision-making. In this situation, we adopt a grey correlation accurate weighted determining method (GCAWD) to compute the weights of decision-makers, which integrates the advantages of the accurate weighted determining method and grey correlation analysis method. Moreover, we utilize the interval-valued intuitionistic fuzzy weighted averaging (IIFWA) operation to count the aggregated scores and the accuracies of the expected losses. By comparing these scores and accuracies, we design a simple and straightforward algorithm to deduce three-way decisions for group decision-making. Finally, we use an illustrative example to verify our results.

On Theory of Multisets and Applications

2016 ◽  
pp. 1-22
Author(s):  
B. K. Tripathy
Keyword(s):  
Fuzzy Sets ◽  
Model Uncertainty ◽  
Rough Sets ◽  
Real Life ◽  
Intuitionistic Fuzzy Sets ◽  
Current Status ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Mathematics ◽  
Basic Sets

Although multiple occurrences of elements are immaterial in sets, in real life situations repetition of elements is useful. So, the notion of multisets (also called as bags) was introduced, where repetition of elements is taken into account. Fuzzy set, intuitionistic (a misnomer here as intuitionistic mathematics has nothing to do with its fuzzy counterpart) fuzzy sets, rough sets and soft sets are extensions of the basic notion of sets as they model uncertainty in data. Following this multisets have been extended to fuzzy multisets, intuitionistic fuzzy sets, rough multisets and soft multisets. Many properties of basic sets have been extended to the context of multisets, fuzzy multisets, intuitionistic fuzzy sets, rough multisets and soft multisets. Several applications of different multisets mentioned above are found in literature. In this chapter, it is our aim to introduce the different concepts of multisets, their properties, current status and highlight their applications.

scholarly journals Multi-Granulation Graded Rough Intuitionistic Fuzzy Sets Models Based on Dominance Relation

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 446 ◽  
Author(s):  
Zhan-ao Xue ◽  
Min-jie Lv ◽  
Dan-jie Han ◽  
Xian-wei Xin
Keyword(s):  
Information Systems ◽  
Fuzzy Sets ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Dominance Relation ◽  
Classification Error ◽  
Type I ◽  
Type Ii ◽  
Intuitionistic Fuzzy ◽  
Relation Type

From the perspective of the degrees of classification error, we proposed graded rough intuitionistic fuzzy sets as the extension of classic rough intuitionistic fuzzy sets. Firstly, combining dominance relation of graded rough sets with dominance relation in intuitionistic fuzzy ordered information systems, we designed type-I dominance relation and type-II dominance relation. Type-I dominance relation reduces the errors caused by single theory and improves the precision of ordering. Type-II dominance relation decreases the limitation of ordering by single theory. After that, we proposed graded rough intuitionistic fuzzy sets based on type-I dominance relation and type-II dominance relation. Furthermore, from the viewpoint of multi-granulation, we further established multi-granulation graded rough intuitionistic fuzzy sets models based on type-I dominance relation and type-II dominance relation. Meanwhile, some properties of these models were discussed. Finally, the validity of these models was verified by an algorithm and some relative examples.

scholarly journals Novel Three-Way Decisions Models with Multi-Granulation Rough Intuitionistic Fuzzy Sets

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 662 ◽  
Author(s):  
Zhan-Ao Xue ◽  
Dan-Jie Han ◽  
Min-Jie Lv ◽  
Min Zhang
Keyword(s):  
Fuzzy Sets ◽  
Rough Sets ◽  
Score Function ◽  
Intuitionistic Fuzzy Sets ◽  
Joint Models ◽  
Calculating Method ◽  
Intuitionistic Fuzzy ◽  
Construction Methods ◽  
Multiple Granularities ◽  
Comprehensive Score

The existing construction methods of granularity importance degree only consider the direct influence of single granularity on decision-making; however, they ignore the joint impact from other granularities when carrying out granularity selection. In this regard, we have the following improvements. First of all, we define a more reasonable granularity importance degree calculating method among multiple granularities to deal with the above problem and give a granularity reduction algorithm based on this method. Besides, this paper combines the reduction sets of optimistic and pessimistic multi-granulation rough sets with intuitionistic fuzzy sets, respectively, and their related properties are shown synchronously. Based on this, to further reduce the redundant objects in each granularity of reduction sets, four novel kinds of three-way decisions models with multi-granulation rough intuitionistic fuzzy sets are developed. Moreover, a series of concrete examples can demonstrate that these joint models not only can remove the redundant objects inside each granularity of the reduction sets, but also can generate much suitable granularity selection results using the designed comprehensive score function and comprehensive accuracy function of granularities.

The Intuitionistic Fuzzy S-Rough Sets Model and Dynamic Transfer Degree

2014 ◽  
Vol 513-517 ◽  
pp. 4352-4356
Author(s):  
Jun Hong Hu ◽  
Guo Dong Gu ◽  
Fu Xian Liu
Keyword(s):  
Fuzzy Sets ◽  
Equivalence Relation ◽  
Fuzzy System ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Rough Sets Theory ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Characteristic ◽  
Sets Theory ◽  
System Movement

The Intuitionistic Fuzzy S-Rough Sets (IFS-RS) is the intuitionistic fuzzy extension of S-Rough sets theory. It has dynamic characteristic of S-Rough sets, as well as intuitionistic fuzzy characteristic of Intuitionistic Fuzzy sets. Based on S-Rough sets theory, this paper introduced the membership and non-membership concepts of Intuitionistic Fuzzy sets, builded the model of IFS-RS under general equivalence relation, put forward the rough property and transfer degree concepts of IFS-RS. By calculating the rough property and transfer degree of IFS-RS, Thus being able to describe the transformation degree of the elements in fuzzy system movement into or movement out more clearly and precisely.

Generalized Set Theories Applied in Uncertain Information Processing

2014 ◽  
Vol 644-650 ◽  
pp. 2419-2423
Author(s):  
Qing Bo Yang ◽  
Jian Long Zhou
Keyword(s):  
Information Processing ◽  
Fuzzy Sets ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Uncertain Information ◽  
Vague Sets ◽  
Intuitionistic Fuzzy

Uncertain factors in information bring us serious challenges. In order to apply information effectively, many researchers are committed to the research on uncertain information processing. Generalized set theories are widely used in the research. Several kinds of theories such as Fuzzy sets, Intuitionistic fuzzy sets, Vague sets, Rough sets and Extension sets are introduced in this paper. And a comparation and analysis of them is given in the following.

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