NOVEL APPROACHES FOR THE TRANSFORMATION OF FUZZY MEMBERSHIP FUNCTION INTO BASIC PROBABILITY ASSIGNMENT BASED ON UNCERTAINTY OPTIMIZATION

2013 ◽  
Vol 21 (02) ◽  
pp. 289-322 ◽  
Author(s):  
DEQIANG HAN ◽  
CHONGZHAO HAN ◽  
YONG DENG
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set Theory ◽  
The Body ◽  
Random Sets ◽  
Fuzzy Membership Function ◽  
Uncertain Information ◽  
Unified Framework ◽  
Theoretical Frameworks ◽  
Uncertainty Reasoning

With the development of uncertainty reasoning and information fusion, there have emerged several theories including fuzzy set theory, Dempster-Shafer evidence theory, probability theory and rough set theory, etc., for representing and dealing with the uncertain information. When the fusion of the uncertain information originated from different sources is needed, how to construct a general framework for different theories of uncertainty or how to establish the connection between different theoretical frameworks has become a crucial problem. Particularly, to combine two kinds of information represented respectively by the BPA and the FMF, this paper proposes two transformations of an FMF into a BPA by solving a constrained maximization or minimization optimization problem. The objective function is the uncertainty degree of the body of evidence (BOE) and the corresponding constraints are established based on the given FMF. In fact the transformation of an FMF into a BPA is the transformation of fuzzy sets into random sets, which is currently accepted as a unified framework for several theories of uncertainty. Our proposed approaches have no predefinition of focal elements and they can be used as the general transformations of fuzzy sets into random sets. Some examples and analyses are provided to illustrate and justify the rationality and effectiveness of the proposed approaches.

Fuzzy Lattice Ordered G-modules

2019 ◽  
Vol 8 (3) ◽  
pp. 94-107
Author(s):  
Ursala Paul ◽  
Paul Isaac
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set Theory ◽  
Real Life ◽  
Uncertain Information ◽  
Algebraic Structures ◽  
Ordered Groups ◽  
Lattice Ordered Groups ◽  
Fuzzy Lattice ◽  
Novel Concept

The study of mathematics emphasizes precision, accuracy, and perfection, but in many of the real-life situations, people face ambiguity, vagueness, imprecision, etc. Fuzzy set theory and rough set theory are two innovative tools in mathematics which are used for decision-making in vague and uncertain information systems. Fuzzy algebra has a significant role in the current era of mathematical research and it deals with the algebraic concepts and models of fuzzy sets. The study of various ordered algebraic structures like lattice ordered groups, Riesz spaces, etc., are of great importance in algebra. The theory of lattice ordered G-modules is very useful in the study of lattice ordered groups and similar algebraic structures. In this article, the theories of fuzzy sets and lattice ordered G-modules are synchronized in a suitable manner to evolve a novel concept in mathematics i.e., fuzzy lattice ordered G-modules which would pave the way for new researchers in fuzzy mathematics to explore much more in this field.

A FPGA-Based Discretization Algorithm of Continuous Attributes in Rough Set

2013 ◽  
Vol 278-280 ◽  
pp. 1167-1173
Author(s):  
Guo Qiang Sun ◽  
Hong Li Wang ◽  
Jing Hui Lu ◽  
Xing He
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Processing Speed ◽  
Field Programmable Gate Array ◽  
Rough Set Theory ◽  
Continuous Data ◽  
Uncertain Information ◽  
Discretization Algorithm ◽  
Field Programmable ◽  
Speed Advantage

Rough set theory is mainly used for analysing, processing fuzzy and uncertain information and knowledge, but most of data that we usually gain are continuous data, rough set theory can pretreat these data and can gain satisfied discretization results. So, discretization of continuous attributes is an important part of rough set theory. Field Programmable Gate Array(FPGA) has been became the mainly platforms that realized design of digital system. In order to improve processing speed of discretization, this paper proposed a FPGA-based discretization algorithm of continuous attributes in rough ret that make use of the speed advantage of FPGA and combined attributes dependency degree. This method could save much time of pretreatment in rough ret and improve operation efficiency.

Application of Uncertainty Models in Bioinformatics

2016 ◽  
pp. 169-182 ◽  
Author(s):  
B.K. Tripathy ◽  
R.K. Mohanty ◽  
Sooraj T.R.
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set Theory ◽  
Rough Set Theory ◽  
Life Sciences ◽  
Uncertain Information ◽  
Main Emphasis ◽  
Vague Data ◽  
Uncertainty Models ◽  
Theoretical Results

This chapter provides the information related to the researches enhanced using uncertainty models in life sciences and biomedical Informatics. The main emphasis of this chapter is to present the general ideas for the time line of different uncertainty models to handle uncertain information and their applications in the various fields of biology. There are many mathematical models to handle vague data and uncertain information such as theory of probability, fuzzy set theory, rough set theory, soft set theory. Literatures from the life sciences and bioinformatics have been reviewed and provided the different experimental & theoretical results to understand the applications of uncertain models in the field of bioinformatics.

A sequential three-way decision model based on hesitant fuzzy sets

2021 ◽  
pp. 1-12
Author(s):  
Mo Zhang ◽  
Qinghua Zhang ◽  
Man Gao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Decision Model ◽  
Hesitant Fuzzy Set ◽  
Extended Model ◽  
Uncertain Information ◽  
Fuzzy Distance ◽  
Shadowed Set ◽  
Multi Attribute Decision Making

As a new extended model of fuzzy sets, hesitant fuzzy set theory is a useful tool to process uncertain information in decision making problems. The traditional hesitant fuzzy multi-attribute decision making (MADM) can only choose an optimal strategy, which is not suitable for all of the complex scenarios. Typically, in practical application, decision making problems may be more complicated involving three options of acceptance, non-commitment and rejection decisions. Three-way decisions, which divide universe into three disjoint regions by a pair of thresholds, are more efficient to deal with these problems. Therefore, how to utilize three-way decision theory to process hesitant fuzzy information is an essential issue to be studied. In this paper, from the perspective of hesitant fuzzy distance, a hesitant fuzzy three-way decision model is proposed. First, because hesitant fuzzy element (HFE) is a set of several possible membership degrees, it cannot be compared with thresholds directly. Hence, this paper converts it into the comparison between the distance and the thresholds. Then, to calculate thresholds more reasonably, shadowed set theory is introduced to avoid the subjectivity of threshold acquisition. Furthermore, sequential strategy is adopted to solve the multi-attribute decision making problems. Finally, an example of medical diagnosis and simulation experiments are given to prove the accuracy and efficiency of the proposed hesitant fuzzy three-way decision model.

Application of Uncertainty Models in Bioinformatics

Biotechnology ◽  
2019 ◽  
pp. 141-155
Author(s):  
B.K. Tripathy ◽  
R.K. Mohanty ◽  
Sooraj T. R.
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set Theory ◽  
Rough Set Theory ◽  
Life Sciences ◽  
Uncertain Information ◽  
Main Emphasis ◽  
Vague Data ◽  
Uncertainty Models ◽  
Theoretical Results

This chapter provides the information related to the researches enhanced using uncertainty models in life sciences and biomedical Informatics. The main emphasis of this chapter is to present the general ideas for the time line of different uncertainty models to handle uncertain information and their applications in the various fields of biology. There are many mathematical models to handle vague data and uncertain information such as theory of probability, fuzzy set theory, rough set theory, soft set theory. Literatures from the life sciences and bioinformatics have been reviewed and provided the different experimental & theoretical results to understand the applications of uncertain models in the field of bioinformatics.

On Multi-Fuzzy Rough Sets, Relations, and Topology

2019 ◽  
Vol 8 (1) ◽  
pp. 101-119
Author(s):  
Gayathri Varma ◽  
Sunil Jacob John
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Primitive Concept ◽  
Closed Sets ◽  
Fuzzy Topological Spaces

This article describes how rough set theory has an innate topological structure characterized by the partitions. The approximation operators in rough set theory can be viewed as the topological operators namely interior and closure operators. Thus, topology plays a role in the theory of rough sets. This article makes an effort towards considering closed sets a primitive concept in defining multi-fuzzy topological spaces. It discusses the characterization of multi-fuzzy topology using closed multi-fuzzy sets. A set of axioms is proposed that characterizes the closure and interior of multi-fuzzy sets. It is proved that the set of all lower approximation of multi-fuzzy sets under a reflexive and transitive multi-fuzzy relation forms a multi-fuzzy topology.

A HISTORICAL OVERVIEW OF FUZZY MATHEMATICS

2005 ◽  
Vol 01 (01) ◽  
pp. 1-26 ◽  
Author(s):  
ETIENNE E. KERRE ◽  
JOHN N. MORDESON
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Rough Set Theory ◽  
Fuzzy Mathematics ◽  
Mathematical Representation ◽  
Uncertain Information ◽  
Historical Overview ◽  
The Many

In this paper, we present a historical overview of the development of fuzzy mathematics. We mainly concentrate on the evolution of the mathematical representation of fuzziness by means of fuzzy set theory. From the many remaining recently introduced models to represent imprecise and uncertain information, we briefly treat rough set theory.

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