Interval-Valued Agent Belief Model Based on New Fuzzy Set Theory

2007 ◽  
Author(s):  
Yunguo Lin ◽  
Xiaoyun Chen ◽  
ShanLi Hu
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Model Based ◽  
Belief Model ◽  
Interval Valued

Negations With Respect to Admissible Orders in the Interval-Valued Fuzzy Set Theory

2018 ◽  
Vol 26 (2) ◽  
pp. 556-568 ◽  
Author(s):  
Maria J. Asiain ◽  
Humberto Bustince ◽  
Radko Mesiar ◽  
Anna Kolesarova ◽  
Zdenko Takac
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Admissible Orders ◽  
Interval Valued

Evaluation Model of Conceptual Design Scheme Based on Engineering Fuzzy Set Theory

2012 ◽  
Vol 479-481 ◽  
pp. 1741-1744
Author(s):  
Hong Bin Miao
Keyword(s):  
Conceptual Design ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Evaluation Model ◽  
Objective Evaluation ◽  
Evaluation Indexes ◽  
Model Based ◽  
Mechanical Products ◽  
Fuzzy Pattern

The evaluation of conceptual design schemes of mechanical products is an essential problem in the process of its conceptual design. At the stage of conceptual design, whether a correct and objective evaluation can be made on these design schemes will ultimately decide a good or bad performance, even its success or failure. The evaluation of conceptual design is a semi-structural decision-making that includes qualitative indexes and quantitative indexes, so it is difficult to select the best design concepts from a number of schemes. Therefore, an evaluation model based on the engineering fuzzy set theory is developed in this paper. First, the paper makes a detailed hierarchy analysis of evaluation indexes system and constructs some evaluation units according to evaluation indexes system. The whole evaluation of schemes is translated into a series of evaluation of basic units or comprehensive cells. Second, a multi-pole fuzzy pattern recognition model based on the engineering fuzzy set theory is established and the relative membership degree matrix can be obtained by the model, the matrix shows the order of excellence. An example is given for demonstration of its application. It shows that the method is feasible and reasonable.

Decision Making in Medical Diagnosis via Distance Measures on Interval Valued Fuzzy Sets

2017 ◽  
Vol 6 (4) ◽  
pp. 63-83 ◽  
Author(s):  
Palash Dutta
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Distance Measures ◽  
Medical Documentation ◽  
Interesting Area ◽  
Interval Valued

The uncertain and sometimes vague, imprecise nature of medical documentation and information make the field of medical diagnosis is the most important and interesting area for applications of fuzzy set theory (FST), intuitionistic fuzzy set (IFS) and interval valued fuzzy set (IVFS). In this present study, first resemblance between IFS and IVFS has been established along with reviewed some existing distance measures for IFSs. Later, an attempt has been made to derive distance measures for IVFSs from IFSs and establish some properties on distance measures of IVFSs. Finally, medical diagnosis has been carried out and exhibits the techniques with a case study under this setting.

scholarly journals A (Basis for a) Philosophy of a Theory of Fuzzy Computation

2018 ◽  
Vol 20 (1) ◽  
pp. 181-201 ◽  
Author(s):  
Apostolos Syropoulos
Keyword(s):  
Mathematical Model ◽  
Turing Machine ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Computing Device ◽  
Models Of Computation ◽  
Model Based ◽  
Physical Objects ◽  
Linguistic Phenomenon

Abstract Vagueness is a linguistic phenomenon as well as a property of physical objects. Fuzzy set theory is a mathematical model of vagueness that has been used to define vague models of computation. The prominent model of vague computation is the fuzzy Turing machine. This conceptual computing device gives an idea of what computing under vagueness means, nevertheless, it is not the most natural model. Based on the properties of this and other models of vague computing, an attempt is made to formulate a basis for a philosophy of a theory of fuzzy computation.

scholarly journals REPRESENTABILITY IN INTERVAL-VALUED FUZZY SET THEORY

2007 ◽  
Vol 15 (03) ◽  
pp. 345-361 ◽  
Author(s):  
GLAD DESCHRIJVER ◽  
CHRIS CORNELIS
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Theoretical Approach ◽  
Fuzzy Set Theory ◽  
Logical Connectives ◽  
Representation Method ◽  
Application Developers ◽  
Interval Valued

Interval-valued fuzzy set theory is an increasingly popular extension of fuzzy set theory where traditional [0,1]-valued membership degrees are replaced by intervals in [0,1] that approximate the (unknown) membership degrees. To construct suitable graded logical connectives in this extended setting, it is both natural and appropriate to "reuse" ingredients from classical fuzzy set theory. In this paper, we compare different ways of representing operations on interval-valued fuzzy sets by corresponding operations on fuzzy sets, study their intuitive semantics, and relate them to an existing, purely order-theoretical approach. Our approach reveals, amongst others, that subtle differences in the representation method can have a major impact on the properties satisfied by the generated operations, and that contrary to popular perception, interval-valued fuzzy set theory hardly corresponds to a mere twofold application of fuzzy set theory. In this way, by making the mathematical machinery behind the interval-valued fuzzy set model fully transparent, we aim to foster new avenues for its exploitation by offering application developers a much more powerful and elaborate mathematical toolbox than existed before.

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