The Archimedean property for t-norms in interval-valued fuzzy set theory

2006 ◽  
Vol 157 (17) ◽  
pp. 2311-2327 ◽  
Author(s):  
Glad Deschrijver
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Archimedean Property ◽  
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

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 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.

Research on Interval-valued Intuitionistic Fuzzy Multi-attribute Decision Making Based on Projection Model

2019 ◽  
Vol 13 ◽  
Author(s):  
Sha Fu ◽  
Xi-long Qu ◽  
Ye-zhi Xiao ◽  
Hang-jun Zhou ◽  
Yun Zhou
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Ideal Point ◽  
Projection Model ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Ideal ◽  
Multi Attribute Decision Making ◽  
Interval Valued

Background: Regarding the multi-attribute decision making where the decision information is the interval-valued intuitionistic fuzzy number and the attribute weight information is not completely determined. Method: Intuitionistic fuzzy set theory introduces non-membership function, as an extension of the fuzzy set theory, it has certain advantages in solving complex decision making problems. a projection model based interval-valued intuitionistic fuzzy multi-attribute decision making scheme was proposed in this study. The objective weight of the attribute was obtained using improved interval-valued intuitionistic fuzzy entropy, and thus the comprehensive weight of the attribute was obtained according to the preference information. Results: In the aspect of the decision-making matrix processing, the concept of interval-valued intuitionistic fuzzy ideal point and its related concepts were defined, the score vector of each scheme was calculated, the projection model was constructed to measure the similarity between each scheme and the interval-valued intuitionistic fuzzy ideal point, and the scheme was sorted according to the projection value. Conclusion: The efficiency and usability of the proposed approach are considered on the case study.

SMETS-MAGREZ AXIOMS FOR R-IMPLICATORS IN INTERVAL-VALUED AND INTUITIONISTIC FUZZY SET THEORY

2005 ◽  
Vol 13 (04) ◽  
pp. 453-464 ◽  
Author(s):  
GLAD DESCHRIJVER ◽  
ETIENNE E. KERRE
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Intuitionistic Fuzzy Set ◽  
Membership Degree ◽  
Triangular Norms ◽  
Intuitionistic Fuzzy ◽  
Special Lattice ◽  
Interval Valued

Interval-valued fuzzy sets constitute an extension of fuzzy sets which give an interval approximating the "real" (but unknown) membership degree. Interval-valued fuzzy sets are equivalent to intuitionistic fuzzy sets in the sense of Atanassov which give both a membership degree and a non-membership degree, whose sum must be smaller than or equal to 1. Both are equivalent to L-fuzzy sets w.r.t. a special lattice L*. In fuzzy set theory, an important class of triangular norms is the class of those that satisfy the residuation principle. In a previous paper5 we gave a construction for t-norms on L* satisfying the residuation principle which are not t-representable. In this paper we investigate the Smets-Magrez axioms and some other properties for the residual implicator generated by such t-norms.

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