A construction method of interval-valued Fuzzy Sets for image processing

2011 ◽  
Author(s):  
A. Jurio ◽  
D. Paternain ◽  
C. Lopez-Molina ◽  
H. Bustince ◽  
R. Mesiar ◽  
...  
Keyword(s):  
Image Processing ◽  
Fuzzy Sets ◽  
Construction Method ◽  
Interval Valued

scholarly journals Constructions for t-conorms and t-norms on interval-valued and interval-valued intuitionistic fuzzy sets by paving

2020 ◽  
Vol 26 (3) ◽  
pp. 1-12
Author(s):  
Martin Kalina ◽  
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Construction Method ◽  
Unit Interval ◽  
The Real ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Paving is a method for constructing new operations from a given one. Kalina and Kral in 2015 showed that on the real unit interval this method can be used to construct associative, commutative and monotone operations from particular given operations (from basic ‘paving stones’). In the present paper we modify the construction method for interval-valued fuzzy sets. From given (possibly representable) t-norms and t-conorms we construct new, non-representable operations. In the last section, we modify the presented construction method for interval-valued intuitionistic fuzzy sets.

On δ-ϵ-Partitions for Finite Interval-Valued Hesitant Fuzzy Sets

2016 ◽  
Vol 24 (Suppl. 2) ◽  
pp. 145-163 ◽  
Author(s):  
Pelayo Quirós ◽  
Pedro Alonso ◽  
Irene Díaz ◽  
Susana Montes
Keyword(s):  
Image Processing ◽  
Decision Making ◽  
Fuzzy Sets ◽  
Open Problem ◽  
Finite Interval ◽  
Intuitionistic Fuzzy Sets ◽  
Hesitant Fuzzy Sets ◽  
Definition Of ◽  
Interval Valued ◽  
Atanassov’S Intuitionistic Fuzzy Sets

Hesitant fuzzy sets represent a useful tool in many areas such as decision making or image processing. Finite interval-valued hesitant fuzzy sets are a particular kind of hesitant fuzzy sets that generalize fuzzy sets, interval-valued fuzzy sets or Atanassov’s intuitionistic fuzzy sets, among others. Partitioning is a long-standing open problem due to its remarkable importance in many areas such as clustering. Thus, many different partitioning approaches have been developed for crisp and fuzzy sets. This work presents a partitioning method for the so-called finite interval-valued hesitant fuzzy sets. The definition of this partitioning method involves a definition of an ordering relation for finite interval-valued fuzzy sets membership degrees, i.e, finitely generated sets, as well as the definitions of t-norm and t-conorm for these kinds of sets.

Interval‐valued equivalence measures respecting uncertainty in image processing

2021 ◽  
Author(s):  
Barbara Pȩkala ◽  
Urszula Bentkowska ◽  
Dawid Kosior ◽  
Zdenko Takáč ◽  
Aitor Castillo ◽  
...  
Keyword(s):  
Image Processing ◽  
Interval Valued

Width-based distance measures on interval-valued intuitionistic fuzzy sets

2021 ◽  
pp. 1-13
Author(s):  
Xi Li ◽  
Chunfeng Suo ◽  
Yongming Li
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Dissimilarity Function ◽  
Better Than

An essential topic of interval-valued intuitionistic fuzzy sets(IVIFSs) is distance measures. In this paper, we introduce a new kind of distance measures on IVIFSs. The novelty of our method lies in that we consider the width of intervals so that the uncertainty of outputs is strongly associated with the uncertainty of inputs. In addition, better than the distance measures given by predecessors, we define a new quaternary function on IVIFSs to construct the above-mentioned distance measures, which called interval-valued intuitionistic fuzzy dissimilarity function. Two specific methods for building the quaternary functions are proposed. Moreover, we also analyzed the degradation of the distance measures in this paper, and show that our measures can perfectly cover the measures on a simpler set. Finally, we provide illustrative examples in pattern recognition and medical diagnosis problems to confirm the effectiveness and advantages of the proposed distance measures.

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