6.1 and resources. To avoid problems when using

6.1 Some Recent Research On Of Fuzzy
Similarity Measure


6.1.1 Water Quality Evaluation Of Haihe River With Fuzzy
Similarity Measure        Methods (Wang,
X., Zou, Z., & Zou, H., 2013)

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Water quality
concerns are often neglected as quality water supplies are abundant and
available. This situation is to changing in many areas.  The new irrigation projects and old projects
seeking new or additional supplies should depend on the lower quality of water
and resources.


To avoid
problems when using this low quality water supply, there must be good planning
to ensure that the water quality available for use and fuzzy similarity measure
has been used as an effective tool for assessing the quality of water in the
Haihe River.


To evaluate the quality of Haihe River
water, two fuzzy set of fuzzy similarity measures have been applied to evaluate
the proximity. To classify 299 samples into a water quality standard, the skill
function and variation of the coefficient as weight, four fuzzy similarity
measures (including Lattice similarity measure, Hamming similarity measure,
Euclidean similarity measure and the max-min similarity measure) are used. The
results are compared with traditional distance discrimination methods. The
calculation of the two traditional distance discrimination methods (both distance
Euclidean and absolute value distance) is also based on the use of variation
coefficients as the weight.


Without the measure of Lattice
similarity, for this method loss of some information, the correct collection of
samples classified into the same water quality rank is 75.92% with three other
similarities and two methods of distance discrimination. This result shows the
reliability of five methods. Only considering the three similarity measures,
there were only 1.01% of the samples that were not classified to the same rank,
while the ratio corresponding to the two methods of distance discrimination was
5.69%. As a result of a leave-one-out cross validation test shows that more
than 88% of the samples are classified to the correct rank, indicating that the
similarity measure is appropriate for assessing the quality of Haihe River

If the water quality is not classified
into a given rank according to the monitored indicator, the fuzzy set is a
suitable concept to describe the state of water quality.



6.1.2 Performance Comparison of Cosine, Haar,
Walsh-Hadamard,Fourier and Wavelet Transform for shape based image retrieval
using Fuzzy Similarity Measure (Banerjee, A., & Dutta, A., 2013)


Shape is one of the most important
features in Content Based Image Retrieval (CBIR). When the shape is used as a
feature, edge detection may be the first step of character extraction. Adaptations
to different transformations such as translation, rotation, and scale are
required by good shape representation. In this paper, performance comparison is
performed on various image transformations such as Wavelet transform, Fourier
transform, Haar transform, Walsh-Hadamard transform and discrete cosine
transform by using fuzzy similarity measure. It is informed that according to
the performance of the Wavelet transform takes the best result among the
changes mentioned. It has higher values ??of accuracy and accuracy and higher
crossover points.


Content-based imagery existed in the
early 90’s using low-level features such as textures, colors, shapes and
structures. Extensive research has been done to extract image features and
measure similarities between images so that relevant images can be taken.In the
CBIR, images are indexed by features extracted from the image itself. Here,
manual annotations are not required. The information taken from the image is a
relatively low level such as their colors, textures, shapes, structures and
combinations. The main focus of CBIR is extraction of image features and
computational measurement of the characteristics. Image content representation
can be arranged into a feature vector of d dimensions.


6.1.3 A Triparametric Family Of Cardinality-Based Fuzzy
Similarity Measures By (Bosteels, K., & Kerre, E. E., 2007)


In this paper, a general family study
for the specific value of a third parameter. More precisely, it shows that for
particular values ??of this parameter and certain properties can be determined
by imposing constraints on the remaining two parameters.


The task of measuring similarity takes
place in many areas. Because the object being compared is often described by
the set, this task is frequently performed by means of measures that compare
sets. Such measures are usually called the similarity measures. However, in
many applications, the fuzzy set is more appropriate than the crisp sets to represent
the object concerned. Therefore, there is a need fuzzy similarity measure,
i.e., measures that compare fuzzy sets.


Since the most commonly used
commonality measures are based on the set cardinality involved, many research
has been devoted to cardinality-based fuzzy similarity measures. Particularly
interesting is the work on the fuzzification scheme for the class of crisp
cardinality-based similarity measures are presented. More specifically, the
development of meta-theorems that ensures transit is a recent progress that
promises this research, since the theorem can be used systematically to develop
appropriate measures for specific applications.


However, this approach also has some
disadvantages, that is, the fuzzy family is limited to cardinality and
reflexivity equality measures generally only preserved when fuzzification is
based on the minimum operator. We really feel the second weakness, because
reflexivity can be regarded as a very natural and intrinsic equation.The
systematic way to construct and analyze cardinality-based fuzzy similarity
measures that is not restricted to rational measures had presented This is
accomplished by introducing a general form that depends on two parameters.


6.1.4  On the
TL-transitivity of fuzzy similarity measures (He, X., Li, Y., Qin, K., &
Meng, D., 2016)


In the fuzzy neural network, it is
usually to do rule regulation by using fuzzy similarity measures. The fuzzy size
measure is reserved for fuzzy binary relationships. In the fuzzy relational
calculus, T-transitivity is indispensable because it relates to the concept of
metrics. In this study, we evaluate whether the two types of fuzzy similarity a
measure is satisfy TL-transitivity. It also investigates the TL’s TL-transitivity
of fuzzy equivalencies.


Similarity can be used as a principle
of organizer to classify objects, form concepts, and make generalizations.
Hence, it is an important concept in the field of psychology as well as in many
areas of research, such as biology, chemistry, retrieval in form, machine
learning, and statistics. In a fuzzy neural network, it is usually to do a rule
match, where a dimension of fuzzy similarity measure is used to determine
whether the rules should be fired for specific observations. The concept of one
measure of fuzzy similarity measure has considered regarded in previous


previous researchers disagree with any of the axioms that must be required by
such a function. Therefore, different axiomatic definitions on the size of the fuzzy
similarity measures exist and the axiomatic definition depends on the context
in which it is built. Some of the key features of the fuzzy similarity measures
are discussed and compared.


Transitivity is a simple yet powerful property
of relations, which plays an important role in many areas, such as graph
theory, clustering techniques, and decision theory. For example, in
prioritizing modeling, rational considerations often lead to demand for transitivity.
If we want to classify based on the concept of similarity or
indistinguish-bility, then we face transitivity. In the fuzzy relaton calculus,
the notion T transitivity is indispensable because it relates to the concept of
metrics. The fuzzy similarity measure is reserved for fuzzy binary relation on
F (X). Fuzzy similarity measures are defined as fuzzy relations and T-transitivity
is one of the most important attributes that can be attributed to fuzzy relation,
so it is useful to research the T-transitivity of fuzzy similarity measures. In
recent years, many researchers have conducted deep investigations into the T-transitivity
of fuzzy similarity measures, thereby generating a number of proposals.  


6.1.5 Summary


The suitable concept to describe the
situation of the water quality is fuzzy set. Through comparison with the
traditional methods, Euclidean distance and absolute value distance, the
results of Lattice similarity measure can be seen to be inappropriate. For the
remaining three similarity measure methods, all the information provided is
used. Only 3 samples are not in the same ranks and the evaluated results are
more stable and reliable. For the evaluated results, leave-one-out cross
validation is applied to test whether the ranks each sample classified into are


In this paper, a comparison is done
between various transforms on a fuzzy similarity measure for retrieval of 2
dimensional shapes. It is seen that according to retrieval performance Wavelet
transform gives the best result with respect to average precision and recall
values among the transforms used in comparison. It has higher recall and
precision values and higher crossover point. In future, the method could
further be improved so as to achieve higher precision and recall values. This
method is applicable to just 2D shapes. So it can be thought to incorporate it
in 3D shape matching with some modification.


The introduced a triparametric family
of cardinality-based fuzzy similarity measures, together with several
constraints on its parameters that ensure certain properties of the generated
measures. As illustrated by the examples in the previous section, this leads to
a convenient framework for constructing and analysing cardinality-based fuzzy
similarity measures. This framework has two important advantages in comparison
with already existing approaches, namely, it is not limited to rational
measures and, even more importantly, the generated fuzzy similarity measures
are always reflexive. Another positive feature of the proposed framework is
that it provides the possibility to ensure several forms of restrictability,
which allows reducing the computation time in practical implementations. The
fact that many of the considered examples were found to satisfy some
form of restrictability, illustrates that it can be worthwhile to analyse the
properties of existing fuzzy similarity measures by means of the presented


In this study, the investigated
whether the two types of fuzzy similarity measures given in are satisfy
TL-transitivity. The showed that the fuzzy similarity measures given are
constructed by fuzzy equivalencies, and thus whether the fuzzy similarity
measures satisfy TL-transitivity will depend on whether their corresponding
fuzzy equivalencies satisfy TL-transitivity. The TL-transitivity of fuzzy
equivalencies and obtained some TL-transitive fuzzy equivalencies. The
TL-transitivity of the two types of fuzzy similarity measures and the first
type of fuzzy similarity measure depends on the TL-transitivity of its
corresponding fuzzy equivalence, and that the TL-transitivity of the second
type of fuzzy similarity measure depends on the range of its parameter.
Finally, TL-transitive fuzzy similarity measures by aggregating a family of
TL-transitive fuzzy similarity measures.


Based on the some recent research on
of fuzzy similarity measure, it can be concluding that many of the existing
fuzzy similarity measures have been provided with different function. However,
fuzzy is represented by a fuzzy membership function. In addition, fuzzy similarity
can be generalizing with a new similarity measure. Therefore, the obtained
result can simplify the choice of similarity measures, from numerous existing
measures in literature, for any research topic.