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)

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

water.

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

studies.

However,

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

reasonable.

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

framework.

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.