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Modeling, of a description of a system in

Modeling, in general logic
refers to the establishment of a description of a system in mathematical terms,
which describes the behaviour of the original organism. Such a design of
mathematical representation is called a mathematical model, of the physical system.
In numerous realistic disciplines such as medicine, engineering and ?nance,
amongst others, modeling and investigating lifespan data is essential.

Researchers in mathematics
are in the habit of dividing the universe into two parts: mathematics, and
everything else,that is, the rest of the world, sometimes called “the real
world”. As soon as you practice mathematics to know a situationin the actual world,and
then feasibly practice it totake an action or event of forecast the future, together
the actual world condition and the resultant mathematics methods are taken seriously.The
circumstances and the queries related with them can be any extent from enormous
to tiny. The enormous ones may lead to lifetime careers for those who study
them deeply and special curricula or whole university departments may be set up
to prepare people for such careers. Bioorganism, hormones study, medical
imaging, and cryptography are some such examples. At the another end of the extent,
there are slight circumstances and equivalent interrogations, although they may
be of great importance to the individuals involved: planning a trip, scheduling
the time-table, man requirtment methods, or bidding in an auction. Whether the problem is enormous or
tiny, the procedure of “interface” between the mathematics and the physical world
is the same: the actual circumstances frequently has numerous sides that you
can’t take all into account, so you choose which characteristics are most
significant and retain those. At this instant, you have an perfect description
of the actual condition, which you can then interpret into mathematical
relations. Now you have a mathematical model of the idealized question. Then
you relate your mathematical characters and facts to the model, and gain
exciting understandings, examples, designs, formulas, and algorithms. You
decode all this back into the actual situation, and you assurance to have a
model for the idealized question. But you have to check back: the results are practical,
the answers are reasonable, the consequences are acceptable? If so, then we
have the mathematical model for the actual world problem, If not, take another
look at the choices you made at the beginning, and try again. This entire
process is called mathematical modeling.

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The objectives of the mathematical modelling are increasing
scienti?c realizing over measurable expression of present information of a
system (as well as displaying what we know, this may also show up what we do
not know), examination the e?ect of variations in a system, aid result producing,
including tactical decisions and strategic decisions. When learning models, it
is useful to identify wide categories of models. Classi?cation of distinctmodels
into these categories expresses us systematically some of the fundamentals of
their structure.One separation among models is built on the kind of consequence
they forecast. Deterministic model sign are random variation, and so always
forecast the identical consequence from a specified starting point. On the
other hand, the model may be more statistical in nature and so may forecast the
distribution of probable outcomes. Such models are said to be stochastic.

An additional method of differentiate among the kinds
of models is to reflect the level of understanding on which the model is based.
A model which uses a huge volume of theoretic information commonly defines what
occurs atone level in the hierarchy by considering procedures at lower stages,
these are called mechanistic models, since they take interpretation of the
mechanisms over which variations happen. In empirical models, nointerpretation
is taken of the mechanism by which variations to the system occur. As an
alternative, it is only renowned that they do occur, and the model trys to
interpretation quantitatively for variations related with various circumstances.

In this
research work, we were developed various fuzzy mathematical model based on
different distributions to  investigate
the effect of oxytocin.The hind paw with drawl latency (HWL) in mature mice increased with the increase of oxytocin concentration.
The changes in HWL after a microinjection of dissimilar doses of oxytocin
consider as random variable following fuzzy generalized gamma distribution and
fuzzy log logistic distribution.

The
changes in cardiac output and stroke volume after the administration of
oxytocin taken as a random variable follows the generalized Rayleigh
distribution. Fuzzy mathematical model was established to measure the
haemodynamic effects of oxytocin by using generalized Rayleigh distribution.
The oxytocin concentration in salaivary samples following intranasal oxytocin
administration fix as random variable follows the Rayleigh distribution in
fuzzy environment.

Clinically,
oxytcoin infusion is used for induction and augmentation of labor and for the
prevention and treatment of postpartum hemorrhage (PPH). The maternal heart
rate after the study medication treated as a random variable follows the Nadarajah and Haghighi distribution,
Exponentiated
Nadarajah and Haghighi
distribution in fuzzy state.

            Fuzzy
mathematical models were established by using various distribuiton such as
generalized gamma distribution, log-logistic distribution, Rayleigh
distribution, generalized Rayleigh distribution, Nadarajah
and Haghighi (NH) distribution and Exponentiated Nadarajah and Haghighi distribution
(ENH). We compute the fuzzy mean, variance, survival or reliablity and hazard
rate values to analyze the effect of oxytocin. These theoritical outcomes offer
the enthusiastic information of the effects of oxytocin and it  will be useful to the medical field for
further experimental works.

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