1.1.

Fuzzy

Mathematical Modelling

Vagueness is embroiled in

several real phenomena. Whether one contemplates vagueness explicitly when

modeling such a phenomenon is one of the modeling choices, the outcome of which

will rest on on the situation. On the other hand, the modeler chooses to reflect

vagueness, he or she will have to select the method for modeling it. Some

experts assert that one theory, e.g. probability theory, is adequate to model

every kind of vagueness. The excellence of the techniques used in a statistical

analysis rest on extremely on the presumed probability model or distribution.

Some physical systems, those complex

ones, are uncompromising to model by an accurate and precise mathematical

procedure or equation due to the complexity of the system structure,

nonlinearity, uncertainty, randomness, etc.

Therefore, approximation

modeling is often necessary for real-world applications. But, the important questions are what kind of

approximation is upright, where the logic of “goodness” has to be first

defined, of course, and how to formulate such a good approximation in modeling

a system such that it is mathematically rigorous and can produce satisfactory

results in both theory and applications.

It is clear that interval

mathematics and fuzzy logic together can provide a promising alternative to

mathematical modeling for many physical systems that are too vague or too

complicated to be described by simple and crisp mathematical formulas or

equations. When interval mathematics and fuzzy logic are employed, the interval

of confidence and the fuzzy membership functions are used as approximation

measures, leading to the so-called fuzzy systems modeling.

Zimmermann H.-J. 134

proposed a definition of uncertainty: Uncertainty implies that in a certain

situation a person does not dispose about information which quantitatively and

qualitatively is appropriate to describe, prescribe or predict

deterministically and numerically a system, its behavior or other

characteristics. Buckley 12 define fuzzy probabilities, which will be fuzzy

numbers, from a set of confidence intervals and use fuzzy numbers for the

parameters in the probability density functions, to produce fuzzy probability

density functions.

Once dealing with the usual

probability concept, an occurrence has its specific limit. For take a

situation, if an event is X= {2, 4, 7, 9, 11}, its margin is sharp and

consequently, it can be characterized as a crisp set. As soon as we deal an

occurrence whose limit is not sharp, it can be measured as a fuzzy set, that

is, a fuzzy event. We can recognize the probability of two behaviors. One is

dealing with the probability of a crisp value (crisp probability) and the other

as a fuzzy set (fuzzy probability).

A hormone activity is a very

complex system, where it secretion processing is narrowly connected to

life-sustaining developments. It is evident now that there are a number of

amino acid combinations in the hormone that keep up its activity. Some details

of hormone activity, like stress or obesity, anxiety are well understood, while

others, like fetal growth, uterus contraction during cesarean and normal

delivery, primary postpartum hemorrhage effects and many others are still

ambiguous.

This means that a reasonable

explanation of the performance of a complex organism similar to a hormone’s

function is expressed in a natural-linguistic method with “sensitive” notations

like great excitability, weak damage, the low anticipation of punishment and so

on, which cannot be through statistically assigned.So, if we need to improve an

adequate tool for the logical theory of a hormone’s effective, in some sense,

we are bound to search for a mathematical tool, which could rightly work with

“perceptions” as with mathematical objects. Such mathematical tool was proposed

by Zadeh 131 and has been further developed during the last decades. It is

called fuzzy logic and fuzzy set theory. Guanrong Chen and Trung Tat Pham 50

give an example for fuzzy rule-based health monitoring expert systems, fuzzy

logic rules to control a focus ring of a camera to allow automatic focusing for

a sharp image, application of fuzzy control to a general class of servo

mechanic systems, the fuzzy controller for the robotic manipulator. The fuzzy

terms and definitions are defined in the following section 67, 135.

1.1.1.

Fuzzy set

If X is a cluster of items indicated by x, then a fuzzy set

in X is a set of ordered pairs:

is called the membership function or grade of

membership (also degree of compatibility or degree of truth) of x in

that maps X to the membership space M=0,1. ( The membership

function is not constrained to values between 0 and 1.)

1.1.2.

Cut

The

(crisp) set of elements that belongs the the fuzzy set

at least to the degree

is called the

cut:

is called strong

cut or “strong level set”

1.1.3.

Triangular

Fuzzy Number

Among the various shapes of fuzzy number, triangular fuzzy number

is the most popular one. It is a fuzzy number represented with three points as

follows:

The

above description interpreted as membership functions in Fig. 1.1.

Fig.1.1.

Triangular fuzzy number

1.1.4.

Arithmetic

operations on fuzzy triangular number

Let A and

B be two triangular fuzzy numbers defined as

.

Some

important properties of operation of fuzzy numbers are summarized

(i) Addition

: Triangular fuzzy number

(ii) Subtraction

: Triangular

fuzzy number

(iii)

Symmetric image

:

Triangular fuzzy number

(iv) The results from multiplication or division

are not triangular fuzzy numbers.

(v) Max or min

operation does not give triangular fuzzy numbers.

1.2.Oxytocin

Oxytocin is a mammalian neurohypophysial nonapeptide hormone

secreted by the posterior pituitary gland. Oxytocin is a nine amino acid long

peptide. The amino acid organization of oxytocin is:

cysteine-tyrosine-isoleucine-glutamine-asparagine-cysteine-proline-leucine-glycine-amide(Cys-Tyr-Ile-Gln-Asn-Cys-Pro-Leu-Gly)

and its molecular formula is C43H66N12O12S2. The molecular mass of oxytocin is

1007.187 Da.Oxytocin plays vital parts in several regulatory tasks. For

example, oxytocin performs as a neuromodulator and has been revealed to be

involved in strain, agitation, faith, benevolence, societal credit, orgasm, parturition,

lactation, maternal behaviors, mother-child, duo closeness and these protagonists

altered by variations in both oxytocin and oxytocin receptor concentrations.

The molecule structure andchemical stucture of oxytocin was presented in

Fig.1.1. and Fig. 1.2.

Fig. 1.2 Molecule

structure of oxytocin

Fig. 1.3. Chemical structure of oxytocin.

1.3.

Oxytocin

effects on social behaviour

Amid its numerous protagonists in body and brain, oxytocin

impacts societal manners. Compassionate the particular nature of this influence

is crucial, mutually within the abundant hypothetical background of

neurobiology, social neuroscience, and intellect evolution, but in the same way

within a clinical background of syndromes such as nervousness, schizophrenia,

and autism. Exploration discovering oxytocin’s role in human social behavior is

challenging due to its release in both body and brain and its interconnecting

effects with other hormones and neuromodulators.

1.4.

Oxytocin

role in love

Burman and Margolin 14

conversed the loving relations can have an intense consequence on adults’

healthiness. The central role of oxytocin in pair bonding and human imaging

studies implicate oxytocin-rich brain areas in early romantic love explained by

Inna Schneiderman et al. 58. Also, the areas of the brain are those rich in

oxytocin receptors supportive the creation of quixotic affection queried by

Acevedo et al. 1. Oxytocin stimulates a common sense of well-being comprising

calm, better social interactions, amplified faith, and condensed fear as well

as endocrine and physiological changes according to IsHak et al.126.

1.5.

The role of oxytocin in women

The release of oxytocin by

the pituitary gland acts to regulate some female reproductive functions.

1.

Stretch of the uterus and the

uterine cervix or stimulation of the breasts nipples increases action

potentials in axons of oxytocin-secreting neurons.

2.

Action potentials are conducted by

sensory neurons from the uterus and breast to the spinal cord and up ascending

tracts to the hypothalamus.

3.

Action potentials are conducted by

axons of oxytocin-secreting neurons in the hypothalamohypophysical tract to the

posterior pituitary, where they increase oxytocin secretion.

4.

Oxytocin enters the circulation,

increasing contractions of the uterus and milk ejection from the lactating

breast.

Fig. 1.3. Oxytocin role in women

Oxytocin

is a signaling substance in the brain that when released during birth, skin to skin

interaction and breast feeding induces important physiological and

psychological acclimatisation in the mother and infant. The way we give birth, feed,

and interrelate with our progenies may influence the release of oxytocin and

the development of both stop gap and enduring oxytocin-linked effects in both

mother and infant. Medicinal intrusions in birth may influence the discharge of

oxytocin and the development of the oxytocin-linked effects.

1.6.

Oxytocin

role in enhancing well-being

Oxytocin convinces a general wisdom of well-being as well as composed,

enhanced societal contact, amplified faith, and condensed distress, endocrine

and physiological changes. Some significant effects of oxytocin are momentary

and its discharge is concomitant with induction of ancillary biochemical happenings

which intervene long-term benefits together with blood pressure decline, serene

and affiliative behavior. As oxytocin release is amplified by touch and

physiological support so the hormone is involved in both source and benefits of

social interactions. Just as oxytocin has pervasive effects in factors

encompassing well-being, its dysfunction is associated with morbidity and

decreased the quality of life as observed neuropsychiatric conditions such as

autism, schizophrenia and social phobias (IsHak et al.126).