proposed Predictive Mean Vote and the PMV-model
that takes into account the effect of clothing and
activity (Fanger, 1972). This is a static heat balance
model and predicts the percentage of people in a
given group experiencing thermal comfort.
There are also other factors that affect sensible
temperature. In addition to tactile stimuli, such as
temperature and humidity, it is affected by visual,
audio, and olfactory stimuli. For example, scent is
known to have psychological and physiological
impacts on humans. A research showed that
refreshing scents such as mint flavour reduces
apparent temperature (Shoji, 2005).
However, not many researches have been done
on the methods to measure sensible temperature that
take into account the effect of visual images and
scent and how much these factors change sensible
temperature.
3 THEORY OF SENSIBLE
TEMPERATURE
3.1 Definition of Sensible Temperature
In this section, we propose a new definition of
sensible temperature, which will be adapted in the
rest of this paper. The key idea is to focus on
similarity in psychological reaction. To explain this
idea, imagine two environments, e
1
, with a
temperature of 26°C and humidity of 80%, and e
2
,
with a temperature of 28°C and humidity of 30%.
Suppose that environment e
1
feels as warm as
environment e
2
. This is entirely conceivable as we
know from experience that increased humidity leads
to increased sensible temperature, just like many
formulae for sensible temperature, such as the heat
index equation, indicate (Steadman, 1979).
Then, the sensible temperature in the two
environments is the same. In other words, the
subjective evaluation of the environments is equal,
at least in respect to the temperature. Also, when one
is initially in environment e
0
, with a physical
temperature of 26°C and humidity of 30%, that
gradually changes into e
1
, one would feel as if the
temperature of the environment increased by 2°C.
This means the effect of increasing humidity by 50%
is equivalent to that of increasing physical
temperature by 2°C. These considerations suggest
that apparent change in temperature can be gauged
by making use of the similarity of psychological
reaction to the apparent heat of the environments.
To formalize these ideas, first let x
1
, x
2
, …, x
n
be
environmental factors that affect sensible
temperature, such as physical temperature and
humidity, and form an environment space, E, by
collecting the ordered tuples comprising of these
factors, i.e. E=
{
≡
(
,
,…,
)|
∈ℝ
}
=ℝ
,
where x
1
denotes physical temperature, and x
2
humidity. Then, sensible temperature can be
expressed as a function over E. Call this function
:E→ℝ a sensible temperature function. Here, the
subscript i indicates individual dependence of the
function. Hereafter, the existence and uniqueness of
the sensible temperature function is assumed.
Then, we divide E into equivalent sets based on
similarity in psychological reaction related to
apparent temperature. For this purpose, we introduce
a function S:E×E→ℝ
called the similarity
function. Given two environments, e
1
and e
2
, S(e
1
,e
2
)
indicates similarity in psychological reaction to
these two environments. The smaller the value of
this function, the more similar the reactions are. The
precise definition of this function is given later. With
this function, we partition E into the following
equivalent sets:
ℇ
=
{
∈E
|(
∀∈ℕ
)
S
(
,
,…,
)
,
≤S(
(
,
,…,
)
,))}
where c
2
, c
3
,…, c
n
are arbitrary constants. Note that
these equivalent sets are formed first by picking up
discrete points on the line L={
(
,
,
,…,
)
|∈
ℝ}, and then by making an environment belongs to
the equivalent set represented by the point closest to
it among those picked up points. Although it might
seem appropriate to form an equivalent set for each
value of sensible temperature, for the following two
reasons, our equivalent sets are countable and not
continuous.
1) Sensible temperature is a fuzzy quantity
2) E is partitioned into equivalent sets using a
similarity function, which gives a relative measure
of similarity in psychological reaction, and due to
the fuzziness coming from psychological evaluation
and fuzziness of sensible temperature itself, cannot
confirm identicalness of psychological reactions in
the two environments.
Now, since one feels as hot in any environment
belonging to the same equivalent set by definition,
the following approximation holds:
|
ℇ
≈.
(3)
Thus, we can reduce the problem of defining T
into
that of defining
:→ℝ, where={ℇ
|∈ℕ}.
There are several possible ways to define
, and
below are the examples:
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