Computational Intelligence - May 2013 - 38

III. IT2 FS Model for the Meaning
of Emotion Words

Perceptual Computer for Translation
Word in
Language 1
Encoder

Fuzzy
Sets

Computing with
Words (CWW)
Engine

Fuzzy
Sets

Word in
Language 2
Decoder

Figure 1 Translation as a perceptual computer.

The second model we propose takes a different perspective.
Rather than having theoretically motivated scales for various
characteristics of emotions, the second model aims to represent
the intentional meaning of emotion words in terms of natural
language propositions that can be assented to or dissented
from. This view could also be construed as an abstract scale of
truth with respect to various propositions (which has been
considered in the study of veristic fuzzy sets [33]-[35]), but we
see this view as qualitatively different from the first model. The
reason why we see the propositional model as different from
the scale-based model is that, first, the number of propositions
about emotions will generally be larger than the number of
emotion words, whereas in the case of the scale-based representation the number of scalar dimensions will be smaller than
the emotion vocabulary size. Another reason that the propositional model can be considered qualitatively different than the
scale-based model is that propositions can be verbally (or
orthographically) expressed as linguistic stimuli, whereas
abstract scales carry more cognitive implications and are language independent. Some questions from EMO20Q closely
correspond to the scales in the first model, e.g., "is it positive?"
is similar to valence, "is it a strong emotion?" is similar to activation, and "is it related to another person?" hints at dominance. However, model 2 contains many questions
that are very specific, such as "would you feel this emotion on
your birthday?".
The models we propose can be seen as an algebraic representation where theoretical entities like emotion concepts are
considered virtual objects [36] with abstract scales. In this view,
a collection of scales that describe an object can be seen as a
suite of congruence relations. Recall that a congruence relation /
(mod P ) is an equivalence relation that holds given some
property or function P. A suite of congruence relations is a
bundle of equivalence relations " +i: i d I , , again, given some
property P. In both of the models we present, P are fuzzy sets
in an emotion space. In the case of the first model we present,
I is a set which can contain valence, activation, and/or dominance. In the case of the second model, I is a set of propositions derived from the EMO20Q game [37]-[40]. For example, for the statement that " f makes you smile," we can say that
happy and amused are congruent given this statement about
smiling behavior. In terms of the scales, the equivalence relations on each scale divide the scale space into equivalence
classes. In the next section, we describe this space of emotions
in more detail.

IEEE ComputatIonal IntEllIgEnCE magazInE | may 2013

A. Emotion Space
and Emotional Variables

Let E be an emotion space, an abstract space
of possible emotions (this will be
explained later in terms of valence, activation, and dominance, but for the time
being we will remain agnostic about the
underlying representation). An emotion variable f represents an
arbitrary region in this emotion space, i.e., f 1 E , with the
subset symbol 1 used instead of set membership ^! h because
we wish to represent regions in this emotion space in addition to single points.
The intensional meaning of an emotion word can be represented by a region of the emotion space that is associated with
that word. An emotion codebook C = ^W C, eval C h is a set of words
W C and a function eval C that maps words of W C to their corresponding region in the emotion space, eval C :W C " E. Thus, an
emotion codebook can be seen as a dictionary for looking up the
meaning of words in a vocabulary. Words in an emotion codebook can also be seen as constant emotion variables. The region
of the emotion space that eval C maps words to is determined by
interval surveys, as described in Section III-D.
We consider two basic relations on emotion variables: similarity and subsethood. Similarity, sm : E # E, is a binary equivalence relation between two emotion variables (we will see that
the fuzzy logic interpretation of similarity will actually be a
function, sm : E # E " 60, 1@, which measures the amount of
similarity between the variables rather than being true or false).
Subsethood, ss : E # E, is a binary relation between two emotion variables that is true if the first variable of the relation is
contained in the second. Like similarity, the fuzzy logic interpretation of subsethood is a value between zero and one. Further details are provided in Section III-C, where we will define
the fuzzy logic interpretation of these relations.
Finally, a translation is a mapping from the words of
one vocabulary to another, as determined by the corresponding codebooks:
translate :W 1 # C 1 # C 2 " W 2 ,

(1)

which is displayed schematically in Figure 1. This can be
decomposed by thinking of C 1 # C 2 as a similarity or subsethood matrix, which is denoted as the CWW engine in the
figure. Translation can be seen as selecting the word from the
output language w output ! W 2 such that the similarity or subsethood is maximized for a given w input ! W 1 . In the case of
similarity, the translation output is
w output = arg max
sm ^eval C2 ^w 2h, eval C1 ^w inputhh ,
!
w2

(2)

where the argmax functions as the decoder in Figure 1. The
formulation of similarity and subsethood in terms of IT2 FSs

Table of Contents for the Digital Edition of Computational Intelligence - May 2013