## 5 Fuzzy-Genetic Articulatory Model  
We describe here the basis of our algorithm, which is developed upon a fuzzy-genetic articulatory model, proposed in Reference [32] This model estimates, with a genetic optimization algorithm, the places of articulation membership degrees of a user speech. The parameters are used to produce synthetic speech which is compared to the input signal using a genetic approach. In this paper, the approach has been extended to cover the IPA phonetic symbols rather than the phonetic rules of a particular language, and the mimicking system has been extended to cover unrestricted text. According to our point of view, however, the place of articulation is characterized in fuzzy form. Each phoneme is described with eighteen variables, six of which are Boolean and represent the manner of articulation while the remaining twelve are fuzzy and represent the place of articulation. Therefore, our phonetic description appears as an extension of the classical Distinctive Feature Theory, because a certain vagueness is introduced in the definition of the place of articulation. For example, with a fuzzy description, an /_a_/ phoneme can be represented as:  
\[[0.32,0.9,0.12,1,0,0,0,0,0,0,0],\]  
which means that /_a_/ is a is vowel with a frontness of 0.12, an openness of 0.9 and a roundness of 0.32. It is important to remark that :  
* All the fuzzy sets for acoustic parameters have trapezoidal shape and are defined as follows: L1 (Initial locus), I (Initial range), D (Duration), F (Final interval), L2 (Final position). The values are divided in High, Medium, Low. * The estimation of degrees of membership of the places of articulation is made when the manner of articulation of an utterance is known, because the fuzzy rules are structured in banks. The easier way to perform manner of articulation estimation is from the text of the input utterance. However, this is not a limit because normally the estimation of facial movements, which is the goal of our algorithm, is needed to move talking heads during text to speech translation. * Since the degrees of membership of the places of articulation depend from the phonetic context, their optimal estimation should be performed in real time. This would require an excessive computational power. Our approximated but feasible approach is to estimate the degrees of membership once for a given phonetic context and a given speaker, stored in the knowledge base and used in any context and for any speaker. As regards the fuzzy rules, consider for example the following consonants: /_p_/, /_t_/. According to IPA, they are described as voiceless, bilabial, plosive and voiceless, alveolar, plosive respectively. Calling textt p0 and textit p1 respectively the first and second phonemes, some of the fuzzy rules involved in generating the acoustic parameters for the generation of the transitions /_pa_/, /_pi_/, /_tu_/, /_ti_/, /_tu_/, where /_a_/, /_i_/, /_u_/ are vowels, are the following:  
if p0 is plosive and p1 is voiced then L1(AH) is high; I(AH) is medium; D(AH) is low; F(AH) is low; if p0 is plosive and p1 is open then L2(F1) is medium if p0 is alveolar and p1 is voiced then L1(F1) is medium; L1(F2) is medium; L1(F3) is medium; if p0 is alveolar and p1 is open then L1(F1) is low; L1(F2) is low; L2(F3) is low;  
Clearly, the goal of these fuzzy rules is to generate the transitions of the acoustic parameters \(AH,F1,F2,F3\) that generate the correct transition. The rule decoding process is performed by a de-fuzzification operation with the fuzzy centroid approach. Another example is a transition of a vowel towards a vowel. In this case, the opening and the anteriority of the target phoneme determine the values of the first three formants.