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Miyahira et al. Journal of Translational Medicine 2011, 9:134 http://www.translational-medicine.com/content/9/1/134 RESEARCH Open Access Fuzzy obesity index (MAFOI) for obesity evaluation and bariatric surgery indication Susana Abe Miyahira1,2,3*, João Luiz Moreira Coutinho de Azevedo1 and Ernesto Araújo1,2,3 Abstract Background: The Miyahira-Araujo Fuzzy Obesity Index (MAFOI) for being used as an alternative in bariatric surgery indication (BSI) is validated in this paper. The search for a more accurate method to evaluate obesity and to indicate a better treatment is important in the world health context. Body mass index (BMI) is considered the main criteria for obesity treatment and BSI. Nevertheless, the fat excess related to the percentage of Body Fat (%BF) is actually the principal harmful factor in obesity disease that is usually neglected. The aim of this research is to validate a previous fuzzy mechanism by associating BMI with %BF that yields the Miyahira-Araujo Fuzzy Obesity Index (MAFOI) for obesity evaluation, classification, analysis, treatment, as well for better indication of surgical treatment. Methods: Seventy-two patients were evaluated for both BMI and %BF. The BMI and %BF classes are aggregated yielding a new index (MAFOI). The input linguistic variables are the BMI and %BF, and the output linguistic variable is employed an obesity classification with entirely new types of obesity in the fuzzy context, being used for BSI, as well. Results: There is gradual and smooth obesity classification and BSI criteria when using the Miyahira-Araujo Fuzzy Obesity Index (MAFOI), mainly if compared to BMI or %BF alone for dealing with obesity assessment, analysis, and treatment. Conclusion: The resulting fuzzy decision support system (MAFOI) becomes a feasible alternative for obesity classification and bariatric surgery indication. Background use as a leading cause of death, where obesity contri- The clinical conditions that are characterized as over- butes directly to the severity of the comorbities [12-15]. weight (pre-obesity) and obesity are currently a universal Therefore, a great clinical interest exists for evaluating epidemic of critical proportions. Efforts have been made overweight and obese patients to determine the risks to minimize this public health problem, but the preva- inherent with these conditions, to prescribe and control lence of obesity is still growing in both developed and conservative treatments, and to indicate when surgical developing countries [1-6]. treatment is needed. In the last 30 years, only the over- An excess of fat tissue (obesity) has been shown to be weight and obesity rating system, which uses the body harmful for multiple organs and systems through trom- mass index (BMI), has been internationally recognized bogenic, atherogenic, oncogenic, hemodynamic, and [16] (Table 1). neuro-humoral mechanisms [7-11]. Recently, obesity BMI is a mechanism to measure weight excess exten- and related diseases (comorbidities), including diabetes sively used in a myriad of epidemiologic studies, and is mellitus, hypertension, coronary artery disease, cancer, incorporated with clinical practice because of its simpli- sleep apnea, and osteoartrosis, have replaced tobacco city [17]. However, it does not properly evaluate the body fat (BF) proportion because it fails to distinguish lean muscle mass from body fat [18]. The BF measure- ment has more value than global body mass measure- * Correspondence: susana_miyahira@uol.com.br 1 Universidade Federal de São Paulo (UNIFESP), Brazil. R. Botucatu 740 - São ments since the harmful factor in obesity is the Paulo, SP, CEP 04023-900, Brazil accumulation of fat in the body, and lean muscle mass Full list of author information is available at the end of the article © 2011 Miyahira et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Miyahira et al. Journal of Translational Medicine 2011, 9:134 Page 2 of 10 http://www.translational-medicine.com/content/9/1/134 Table 1 Guidelines for the classification of overweight Table 3 Obesity classified by BF and obese adults using BMI BF (%) Women Men Condition Classification BMI ADEQUATE 30% Clinical guidelines on the identification, evaluation, and treatment of Guideline for the classification of obesity in adults. National Institute of overweight and obesity in adults. Washington, National Institute of Health, Diabetes and Digestive and Kidney Diseases. U.S. Department of Health and 1998. (Modified). Human Services. (Modified). does not burden the individual health [19,20]. Addition- 2) To validate Miyahira-Araujo Fuzzy Obesity Index ally, the BMI itself is revealed as an imprecise and inac- (MAFOI) in indicating bariatric surgery. curate method to measure the percentage of Body Fat (%BF), especially when people from different categories Methods are took into account, which happens in populations of This prospective study was carried out at the Hospital different ages and with different body types [21,22]. Municipal Dr. José de Carvalho Florence (HMJCF), in Despite of these limitations, the BMI is often used in the city of São José dos Campos, São Paulo state, Brazil the therapeutic approach to obesity classification, analy- from December of 2008 to August of 2009. Such a sis, and treatment as well as to determine bariatric sur- research is approved by the Ethic and Research Com- gery (Table 2) [1]. mission (CEP) of the Universidade de Taubaté (UNI- Taking into account that the BF percentage is the most TAU) (Exhibit I) and the Universidade Federal de São reliable indicator of obesity and that the BMI is used to Paulo (UNIFESP) (Exhibit II). All participants in the prescribe surgery, it would also be convenient to simulta- study signed an informed consent form that was in neously consider BF when approaching the patient to accordance with Decree no. 196/96 of the National recommend bariatric surgery (Table 3) [23-25]. In this Health Council (CNS)/Health Ministry (MS) and its sense, the BMI should be included in conjunction with complements (Decrees 240/97, 251/97, 292/99, 303/00, the %BF when evaluating the condition of the patient and and 304/00 of the CNS/MS) (Exhibit III). This research determining an obesity treatment algorithm [18,26]. was sponsored by the funding agency Fundação de Therefore, the search for a more accurate model that Amparo à Pesquisa do Estado de São Paulo (FAPESP), evaluates overweight and obese patients with apparent process # 2009/07956-7. body mass excess led to the conception that indicates when Inclusion criteria were the following: patients from surgery is appropriate for these patients. Previously pre- emergency and nursing rooms in the HMJCF, of both sented, the Miyahira-Araujo Fuzzy Obesity Index (MAFOI) gender, and aged 18 years and older, and patients fasting evaluates the obesity by correlating BMI and the BF in the at least for 6 hours of solid food and 4 hours of liquids. context of fuzzy set theory and fuzzy logic. MAFOI must Exclusion criteria were the following: patients who also have the ability to accurately recommend which refused to take part in the study, pregnant women, and patients should be referred for bariatric surgery. patients with kidney failure, hydroelectrical alterations, inadequate hydration, fever (T>37.8°C), ascites, hepatic Objectives cirrhosis, a coronary by-pass, or an amputation of the General: To determine a more accurate parameter for inferior or superior members. the evaluation of obesity and in bariatric surgical The weight, height, and BF of the patients were mea- indication. sured during the same day and at subsequent time Specifics: points. 1) To evaluate the use of Miyahira-Araujo Fuzzy Obe- sity Index (MAFOI) in a random sample of the obese BMI Calculation population. To calculate the BMI, a stadiometer, which was graded at every 0.5 cm, and a digital scale, with 0.1-kg sensitiv- ity, were used. Table 2 Indication of bariatric surgery according to the BMI and comorbidities BF Calculation BMI >35 and 40 Kg/m2 To obtain BF and fat-free mass (FFM) values, a body Without comorbidities Without indication With indication composition analyzer was used, a method that uses With comorbidities With indication With indication direct multi-frequency bio-impedance (BIA) and the
Miyahira et al. Journal of Translational Medicine 2011, 9:134 Page 3 of 10 http://www.translational-medicine.com/content/9/1/134 Segmental-model InBody230 (Biospace Co., Ltd. Seoul output classes and values resulting in a new index 135-784 KOREA) Tetra-polar System with 8-points. The named the Miyahira-Araujo Fuzzy Obesity Index BF values and FFM system were obtained through the (MAFOI) (Figure 4). MAFOI was, then, used to classify BIA from equations that were incorporated in the individuals in relation to their obesity condition and equipment, as described by Bedogni [35]. establish a criterion that provides a decision-making sys- tem that can recommend bariatric surgery, as well. Protocol for the evaluation 1) The patients were instructed to refrain from drinking These described steps embrace the mapping process alcohol and to not perform heavy physical activity dur- that includes the following: (i) the knowledge basis, (ii) ing the day prior to the exam. the fuzzification that translates the crisp value (classical 2) Fasting at least for 6 h of solid food and 4 h of number) of the input variable into a fuzzy value, (iii) the liquids prior to the exam. cylindrical extension, the aggregation, the conjunction, 3) The patients were instructed to use the rest room and the projection, and ( iv ) the defuzzification that before the test. translates the output linguistic variable in a crisp value. 4) The patients wore light clothes or a hospital gown. To build the input variable for the fuzzy BMI, the 5) The patients did not wear watches or jewelry in the WHO classification (Table 1) was used. The fuzzy sets vicinity of the electrodes. for the fuzzy BMI are assigned the following linguistic 6) The patients remained standing for 5 minutes terms: overweight (OW), obesity class I (OI), obesity before the exam performance. class II (OII), and obesity class III (OIII). 7) The room temperature at the exam was maintained To build the input variable for the fuzzy %BF, the from 20°C to 25°C. NIDDK classification of overweight and obesity was used (Table 3). The fuzzy sets for the fuzzy %BF are Fuzzy Set Theory and Fuzzy Logic for Fuzzy BMI, Fuzzy %BF assigned the following linguistic terms: adequate (AD), and Fuzzy Obesity Output Classes and Values in Obesity light obesity (LI), moderate obesity (MDE), high obesity Assessment Initially, the BMI was modified by the treatment of the (HI), and morbid obesity (MOR). crisp classes, as adopted by the World Health Organiza- The fuzzy obesity or surgical-treatment-indication eva- tion (WHO), into fuzzy sets, i.e., fuzzy classes (Figure 1 luation constituted the output linguistic variable (conse- and 2). While the classical set theory is based on the quent of the rule). The fuzzy sets for the fuzzy obesity excluded middle principle where an element belongs, or or surgical-treatment indication are assigned the follow- not, to a set (crisp set/class), the fuzzy set theory allows ing linguistic terms: thin (TH), muscular hypertrophy a relation of gradual membership of an element to a (MUH), excess of weight (EW), sutomori (SUT), fuzzy determined set [27,28]. Such an approach was, thus, obesity (FZOB), and morbid obesity (MOR). The rules extended to the %BF classes (Figure 3). The fuzzy BMI were restricted to those classes considered relevant, i.e. and fuzzy %BF classes were aggregated by employing restricted to only those than can happen in ordinary logical connectives and mapped into fuzzy obesity practice (Table 4). The base of rules is represented as a fuzzy matrix in table 4. Fuzzy BMI, % Fuzzy BF, Fuzzy Obesity Output Classes, and MAFOI performance to obesity diagnosis and to surgical treatment indication The WHO reference standard is employed to evaluate the obesity diagnosis performance, which is evaluated by using the BMI (Table 1). Values that are already described in the literature were used to evaluate the obe- sity-diagnosis performance, which was evaluated using the %BF cut-off value [25]. To evaluate the MAFOI, a value defined by the defuzzification of the output variable is used by using the center of area method. Statistical analysis The continuous variables are presented as mean and standard deviation (SD) and numbers and percentages Figure 1 Classical BMI. BMI classical set, with the linguistic values: as categorical variables. The Pearson coefficients of cor- slim (S), overweight (OW), obesity class I (OI), obesity class II (OII), relation and the respective intervals of confidence (IC) obesity class III (OIII). (95%) are estimated to compare BMI, BF and MAFOI
Miyahira et al. Journal of Translational Medicine 2011, 9:134 Page 4 of 10 http://www.translational-medicine.com/content/9/1/134 Figure 2 Fuzzy BMI. BMI fuzzy set, with the linguistic terms: overweight (OW), obesity class I (OI), obesity class II (OII), obesity class III (OIII). by genre. The McNemar test [29] is used to compare of evaluation. Within the 72 patients, 42 were female the percentage of the individuals considered obese by and 30 were male. The mean age standard deviation the BMI versus BF, BMI versus MAFOI and BF and BF (SD) was 39.5 ± 11.2 years old for women and 43.5 ± versus MAFOI. 15.8 years old for men. The mean weight SD was 70.0 ± 14.5 kg for women and 79.6 ± 25.3 kg for men. The mean BMI SD was 27.1 ± 5.8 kg/m2 for women and 27 Results ± 7.4 kg/m 2 for men. The mean %BF SD was 38.7 ± In the current study, 81 patients were evaluated and 72 out of the 81 were evaluated by analyzing the BMI and 6.7% for women and 26.3 ± 7.9% for men. The demo- %BF. Among the excluded patients, 7 were not fasting, a graphic data are described in Table 5. patient had consumed alcohol within 24 h prior to the The maximum and minimum BMI, %BF, and MAFOI test, and a patient had a fever (T = 38.2°C) at the time values are presented in Table 6. Mean and SD values Figure 3 Fuzzy BF. BF fuzzy set, with the linguistic terms: adequate (AD), light obesity (LI), moderate obesity (MDE), high obesity (HI), morbid obesity (MORB).
Miyahira et al. Journal of Translational Medicine 2011, 9:134 Page 5 of 10 http://www.translational-medicine.com/content/9/1/134 Figure 4 Fuzzy Obesity-Degree/Surgical-Treatment-Indication Classes. Obesity-Degree/Surgical-Treatment-Indication classes set, with the linguistic terms: thin (TH), muscular hypertrophy (MUH), excess of weight (EW), sutomori (SUT), fuzzy obesity (FZOB), and morbid obesity (MOR). are given for BMI and %BF. Table 7 displays the Pear- The correlation between the BMI and %BF for women son linear correlation coefficients between BMI (Kg/m2) was stronger than for men. When comparing BMI to and the remaining variables: BF, FFM, and MAFOI for FFM, the correlation was better for men. The groups both genders. show a strong correlation for all of the variables in both The low bound value of BMI obesity class I classifica- genders. Regarding the BMI and MAFOI, the correlation tion (OI) = 30 and the low bound value of %BF high was strong for both women and men. The correlation obesity classification (HI) = 35 (women = 35; men = 25 between BF and MAFOI was the best one for both +10), which are defined by the WHO/NIDDK [16,25] genders. were used as input values of the fuzzy model. The fuzzy The percentages of individuals that were considered inference was performed. The outcome was the cut-off obese by the BMI, %BF, and MAFOI criteria are pre- value of index MAFOI/BSI (MAFOI) = 68. sented in Table 11. The percentage of individuals con- The percentage of individuals that were considered sidered obese by the %BF criteria (63.9%) was obese by the BF criteria was statistically lower than by statistically higher than the BMI criteria (23.9%) (p < the BMI criteria (Table 8). 0.001). The percentage of individuals considered obese The percentage of obese individuals determined by the by the MAFOI criteria (41.7%) was statistically higher MAFOI criteria was statistically higher than by the BMI than the BMI criteria (23.6%) (p < 0.001). The percen- criteria (Table 9). The percentage of obese individuals tage of individuals considered obese by the %BF criteria determined by the BF criteria was statistically higher (63.9%) was statistically higher than the MAFOI criteria than the MAFOI criteria (Table 10). (41.7%) (p < 0.001) [30]. Discussion Table 4 Bases of Fuzzy Rules Use of BMI to classify obesity Despite its limitations, the BMI is currently considered BMI/BF TH OW OI OII OIII the most useful measurement of the obesity level of the AD TH MUH MUH MUH X population. Thus, the BMI can be used to estimate the LI TH HM HM HM X prevalence of obesity in the population and the risks MDE EW EW SUT SUT MOR associated with this condition. However, it does not elu- HI EW FZOB FZOB FZOB MOR cidate the wide variation in the nature of obesity MOR X FZOB FZOB FZOB MOR between different individuals and diverse populations. BMI (body mass index), overweight (OW), obesity class I (OI), obesity class II Among sedentary and overfed individuals, the increase (OII), and obesity class III (OIII). BF (body fat percentage), adequate (AD), light obesity (LI), moderate obesity (MDE), high obesity (HI), thin (TH), muscular of body mass is generally due to both body fat and mus- hypertrophy (MUH), excess of weight (EW), sutomori (SUT), fuzzy obesity cle mass. Nevertheless, among men, the increase of body (FZOB), and morbid obesity (MOR).
Miyahira et al. Journal of Translational Medicine 2011, 9:134 Page 6 of 10 http://www.translational-medicine.com/content/9/1/134 Table 5 Standard deviation (SD), body mass index (BMI), body fat (BF) Women (n = 42) Men (n = 30) Mean Minimum Maximum SD Mean Minimum Maximum SD Age 39.5 18.0 60.0 11.2 43.5 18.0 76.0 15.8 (years) Weight 70.0 48.0 113.1 14.5 79.6 32.0 160.0 25.3 (Kg) Height 160.9 148.5 170.0 5.7 172.2 155.5 183.0 7.5 (m) BMI 27.1 18.8 45.9 5.8 27.0 17.6 54.1 7.4 (Kg/m2) BF 38.7 25.2 48.8 6.7 26.3 9.9 40.1 7.9 (%) mass may play a more important role than in women of classification. However, the limits of these artificially which has the increase of body fat the main factor of created classes are inaccurate and badly defined. acquired excess of weight. Thus, the correlation between To justify the use of fuzzy logic in this research, it is the BMI and %BF for women is stronger than for men. worth to consider that the classical procedure for evalu- When comparing BMI to fat-free mass, the correlation ating the results from research in the life-science area was better for men, a feasible explanation is due to the has been the application of descriptive statistics to the greater increase of the muscle mass among them. tabulation and stratification of data. Inferential statistics Regarding the BMI and MAFOI, the correlation was have been used where probabilistic analyses are needed. strong for both men and women. The correlation In the classical logic approach, however, all of the between BF and MAFOI was the best one for both instruments aim at establishing values with a higher rate genders. of occurrence; specific ranges of variables are directly Studies indicate that the BMI has to be adjusted for defined as causes or modulating factors. This treatment diverse ethnical groups as the WHO study of the Wes- is perfectly suited when it refers to results of exact- tern Pacific Region [31]. This study demonstrated that science studies where the objects are simple substances different cut-off values must be adapted for overweight and the samples are homogeneous. However, this is not (>23 kg/m2) and for obesity (>25 kg/m2). Other studies the case in the biological field where the disparity evaluated the Australian aborigine population and observed can be simply due to normal individual varia- showed that the cut-off point was >26 kg/m2 for defin- tion that occurs in a species population [34]. ing overweight [31]. The BMI accuracy in diagnosing obesity is mainly limited in intermediary ranges of BMI Limitations of the study in men and in elders due to a failure in discriminating 1) The membership functions were conceived by the free-fat mass and body fat [32]. authors based on the concepts, classification and knowl- The results of this study were in agreement with the edge about overweight and obesity already described in data found in the literature when the performances of the literature [25]. Therefore others membership func- the BMI and BF in diagnosing obesity were compared tions maybe acceptable. 2) The fact that there is not a [18,32,33]. Analyzing only the BMI, 23% of the sample MAFOI for men and other for women. The only one was considered obese, while this proportion increased to obtained maybe creates a skewness that underestimates 63.9% and 41.7% when evaluated, respectively, with the BSI for men as the BF cut-off for men may be consid- %BF and the MAFOI. ered. 3) The calculus of the MAFOI itself was decided The variability between living things of the same spe- taking into account the lower bounds of two special cies, inherent to the biological condition, allows a range bands of BMI and %BF categorization. This election Table 6 Standard deviation (SD), body mass index (BMI), body fat (BF) Women (n = 42) Men (n = 30) Mean Minimum Maximum SD Mean Minimum Maximum SD BMI 27.1 18.8 45.9 5.8 27.0 17.6 54.1 7.4 BF (%) 38.7 25.2 48.8 6.7 26.3 9.9 40.1 7.9 MAFOI 23.9 91.7 23.9 91.7 The maximum and minimum BMI, BF, and MAFOI values.
Miyahira et al. Journal of Translational Medicine 2011, 9:134 Page 7 of 10 http://www.translational-medicine.com/content/9/1/134 Table 7 Body mass index (BMI), body fat (BF), fat free Table 9 Body mass index (BMI) mass (FFM) MAFOI Women Men >68 (n = 42) (n = 30) BMI OBESE NON-OBESE >30 kg/m BMI and BF Pearson correlation 0.831 0.656 OBESE 12 5 17 (23.6%) Sig. (2-tailed)
Miyahira et al. Journal of Translational Medicine 2011, 9:134 Page 8 of 10 http://www.translational-medicine.com/content/9/1/134 dealing with diverse groups and classes (Figure 2). This Table 11 Body mass index (BMI), body fat (BF) provides the advantage of a more realistic classification BMI = 23.6% BF = 63.9% both for obesity severity and surgical recommendations. >30 >35(women) Taking into account the same patient, a fuzzy set (class) >25(men) assigned Obesity II Class is active with a degree of BMI = 23.6% MAFOI = 41.7% recommendation - i.e., a degree of certainty - for surgical >30 >68 treatment, μrecommendationOBII (x = 39 Kg/m2) = a1, where BF - 63.9% MAFOI = 41.7% 0 35 (women) >68 = 39 Kg/m2) = a1. Observe that this patient may also be >25(men) classified by another fuzzy set labeled Obesity III Class n = 72 achieving another degree of recommendation for surgical The percentages of individuals that were considered obese by the BMI, BF, treatment, μ recommendation OBIII ( x = 39 Kg/m 2 ) = a 2 , and MAFOI criteria. where 0 < a 2 < 1, according to a different degree of membership, μM = OBIII (x = 39 Kg/m2) = a2, such that overweight and obesity in Table 3 is used. The elements a 1 > a 2 [37]. Further, when taking into account two of BMI and the elements of %BF, both being distributed patients with BMI of 39 kg/m2 and BMI of 40 kg/m2, into the universes of discourses X and Y, respectively, are grouped and assigned by classes or linguistic terms. both would be categorized either as OII as OIII. The The BMI obesity classes are assigned the linguist terms difference exists since the first patient presents a class of overweight (OW), obese class I (OI), obese class II (OII), OII that is higher than OIII, whereas the second patient and obese class III (OIII) meanwhile the %BF obesity is more in the OIII group than in the OII group. In this classes are assigned the linguistic terms adequate (AD), case, both patients have a potential to receive or not light obesity (LI), moderate obesity (MDE), high obesity receive a recommendation for surgical treatment. This (HI), morbid obesity (MOR) [26]. determination depends on other factors and not only When employing the classical set theory to classify the BMI value, which is improperly and perhaps incon- obesity and to recommend surgical treatments, or not, sistently used. there is categorical, crisp classes like yes or no, recom- (2) The second step in building up the MAFOI is mendation or no-recommendation for bariatric surgery. fulfilled by satisfying the BMI dependence upon Diverse crisp obesity classes can be employed for surgi- another factor [26]. Fuzzy set theory advantages in cal recommendation, according to the class a patient allowing distinct variables to work together based on belongs to (Figure 1). For instance, a patient with a BMI the aggregation of their respective fuzzy sets. The of 39 Kg/m2 is assigned to the Obesity II class, such that manipulation of sets is chiefly carried out by operators μM = OII (x = 39 Kg/m2) = 1. Observe that all the other of intersection ∩ , union ∪ , and complement, ¬. The classes obtain a null activation status, μ≠OII (x = 39 Kg/ intersection set operation corresponds in logic to the connective, operator of conjunction, ⋀ , and to the m 2 ) = 0 . This category achieves no-recommendation class for bariatric surgery, μno-recommendation (x = 39 Kg/ semantic connective, “and” The union set operation is m2) = 1, or equally null surgical recommendation, μre- associated to the connective operator of disjunction, ⋁, and to the semantic connective “or” The complement 2 commendation ( x = 39 Kg/m ) = 0 [37]. Nevertheless, it seems to be arbitrary to assign a Boolean approach as is related to the logical connective of negation of a the one used for BMI or %BF. Two patients with BMI given proposition presenting the idea of opposition. of 39 kg/m2 and BMI of 40 kg/m2 are, respectively, clas- The BMI and %BF classes were aggregated by employ- sified into the OII and OIII groups receiving each a dis- ing logical connective of conjunction. The %BF vari- tinct treatment recommendations, even if the difference able is the modulation factor for BMI variable in the from one patient to the other is minimal, Δ1. Although obesity degree and surgical recommendation analysis. the first patient is not in the range for a surgical recom- When the sets are considered under the classical set theory, the Cartesian pair, ( x , y ), such that x Î BMI mendation, the second one is in the range for a surgical and y Î %BF, assumes either a unitary value, μ(MBMI × recommendation. In this situation, both patients may %BF not present significant biological, anatomical, or physio- ) (x,y) = 1, for each pair that belongs to the rela- M tionship or a null value, μ(MBMI × M%BF) (x,y) = 0, for pathological differences that justify such a discrepancy in the surgical recommendation. Conversely, fuzzy set each pair that does not belong to the relationship. theory allows simultaneously allocating a patient in When the partition of the universe of discourse for the more than one class, or not, by embodying the inherent BMI and %BF variables is accomplished by using the subjectivity in the obesity and bariatric surgery classifi- fuzzy set theory, each Cartesian pair is also able to cation and analysis processes. Likewise crisp obesity assume an intermediary value between 0 and 1, 0 μ ( M BMI × M %BF ) ( x,y 1, yielding an overlapping of classification, fuzzy obesity classification also allows
Miyahira et al. Journal of Translational Medicine 2011, 9:134 Page 9 of 10 http://www.translational-medicine.com/content/9/1/134 c lasses (overlapped assignments) in a way that the a criterion that provides a decision-making system that patient can be classified in complementary manners. can recommend bariatric surgery [26]. Both BMI and %BF are understood as input variable when dealing with a fuzzy IF-THEN inference mechan- Acknowledgements ism (mapping) and the resulting Cartesian product, X Supported by grant: 2009/07956-7 from Fundação de Amparo à Pesquisa do × Y, is related to the input space. In general, this input Estado de São Paulo (FAPESP), Universidade Federal de São Paulo (UNIFESP), and Associação Paulista para o Desenvolvimento da Medicina (SPDM). space is mapped into an output universe of discourse. (3) This leads to the third step in designing the Miya- Author details hira-Araujo Fuzzy Obesity Index. The obesity-degree/ 1 Universidade Federal de São Paulo (UNIFESP), Brazil. R. Botucatu 740 - São Paulo, SP, CEP 04023-900, Brazil. 2Hospital Municipal Dr. José de Carvalho surgical-treatment-indication evaluation constituted the Florence (HMJCF), Av. Saigiro Nakamura 800 - São José dos Campos, SP, CEP output linguistic variable (Figure 4) [26]. The fuzzy sets 12220-280, Brazil. 3Associação Paulista para o Desenvolvimento da Medicina that part such an output universe of discourse are (SPDM), Av. Saigiro Nakamura 800 - São José dos Campos, SP, CEP 12220- 280, Brazil. assigned the linguistic terms thin (TH), muscular hyper- trophy (MUH), excess of weight (EW), sumotori (SUT), Authors’ contributions fuzzy obesity (FZOB), and morbid obesity (MOR). They SAM made an extensive research on the bibliography, and was the responsible for the data collection. JLMCA designed the study in a were obtained according to the classification of body methodological point of view, and was the principal writer of this study in composition, regarding the weight, muscle mass, and English. EA was the responsible for the fuzzy logic approach. All authors body fat. The sutomori fuzzy set for obesity is also a read and approved the final manuscript. novel obesity class previously introduced by the authors Competing interests and there is no similar in literature. 26 It is a special The authors declare that they have no competing interests. body constitution which is found among sumo wrestlers, Received: 5 July 2011 Accepted: 14 August 2011 characterized by a large amount of both muscles and fat Published: 14 August 2011 tissue. These athletes have a large muscular mass and present a high level of %BF and due to that are usually References considered as obese. However, when compared with 1. Kolata G: Obesity declared a disease. Science 1985, 227:1019-20. 2. 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