Childhood obesity is a precursor for adult obesity (Gonzalez-Suareez
et al., 2009). Obesity and overweight are major risk factors for
a number of chronic diseases, including diabetes, cancer and cardiovascular
disease (WHO, 2010). Obesity and overweight are now dramatically
on the rise in low and middle-income countries, particularly in urban settings.
Most Malaysian people eat based on their appetite without considering the calories,
fat, and all other nutrients in the food. This unhealthy eating habit is responsible
for at least 300,000 deaths each year (Afoakwah and Owusu,
2011). Beside the unhealthy eating habits, people also do not concern about
the price of the foods with the nutrient requirement. To avoid these problems,
people should minimize the cost of buying foods. They should spend less money
but have sufficient nutrients requirement. By minimizing the cost, they still
can fulfill their nutrient requirement everyday (Mamat
et al., 2011). Raffensperger (2008) has conducted
a research about the minimum cost of low-carbohydrate diet. The research found
that the least-cost of low-carbohydrate diet is expensive than the least-cost
of low-fat diet. The study identifies which nutrients had the greatest effect
on cost for a low-carbohydrate and low-fat diet.
Cadenas et al. (2004) has done a research about
diet problem in Argentina farms using an application of fuzzy optimization.
Usually, the livestock is not confined. Therefore it is impossible to assess
the amount of food each animal will eat. Then it makes no sense to design diets
verifying the nutritional requirements exactly. Consequently, a Decision Support
Systems (DSS) named SACRA (a Spanish acronym for support system for the construction
of cattle diets) have been used in order to solve the problem. Karlsson
et al. (2010) has done a research about diet-induced obesity in mice
and has found that Diet-Induced Obese (DIO) mice have increased morbidity and
mortality following secondary influenza infection compared with lean mice.
Therefore, this research concentrates on the human diet problem using Fuzzy Linear Programming approach (FLP). Lack of energy balance in human most often causes overweight and obesity. Overweight and obesity happen over time when the calorie taken is higher than the body needs. There are many types of food that is high in calories. For example Malay pancake (roti canai), bread, eggs, fried chicken, fried noodles and others. People unrecognized the amount of calories in the foods. It shows that people consume food that contains high calories but not enough requirement of nutrient for their body. It leads them to get obesity, overweight and other diseases. Therefore, people need to be extra concern about the food that they eat. They must choose the right food with the right nutrient requirement.
In Malaysia, the trend now that fast food had become part and parcel of our lifestyle. People rely on fast food such as burger, KFC chicken, pizza and others for breakfast, lunch or dinner. Although the price for the food are expensive compared to rice-based food, they still interested to eat fast food because it as a way out or a symbol of modern living. Unfortunately, fast food contain high amount of fat, sugar and salt. Therefore, if taken continuously, it can shorten our lives.
Besides, poverty is a historical fact of life especially in rural areas. Lack of job opportunities in the rural areas is the main cause for the problem. Increasing in food price makes them unable to buy healthy food. Therefore, they need to choose the food that is low price but specify the nutrient requirement for their body.
There are two objectives in this research. First is to help people in choosing the right food with the right nutrient requirement. The second one is to minimize cost in buying healthy food.
MATERIALS AND METHODS
The method used in this research is Fuzzy Linear Programming Approach (FLP). FLP is known as multi-objective.
Raffensperger (2008) has proposed the model of Minimum
Cost Diet Problem (MCDP) which is:
where, j is a food eaten per day, cj is the price of food j, xj is 100 g of food j eaten per day, aij is the amount of nutrient i in 100 g of food j, bi is the required daily amount of nutrient i, di is the maximum daily amount of nutrient i, m is the number of nutrients and n is the number of food.
In this study, the price for the food is uncertain and it is assume as fuzzy numbers. Therefore, this fuzzy price is approached by linear programming with fuzzy objective coefficients. Formula (2) is the model of Minimum Cost Diet Problem (MCDP) with fuzzy objective coefficient (MCDP-FOC):
is the uncertain price of food j per 100 g.
= (cj¯/cj/cj+) are triangular fuzzy
numbers that assign the uncertain price of foods.
Since, the uncertain prices of MCDP-FOC in Formula (2) are assigned by triangular
= (cj¯/cj/cj+), the objective will
become multi-objective Linear Programming.
MULTI OBJECTIVE APPROACH
One of Fuzzy Linear Programming Approach is known as multi-objective. Multi-objective linear programming problems can be found in various fields. This formula focuses on minimizing cost of buying healthy food. Definition 1 shows the membership function of triangular fuzzy number.
Definition 1: The membership function of triangular fuzzy number
= (cj¯/cj/cj+) is:
where, μc¯j(x) is the membership function for uncertain price of food j per 100 g.
Equation 4 show the formula of multi-objective Linear Programming:
The objectives also can be written as:
When there are constraints, the maximum and minimum value for each objective
can be found. It is show as below:
Based on Eq. 6, the membership function of each objective is defined as:
Based on fuzzy decision making proposed by Bellman and
Zadeh (1970), let:
From Eq. 7-9, the model in problem 2 becomes
the following optimization problem:
where, xj≥0, 0≤β≤1
The number of chosen food is 40 and the number of nutrients is 27. The prices of foods (in RM) were collected from local grocery stores in March 2009, Terengganu, Malaysia. Nutrients requirements were for those of a 30 years-old-sedentary woman. The Acceptable Macronutrient Distribution Range (AMDR) for carbohydrate, fat and protein is 45 to 65%, 20 to 35% and 10 to 35% of calories, respectively. For 1982 kcal of energy, at 4 kcal g-1 of calories correspond to a maximum of 322 g of carbohydrate, 35% of calories correspondto maximum of 77.078 of fat.
|| Nutrient requirement per day (Female, 30 years old, sedentary,
BMI 24.99 kg m-2)
Table 1 shows the minimum maximum and actual nutrient requirements. Entering the price of food, nutrient requirements and amount of nutrients in food to the crisp and fuzzy model, the solutions as in Table 1 can be obtained.
THE HEALTH DIET SYSTEM
It is difficult for people to calculate the amount of nutrient in foods that they consume. Thus, a system to calculate it automatically is presented. The system is known as Health Diet System.
Figure 1 show the login page of the system, Fig. 2 show the homepage of the of the system, Fig. 3 show a page to calculate the Body Mass Index (BMI), Fig. 4 show the food taken by people and Fig. 5 show the final result based on the food and the amount of food taken.
The Health Diet System is functioning to calculate the amount of nutrient based
on the food taken. People can choose how many times to eat daily. For example,
minimum is one time and maximum is six time. After choosing the how many times
to eat, the next step is to choose the type of food to be taken. After that,
it will automatically generate the value of nutrients for particular foods.
For example if they take coconut rice (nasi lemak) for breakfast, beriyani rice
(nasi beriyani) for lunch and satay for dinner, it will calculate the amount
of energy, protein, calcium, iron, vitamin and other nutrients based on the
food that have been taken.
|| Health diet system login page
|| Health diet system homepage
Therefore, based on the amount of nutrients, the Health Diet System will determine
the level of nutrients. Then, a graph is plotted to show all the amounts and
types of nutrients taken. The Health Diet System will also help them to choose
the healthy food with minimum cost. For example, if they have RM5, system will
suggest healthy food based on the costs that have been keyed-in. The Health
Diet System also help people in minimizing cost diet problem, manage them to
get a healthy diet and would definitely boost the practice of a healthy lifestylein
the Malaysian society.
|| Food taken page
|| Final result page of health diet system
Fuzzy linear programming approach is used to calculate the amount of nutrient
in food. Thus, the balance diet and nutrient requirement can be determined.
It is very important because mostly people just eat without considering the
amount of nutrient in the food. Nowadays, mostly Malaysian people eat foods
that contain high amount of sugar, fat and calories. This problem will lead
them to get diabetes and cardiovascular disease. They need to prevent it from
happen by taking healthy food. Besides that, when buying food, the price of
food with the nutrient requirement need to be considered. It means that, if
they just have RM5, they need to buy foods that will give them enough nutrients.
It not just helps them to get balance diet but it also prevents them from getting
any chronic diseases and obesity. Therefore, people need to concern about the
food that they take so that they can prevent themselves from getting any disease.
It is because preventing is better than cure.