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Fuzzy Logic for More Rational RDAs

It controls Japanese subways, air-conditioning systems, and camcorders. And it may one day assist health professionals in setting objective Recommended Dietary Allowances (RDAs) if ARS nutritionist Eric O. Uthus has his way.

It's fuzzy logic—a mathematical approach to problems that can't be defined precisely, such as how much of a particular vitamin or mineral an individual needs to consume each day.

That amount varies, depending on many factors including the person's age, gender, heredity, and intake of other nutrients, says Uthus, a biochemist at the Grand Forks (North Dakota) Human Nutrition Research Center.

What’s more, use of scientific data to set an RDA requires judgment calls. For instance, the process poses questions like: Do we want to saturate body tissues with enough of the vitamin to provide a 30-day reserve or a 60-day reserve? There is no specific number that will satisfy everyone involved in determining the RDA.

“Fuzzy logic enables us to deal with situations that are not clear-cut,” says Uthus. “It should make the RDA process more objective.”

Uthus teamed up with German physicist Bernd Wirsam to develop a prototype for establishing an RDA for zinc. Co-owner of a company that uses fuzzy logic to optimize industrial processes, Wirsam was the first to apply the method to nutrition. He developed a computer program to describe the range of intakes of specific nutrients—from deficiency to excess.

The program then calculates, based on the nutrient composition of the foods an individual eats over the course of a week, how closely that total diet meets all the requirements, as defined by the German Society of Nutrition. And it suggests small changes in the diet that allow the individual to meet recommendations.

The mathematics of fuzzy logic were developed in the 1960s by the chairman of the electrical engineering department at the University of California, Berkeley. The Japanese adopted it in the 1980s to control hundreds of household appliances and electronics products that must cater to vague human concepts, such as "the air is cool." Fuzzy logic defines "cool" in computer terms.

Fuzzy Logic Curve for Zinc Consumption

Unlike classical logic in which something belongs exclusively to one set or the other, in fuzzy logic there is no distinct border separating sets. Something can belong to two or more sets—on a binary scale of 0 to 1. But its membership in all of the sets must add up to 1.

Uthus explains: “If we asked 100 people what room temperature is comfortable, we would get a range of answers. These values would fall into a bell-shaped curve with, perhaps, most of the people saying that 70° F was ideal. So the closer the temperature is to 70° F, the greater its membership in the ‘comfortable’ set. But while 70° F may be comfortable to the majority, it may be too cool to some and too warm to others, giving it partial membership in the “cool” and “warm” sets.

Likewise, when volunteers are given a particular vitamin or mineral in graded amounts, there is no definite border where one intake is deficient and a slightly higher intake is adequate. It's a range of values. Wirsam uses fuzzy logic to convert these ranges into a single number, says Uthus, who provides nutritional data and expertise.

A Grand Forks colleague helped to select two fairly sensitive biochemical indicators to use in developing the prototype curve for zinc. The amount of zinc in red blood cells is a good indicator of zinc deficiency, he says, because it falls off rather quickly as intake decreases. For the other end of the curve, zinc excess, they used the activity of superoxide dismutase in red blood cells. This enzyme requires a balance of copper and zinc to function properly, so its activity drops when zinc intake is excessive.

Wirsam uses these findings to describe fuzzy sets based on five intakes: zero intake, minimum intake—the least amount needed to prevent deficiency, optimum intake—the amount that confers the most health, safe upper limit—the most that can be consumed without causing any toxicity, and toxic intake.

Using this method, the researchers came up with a zinc RDA of 9 milligrams per day. That's well below the 15 mg recommended for adult males by U.S. and German committees but close to a 1993 recommendation by Europe's Scientific Committee for Food, says Uthus.

"Intuitively," he notes, "9 mg looks good when considering the fuzzy logic curve [see diagram] because this intake is at the peak, or optimal level, of the curve, while the recommended value of 15 mg is not."

Uthus emphasizes, however, that the recommendation is based on scanty data and is meant to demonstrate the principle of using fuzzy logic to set RDAs.

"The model I envision," he says, "is one in which variables could be easily added as new information comes to light. A highly developed model could be used to study how other nutrients interact with a given vitamin or mineral to alter its requirement." -- By Judy McBride, ARS.

Eric O. Uthus is at the USDA-ARS Grand Forks Human Nutrition Research Center, P.O. Box 9034, University Station, Grand Forks, ND 58202-9034; phone (701) 795-8382.