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  Fuzzy Logic applied to Surveys

1.1 Errors in surveys

There can be numerous errors occurring in surveys. The important ones among them are:

1. Random error: This error is caused due to the sample not being a representative of the population. In order to minimise this error a larger and more representative sample needs to be chosen. But this increases costs and is not feasible. Hence there is always some random error.

2. Measurement error: This refers to the performance of the survey instrument and is directly related to the reliability and validity of survey instrument.

3. Error due to subdivisions: This error occurs when the survey is to be carried out separately for different groups of people. Here the sample is divided into many subdivisions such as rich, middle class and poor or children, adults and senior citizens.

4. Errors due to differing attitudes: Many a times, the personality of the respondent changes the way he/she looks at things. Thus different people may interpret a similar phenomenon in different ways. This may be dependent upon whether the respondent is optimistic or pessimistic, his introversion or extroversion, his mood as also some biases and prejudices that he may have regarding the particular topic.

1.2 Reducing the error due to sub-divisions

In some surveys the sample is divided into subdivisions. These subdivisions have crisp boundaries i.e. the subdivision changes at one particular value of the variable. For example, upper middle class subdivision may range from annual income of Rs1,80,000-Rs3,00,000 while rich may extend from Rs3,00,000 onwards. Consider a survey about a product that targets only rich people. Will a survey of people earning more than Rs3,00,000 suffice? The problem is that this type of survey considers people earning Rs3,00,000 at par with people earning Rs5,00,000. Surely the latter have more buying power compared to the former. The effect of buying power will diminish as the income increases but close to the Rs3,00,000 mark its effect will be the most. The different attitudes of people will ensure that some of them will never think of buying the product. Also the lower income people may put more emphasis on price while the higher income people may prefer extra features and quality. If the company wants to produce a top of the line quality product it will mean that getting the views of those putting more emphasis on price may be unnecessary. Also what about the people earning Rs2,90,000? Are they any different from the people earning Rs3,00,000? So why should they be totally ignored?

One solution is asking the people whether they would consider buying the product before proceeding with the other questions. The downside to this is that many people won't have decided about buying. If forced to make the decision they may either make an arbitrary one or even a wrong one that they may reconsider later. After all one does not spend much time on a questionnaire, does one? Another even bigger pitfall is that the respondent will easily figure out the purpose of the question and be predisposed to reply in the affirmative, as he/she wants to have his/her views considered. Even if information is provided to the respondent about the product he/she may ignore it due to want of time or interest. Also this approach will also take up more time and money due to larger number of respondents to be selected.

Fuzzy logic can provide a more effective solution. This is because it allows incomplete membership of a variable in a set. Thus people having income of Rs4,00,000 and above can be considered to be fully rich; membership to fuzzy set 'rich' is 100%. However, for incomes below Rs3,50,000 the membership slowly decreases from 100% to 50% at Rs3,00,000 and then decreases further to 0% for Rs2,50,000. The values of the limits may be obtained after careful consideration and hence may differ but the basic idea remains the same. Simultaneously the degree of membership (confidence) of the incomes in fuzzy set 'upper middle class' increases from 0% at Rs3,50,000 to 100% at Rs2,50,000. Now for carrying out the survey, people in the income group above Rs2,50,000 can be considered and the weightage given to their responses be made proportional to the confidence in fuzzy set 'rich'.

This will lead to more effective and accurate surveys when the above mentioned fuzzy logic equations are used as a survey tool along with the normal methods.

The same principle may also be used in open questionnaires where the answers consist of gradation of a particular property in the form of numbers. For example when the height of the respondents is obtained through the survey and we want to classify the heights obtained into tall, medium and short, fuzzy equations where there is overlap between short and medium as well as medium and tall can be used. This can be especially useful when the classification is to be obtained to probe a certain association; for example to ascertain whether there is an association between height and good and bad posture.

1.3 Overcoming difficulties in combining different sub-divisions

Sometimes instead of dividing into various sub-divisions there is a need to obtain a somewhat common opinion. Consider the above example itself. Now suppose the company wants to produce something that would cater to both the rich and the upper middle class. Obviously this product will not incorporate a few features, as also it will have a lower price. For this product the views of both sub-divisions are important. One way of doing this is to evaluate responses of fixed number of respondents from each sub-division, study these responses separately and then combine them. The problems will be that usually a two peak result will be obtained, one standing for the upper middle class group emphasising on cost and the other for the rich emphasising on quality. To combine them to obtain a middle ground may prove difficult. Instead, fuzzy logic may be used to make the synthesis simpler.

It is important to note that in this case the people with income around Rs3,00,000 are the key. This is because they represent the middle ground between the two sub-divisions. Hence it is safe to assume that they are most likely to have the middle ground opinion about the product that is being sought by the company. Hence now, their opinion will get the most weightage. As the income increases or decreases the weightage will reduce. This will help to obtain a more accurate opinion.

1.4 Quotients based on attitudes

Many a times surveys are used to rate a particular variable (like cleanliness or a new car). There are three main factors affecting the rating of a particular person, the quality of the variable, the attitudes and personality of the person and any bias that he/she may have regarding the subject. Sometimes the number of times the person has used the product (variable) also affects the rating as frequent use leads to a better understanding of the quality of the variable. In such cases the other factors distort the actual rating due to the quality of the product. It is very difficult to minimise biases but these are a bit easier to detect as the answer may be drastically different from the norm. Fuzzy logic can take into account the personality of the person and also the number of times he/she has used the product to give the likely answer of a standard personality. This standard personality will of course depend on the survey to be carried out and a lot many other factors and will have to be decided by the organisation carrying out the survey. We already have standard questionnaires that measure certain attitudes like miserliness and optimism to a reasonable degree of accuracy. The scores of these questionnaires can be easily incorporated into fuzzy logic equations.

As a final word before proceeding, I would like to clarify that in all the above aspects, fuzzy logic alone will not help in obtaining a more accurate answer. The normal logic results are also very necessary. By comparing the two results a lot of additional information can be obtained. Fuzzy logic is not a survey instrument by itself but just a tool to make surveys more effective.

Get introduced to this very interesting concept

Fuzzy logic and SURVEYS?? Is it possible to relate these diverse fields? Read and find out.

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