Abstract: The Likert scale has often been used in psychological measurement, with quantitative statistical methods being frequently employed to analyze the data so obtained. In fact, the concepts on the Likert scale are fuzzy and thus, fuzzy mathematics would be useful for the analyses of these data.
Due to the vague nature of the data, fuzzy comprehensive evaluation can be used to describe the relations among the variables on the Likert scale. Mathematicians often assume that people use the “maximum minimum operator” when they are forming comprehensive evaluation. However, there is no psychological or empirical evidence for this assumption. To address this question, this study explored which operators were employed and whether everybody used the same operators in fuzzy comprehensive evaluation.
The present study investigated the evaluation made by undergraduates on Master Kong beef instant noodle. The genetic algorithms and fuzzy comprehensive evaluation were used together to analyze the Likert scale data. The consumers’ preference for different attributes of the products and the operators being used were obtained.
According to different compound operators, there are four fuzzy comprehensive evaluation models: i) main factor determined type; ii) main factor prominent I type; iii) main factor prominent II type; and iv) weighted average type.
A total of 643 undergraduate response data on the 5-point Likert scale were obtained, while 287 of them were males and 356 females. The participants rated on their taste, flavor, price, soup base, quantity of noodle, appearance, advertisement and intention to purchase for Master Kong beef instant noodle. The evaluation matrix for males and females were prepared respectively from the empirical data.
For each of the 4 models of fuzzy comprehensive evaluation, the fitness function programs were respec-tively constructed with the MATLAB language. The Euclid distance between the model computed scores and the actual comprehensive evaluation scores were used as a measure of fitness index S.
The results demonstrated that males’ fuzzy comprehensive evaluation complied with model 1, that is, when the “max min” compound operator was used. For the females’ fuzzy comprehensive evaluation complied with model 3, that is, it followed the “limitary sum min” compound operator.
Males’ decision in purchasing is simple, with greatest attention to the appearance, and quantity of noodles. On the other hand, females’ decision in purchasing was relatively more conscious, with most attention to the flavor and appearance of the instant noodle.
The research supported the following findings: (i) Genetic algorithms-based fuzzy comprehensive evalua-tion method could be used to analyze psychological measurement data from the Likert scale. It could be used to obtain the compound operators that subjects used as well as the weight vectors for factors being adopted. (ii) Undergraduate of different genders employed different compound operators and weight distribution when they were asked to assessed the instant noodle comprehensively. (iii) It is useful to apply the genetic algo-rithms-based fuzzy comprehensive evaluation on the research of psychological measurement and consume psy-chology. The method also had other less obvious business applications.

Key words: psychological measurement, fuzzy comprehensive evaluation, genetic algorithms, the Likert scale