تصمیم گیری با محاسبات فازی زبانی توسعه یافته، با برنامه های کاربردی برای توسعه محصول جدید و تجزیه و تحلیل بررسی

Fuzzy set theory, with its ability to capture and process uncertainties and vagueness inherent in subjective human reasoning, has been under continuous development since its introduction in the 1960s. Recently, the 2-tuple fuzzy linguistic computing has been proposed as a methodology to aggregate fuzzy opinions (Herrera and Martinez, 2000a and Herrera and Martinez, 2000b), for example, in the evaluation of new product development performance (Wang, 2009) and in customer satisfactory level survey analysis (Lin & Lee, 2009). The 2-tuple fuzzy linguistic approach has the advantage of avoiding information loss that can potentially occur when combining opinions of experts. Given the fuzzy ratings of the evaluators, the computation procedure used in both Wang, 2009 and Lin and Lee, 2009 returned a single crisp value as an output, representing the average judgment of those evaluators. In this article, we take an alternative view that the result of aggregating fuzzy ratings should be fuzzy itself, and therefore we further develop the 2-tuple fuzzy linguistic methodology so that its output is a fuzzy number describing the aggregation of opinions. We demonstrate the utility of the extended fuzzy linguistic computing methodology by applying it to two data sets: (i) the evaluation of a new product idea in a Taiwanese electronics manufacturing firm and (ii) the evaluation of the investment benefit of a proposed facility site.

The strength of fuzzy set theory, which was first proposed by Zadeh (1965), lies in its ability to represent and process both uncertainties in measurements and vagueness in concepts expressed in the natural language. Unlike the classical set theory in which an element must either belong or not belong to a set of interest, an object in the universe of discourse can instead be a member of a fuzzy set to some degree. This added flexibility allows mathematical representation of non-precise human concepts and enables a proliferation of fuzzy set theory applications in a broad range of industrial engineering and electronics areas today. The pervasiveness of applications of fuzzy set theory in industrial engineering research can in fact be found in the recent issues of Expert Systems with Applications (Chuang et al., 2010, Dursun and Karsak, 2010, Galetakis and Vasiliou, 2010, Lin, 2010, Pan, 2010 and Sen and Baraçlı, 2010): for example, it was used in aggregating evaluators’ opinions in new product development (Wang, 2009) and in survey analysis (Lin & Lee, 2009). As the capability to introduce marketable new products is essential in maintaining and advancing the competitiveness of a firm relative to its rivals, accurate decision making in the domain of new product development becomes increasingly important, and thus the evaluations of new product ideas nowadays are usually carried out by a committee of experts. As pointed out in Hwang and Yoon, 1981 and Wang, 2009, a great deal of fuzziness and inhomogeneity can occur across the experts’ subjective perceptions and cognitions, and as a results, the subsequent information integration could lead to evaluation results being incompatible with the experts’ expectations. Hence, Wang (2009) proposed using a 2-tuple fuzzy linguistic approach for new product development evaluation that can avoid information loss inherent in other fuzzy approaches (Herrera-Viedma, Herrera, Martinez, Herrera, & Lopez, 2004). Similarly, Lin and Lee (2009) applied fuzzy linguistic computing to analyze customer satisfactory level survey data. Vague concepts like strongly unsatisfactory, unsatisfactory, average, satisfactory and strongly satisfactory were represented by fuzzy linguistic terms. In the methodologies of both Lin and Lee, 2009 and Wang, 2009, the evaluators were required not only to rate the sufficiency of a product idea/service under consideration with respect to various pre-determined criteria and sub-criteria, but also to rate the importance of the criteria and sub-criteria themselves, in determining the overall viability of a new product idea or satisfaction level of a service. This double rating helped capture more fully the experiential cognition of the evaluators. The computation procedure used in the above mentioned papers took the fuzzy ratings given by the individual evaluators as inputs and returned a single crisp value describing the average judgment of the evaluators. In this article, we propose to expand the methodology by outputting not a crisp value, but a fuzzy number to represent the aggregation of opinions. This makes logical sense in that one would expect the result of aggregating fuzzy ratings to be fuzzy itself. Furthermore, the resulting fuzzy number can be viewed as a fuzzy set theory analog of the statistical interval used in classical statistics. For example, in the case of customer satisfactory level analysis, a service under consideration might get an overall average crisp rating of “satisfactory.” The fuzzy number that will be obtained with the proposed methodology represents how confident we are that the service is indeed “satisfactory,” reflected by how much of the support of the associated membership function is contained within the support of the linguistic term “satisfactory.” A procedure to formulate and compute statistical confidence intervals for fuzzy data has actually been proposed recently in Wu (2009). It involved the use of α-cut (denoted as h-level set in that paper) and the extension principles in Zadeh, 1975a, Zadeh, 1975b and Zadeh, 1975c, leading to an interesting but mathematically non-trivial optimization problem. In this article, we propose to use an alternative formulation based on sampling distribution, giving an efficient and simple procedure for calculating the fuzzy number. The article is organized as follows: In Section 2, the basic format of the survey questionnaires used in eliciting evaluators’ opinions and the 2-tuple fuzzy linguistic approach for aggregating the opinions used in Lin and Lee, 2009 and Wang, 2009 will be reviewed. After that, we will describe a computationally efficient framework for calculating a fuzzy number representing the aggregation of opinions. In Section 3, we will apply the proposed methodology on evaluating new product development ideas and on survey analysis. A brief summary will be given in Section 4.

The strength of fuzzy set theory, which was first proposed by Zadeh (1965), lies in its ability to represent and process both uncertainties in measurements and vagueness in concepts expressed in the natural language. Unlike the classical set theory in which an element must either belong or not belong to a set of interest, an object in the universe of discourse can instead be a member of a fuzzy set to some degree. This added flexibility allows mathematical representation of non-precise human concepts and enables a proliferation of fuzzy set theory applications in a broad range of industrial engineering and electronics areas today. The pervasiveness of applications of fuzzy set theory in industrial engineering research can in fact be found in the recent issues of Expert Systems with Applications (Chuang et al., 2010, Dursun and Karsak, 2010, Galetakis and Vasiliou, 2010, Lin, 2010, Pan, 2010 and Sen and Baraçlı, 2010): for example, it was used in aggregating evaluators’ opinions in new product development (Wang, 2009) and in survey analysis (Lin & Lee, 2009). As the capability to introduce marketable new products is essential in maintaining and advancing the competitiveness of a firm relative to its rivals, accurate decision making in the domain of new product development becomes increasingly important, and thus the evaluations of new product ideas nowadays are usually carried out by a committee of experts. As pointed out in Hwang and Yoon, 1981 and Wang, 2009, a great deal of fuzziness and inhomogeneity can occur across the experts’ subjective perceptions and cognitions, and as a results, the subsequent information integration could lead to evaluation results being incompatible with the experts’ expectations. Hence, Wang (2009) proposed using a 2-tuple fuzzy linguistic approach for new product development evaluation that can avoid information loss inherent in other fuzzy approaches (Herrera-Viedma, Herrera, Martinez, Herrera, & Lopez, 2004). Similarly, Lin and Lee (2009) applied fuzzy linguistic computing to analyze customer satisfactory level survey data. Vague concepts like strongly unsatisfactory, unsatisfactory, average, satisfactory and strongly satisfactory were represented by fuzzy linguistic terms. In the methodologies of both Lin and Lee, 2009 and Wang, 2009, the evaluators were required not only to rate the sufficiency of a product idea/service under consideration with respect to various pre-determined criteria and sub-criteria, but also to rate the importance of the criteria and sub-criteria themselves, in determining the overall viability of a new product idea or satisfaction level of a service. This double rating helped capture more fully the experiential cognition of the evaluators. The computation procedure used in the above mentioned papers took the fuzzy ratings given by the individual evaluators as inputs and returned a single crisp value describing the average judgment of the evaluators. In this article, we propose to expand the methodology by outputting not a crisp value, but a fuzzy number to represent the aggregation of opinions. This makes logical sense in that one would expect the result of aggregating fuzzy ratings to be fuzzy itself. Furthermore, the resulting fuzzy number can be viewed as a fuzzy set theory analog of the statistical interval used in classical statistics. For example, in the case of customer satisfactory level analysis, a service under consideration might get an overall average crisp rating of “satisfactory.” The fuzzy number that will be obtained with the proposed methodology represents how confident we are that the service is indeed “satisfactory,” reflected by how much of the support of the associated membership function is contained within the support of the linguistic term “satisfactory.” A procedure to formulate and compute statistical confidence intervals for fuzzy data has actually been proposed recently in Wu (2009). It involved the use of α-cut (denoted as h-level set in that paper) and the extension principles in Zadeh, 1975a, Zadeh, 1975b and Zadeh, 1975c, leading to an interesting but mathematically non-trivial optimization problem. In this article, we propose to use an alternative formulation based on sampling distribution, giving an efficient and simple procedure for calculating the fuzzy number. The article is organized as follows: In Section 2, the basic format of the survey questionnaires used in eliciting evaluators’ opinions and the 2-tuple fuzzy linguistic approach for aggregating the opinions used in Lin and Lee, 2009 and Wang, 2009 will be reviewed. After that, we will describe a computationally efficient framework for calculating a fuzzy number representing the aggregation of opinions. In Section 3, we will apply the proposed methodology on evaluating new product development ideas and on survey analysis. A brief summary will be given in Section 4.