Computing with words: from linguistic preferences to decisions

Official URL: http://risc01.sabanciuniv.edu/record=b2061209 (Table of Contents)

Lexicons help to make qualitative assessments in various application areas such as Multi Criteria Decision Making (MCDM), intelligence analysis and human-machine teaming. In order to make quantitative analysis, these qualitative assessments based on the lexicons need to be quantified. During quantification, the linguistic descriptors involved in the lexicons that represent the judgments of the decision makers are mapped to a number. This is often achieved by using a fixed numeric scale. However, for a variety of reasons, such as the vagueness of the linguistic descriptors, the personal differences between the meanings associated to these linguistic descriptors, and the difference between the usage habits of the decision makers, it is not a realistic expectation to perform this mapping with a universal fixed numerical scale. Thus, many researchers frequently criticize this practice. In our study, we focused on the quantification of these linguistic descriptors. The performance of the different approaches used in quantification phase are comparatively assessed and various new proposals are made in order to improve the success of quantification process. Although the quantification of qualitative assessments is a process that has been encountered in many different applications, in this study we have targeted the Analytic Hierarchical Process (AHP) framework, which is proposed by Thomas L. Saaty and widely used in MCDM. In AHP, the relative weights of the criteria and/or the utility of the alternatives for a criterion are determined from the qualitative assessments attained from the decision makers via pairwise comparisons. These qualitative assessments are quantified (often by Saatys 1-9 universal scale) in order to conduct further analysis. Thus, the quantification of the qualitative assessments, which can also contain various rational and/or irrational elements, is naturally a critical step for the success of the whole process. In the scientific literature, various approaches are developed in order to improve the quantification process. Fuzzy AHP (FAHP), which integrates fuzzy set theory to the original AHP, is one of the most popular approach that is proposed for this purpose. Numerous FAHP algorithms were developed, which used fuzzy numbers as a scale to quantify the qualitative assessments. However, there is no numerical or empirical study available that assesses the contribution of FAHP algorithms in MCDM. There is even no study, which evaluates the relative performances i of the FAHP algorithms and provide guideline to the researchers that frequently utilize these techniques as part of their analysis. Thus, in this study, firstly, the relative performances of the five popular FAHP algorithms, which are determined by number of citations they received in scientific literature, were measured by an experimental design study. In this context, four new FAHP algorithms were also developed and included in the experimental analysis. In the experimental analysis, three parameters, namely, the matrix size, the degree of inconsistency and the fuzzification parameter, were considered and the performance of the nine algorithms are assessed in various experimental conditions. This study revealed that the improved LLSM and the FICSM algorithm proposed in this study generally outperform the other algorithms significantly. To our surprise, the most popular algorithm in the literature, namely FEA, was the worst performing algorithm in the experimental analysis. On the other hand, the improved FEA significantly improved the performance of the original FEA. In the second part of the study, the contribution of the FAHP algorithm in MCDM is discussed. Thomas L. Saaty himself criticized fuzzification of AHP arguing that judgments provided by experts are already fuzzy in nature and further fuzzifying them will add more inconsistency in the pairwise comparison matrices. Other researchers have made similar remarks mostly based on various theoretical arguments. However, these arguments are not supported by any numerical or empirical study. In this research, we addressed this gap as well and the contribution of FAHP to MCDM was investigated by means of numerical and empirical analysis. The FAHP algorithms, which outperformed the others in the first part of the study, were compared with the original AHP algorithms. The results revealed that the original AHP algorithms significantly outperformed the existing FAHP algorithms. The results of numerical and empirical analysis suggests that either the existing FAHP methods need to be improved or new ones should be developed in order to benefit the researchers working in MCDM. In addition to the FAHP algorithms, another approach that aims to improve the quantification step is personalization of the numerical step instead of using a universal fixed scale. In the last part of the study we addressed this approach and investigate its performance. Two simple and intuitive heuristics are also developed as an alternative to the existing relatively complex mathematical programming based personalization approach since most of the researchers and practitioners utilizing MCDM techniques might not be familiar with optimization. Both the numerical analysis and the empirical studies demonstrated that the heuristic approaches outperformed the original AHP methods significantly.