Computing with words: from linguistic preferences to decisions
Ahmed, Faran (2019) Computing with words: from linguistic preferences to decisions. [Thesis]
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.
Repository Staff Only: item control page