Algorithms to Detect and Rectify Multiplicative and Ordinal Inconsistencies of Fuzzy Preference Relations

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Consistency, multiplicative and ordinal, of fuzzy preference relations (FPRs) is investigated. The geometric consistency index (GCI) approximated thresholds are extended to measure the degree of consistency for an FPR. For inconsistent FPRs, two algorithms are devised (1) to find the multiplicative inconsistent elements, and (2) to detect the ordinal inconsistent elements. An integrated algorithm is proposed to improve simultaneously the ordinal and multiplicative consistencies. Some examples, comparative analysis, and simulation experiments are provided to demonstrate the effectiveness of the proposed methods

A hybrid performance evaluation system for notebook computer ODM companies

[[abstract]]The aim of the paper is to fulfill this need by building a conceptual framework for measuring the business performance of notebook computer ODM (Original Design Manufacturer) companies carried out to investigate how performance is understood and to identify the potential dimensions to improvement. In the process, a multiple criteria procedure is used to assess the performance in these companies. We explore the performance-evaluation systems by using fuzzy AHP and VIKOR techniques. The evidence from the investigation showed that supply chain capability and manufacturing capability are the top two indicators for the notebook computer ODM companies’ performance. Furthermore, it was found that Quanta and Compal have the relative high business performance among these companies. The research provides evidence which establishes whether benchmarking provides a real and lasting benefit to notebook computer ODM companies. A series of managerial implications are set forth and discussed.[[journaltype]]國外[[incitationindex]]SSCI[[booktype]]紙本[[countrycodes]]NG

Multi-Criteria Decision Making for Sustainability of Renewable Energy System of Nepal

This paper presents an application of Analytic Hierarchy Process for evaluation of the sustainability of renewable energy sources and technology in context of Nepal. Solar energy, biogas, micro hydropower and grid technology have been evaluated based on selected criteria like technical (efficiency and reliability), economic (initial investment, operation & maintenance cost and Benefits), environmental (CO2 emission, land requirement, impact on ecosystem) and social (social acceptability, job creation, social benefits). The importance weights of the criteria and sub-criteria as well as preferential ranking of options have been determined by eliciting expert judgment through pairwise comparisons. The findings show that within the technological constraints, grid technology is the most preferred option followed by micro hydropower and Solar. Biomass is the least preferred sustainable system of Nepal. The finding also shows that technical criteria (33%) is the most important criteria for renewable energy followed by financial (27%), Environmental (22%) and social (18%) being the least. In context of Nepal, Financial criteria has more priority than the environment by the experts for financial sustainability of renewable energy as most of the projects are one time funded by government or donor agencies. The proposed evaluation will help to select the most suitable alternative assisting policy makers to form opinion on sustainability of considered energy systems and make decisions on optimum alternative. However, as time progresses and technology improves, the preferential ranking might change. KEYWORDS: Analytical Heirarchy Process, Sustainability, Renewable Energy, Pairwise Comparison, Alternative

An overview on managing additive consistency of reciprocal preference relations for consistency-driven decision making and Fusion: Taxonomy and future directions

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The reciprocal preference relation (RPR) is a powerful tool to represent decision makers’ preferences in decision making problems. In recent years, various types of RPRs have been reported and investigated, some of them being the ‘classical’ RPRs, interval-valued RPRs and hesitant RPRs. Additive consistency is one of the most commonly used property to measure the consistency of RPRs, with many methods developed to manage additive consistency of RPRs. To provide a clear perspective on additive consistency issues of RPRs, this paper reviews the consistency measurements of the different types of RPRs. Then, consistency-driven decision making and information fusion methods are also reviewed and classified into four main types: consistency improving methods; consistency-based methods to manage incomplete RPRs; consistency control in consensus decision making methods; and consistency-driven linguistic decision making methods. Finally, with respect to insights gained from prior researches, further directions for the research are proposed

Pairwise comparison matrix in multiple criteria decision making

The measurement scales, consistency index, inconsistency issues, missing judgment estimation and priority derivation methods have been extensively studied in the pairwise comparison matrix (PCM). Various approaches have been proposed to handle these problems, and made great contributions to the decision making. This paper reviews the literature of the main developments of the PCM. There are plenty of literature related to these issues, thus we mainly focus on the literature published in 37 peer reviewed international journals from 2010 to 2015 (searched via ISI Web of science). We attempt to analyze and classify these literatures so as to find the current hot research topics and research techniques in the PCM, and point out the future directions on the PCM. It is hoped that this paper will provide a comprehensive literature review on PCM, and act as informative summary of the main developments of the PCM for the researchers for their future research. First published online: 02 Sep 201

Computing with words: from linguistic preferences to decisions

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

A Local Adjustment Method to Improve Multiplicative Consistency of Fuzzy Reciprocal Preference Relations

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Preferences that verify the transitivity property are usually referred to as rational or consistent preferences. Existent methods to improve the consistency of inconsistent fuzzy reciprocal preference relations (FPRs) fail to retain the original preference values because they always derive a new FPR. This article presents a new inconsistency identification and modification (IIM) method to detect and rectify only the most inconsistent elements of an inconsistent FPR. As such, the proposed IIM can be considered a local adjustment method to improve multiplicative consistency (MC) of FPRs. The case of inconsistent FPRs with missing values, i.e., incomplete FPRs, is addressed with the estimation of the missing preferences with a constrained nonlinear optimization model by the application of the IIM method. The implementation process of the proposed algorithms is illustrated with numerical examples. Simulation experiments and comparisons with existent methods are also included to show that the new method requires fewer iterations than existent methods to improve the MC of FPRs and achieves better MC level, while preserving the original preference information as much as possible than the existent methods. Thus, the results presented in this article demonstrate the correctness, effectiveness, and robustness of the proposed method