Some Notes on the Properties of Inconsistency Indices in Pairwise Comparisons

Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies have focused on the means of expressing and measuring this inconsistency, and several inconsistency indices have been proposed as an alternative to Saaty's inconsistency index, CI, and consistency ratio, CR, for reciprocal pairwise comparison matrices. The aims of this paper are threefold: firstly, a row inconsistency index (RIC) is proposed and the properties of this index are examined. Secondly, a comparison of selected inconsistency indices for a corner pairwise comparison matrix is provided. Last, but not least, another axiom about the upper bound on the value of an inconsistency index is postulated, and a set of selected inconsistency indices is examined with respect to this axiom. Numerical examples complete the paper. (original abstract

Knowledge-based Consistency Index for Fuzzy Pairwise Comparison Matrices

Abstract—Fuzzy AHP is today one of the most used Multiple Criteria Decision-Making (MCDM) techniques. The main argument to introduce fuzzy set theory within AHP lies in its ability to handle uncertainty and vagueness arising from decision makers (when performing pairwise comparisons between a set of criteria/alternatives). As humans usually reason with granular information rather than precise one, such pairwise comparisons may contain some degree of inconsistency that needs to be properly tackled to guarantee the relevance of the result/ranking. Over the last decades, several consistency indexes designed for fuzzy pairwise comparison matrices (FPCMs) were proposed, as will be discussed in this article. However, for some decision theory specialists, it appears that most of these indexes fail to be properly “axiomatically” founded, thus leading to misleading results. To overcome this, a new index, referred to as KCI (Knowledge-based Consistency Index) is introduced in this paper, and later compared with an existing index that is axiomatically well founded. The comparison results show that (i) both indexes perform similarly from a consistency measurement perspective, but (ii) KCI contributes to significantly reduce the computation time, which can save expert’s time in some MCDM problems

Analysis of the e-Government stage model evaluation using SWOT-AHP method

Electronic government is no longer optional but essential for states attempting for better services to their citizens. Citizens are the centre of the e-government system and play a key role in making e-government successful and of course with the government's policies. The paper aims to evaluate the proposed stage model based on various criteria that identified by SWOT analysis method. Analytic Hierarchy Process (AHP) method will be merged with SWOT analysis method in order to identify the probability of the elements of the proposed model for implementation

Optimal Inconsistency Repairing of Pairwise Comparison Matrices Using Integrated Linear Programming and Eigenvector Methods

Satisfying consistency requirements of pairwise comparison matrix (PCM) is a critical step in decision making methodologies. An algorithm has been proposed to find a new modified consistent PCM in which it can replace the original inconsistent PCM in analytic hierarchy process (AHP) or in fuzzy AHP. This paper defines the modified consistent PCM by the original inconsistent PCM and an adjustable consistent PCM combined. The algorithm adopts a segment tree to gradually approach the greatest lower bound of the distance with the original PCM to obtain the middle value of an adjustable PCM. It also proposes a theorem to obtain the lower value and the upper value of an adjustable PCM based on two constraints. The experiments for crisp elements show that the proposed approach can preserve more of the original information than previous works of the same consistent value. The convergence rate of our algorithm is significantly faster than previous works with respect to different parameters. The experiments for fuzzy elements show that our method could obtain suitable modified fuzzy PCMs

Barrier analysis approach in metal additive manufacturing implementation with environment consideration

Notwithstanding the developments in additive manufacturing technology have been set to overcome human limitations and improve efficiency in manual restoration activities, their widespread implementation as a disruptive production technology has brought various impacts on the environment, and the environmental assessment is limited in this regard. The Malaysian automotive industry has not seen widespread adoption of Life Cycle Assessment for additive manufacturing implementation. Based on the current literature review, there is a gap as the barriers for implementing Life Cycle Assessment in additive manufacturing technology within the Malaysian automotive manufacturing industry are not critically discussed. There is a need for developing appropriate approaches to weight and determine the interrelationships between these obstacles and the most prevalent ones in order to devise mitigation strategies for them. The purposes of this study are to identify various barriers of implementing Life Cycle Assessment in metal additive manufacturing within Malaysian automotive manufacturing industry and, secondly, to develop an approach to prioritize the barriers and recognize the most critical barriers. In this regard, the extant literature has critically reviewed the barriers of implementing Life Cycle Assessment in metal additive manufacturing within Malaysian automotive manufacturing industry. Fuzzy preference programming, as one of the newest and most accurate fuzzy modifications of the Analytical Hierarchy Process, was used to achieve the research purposes. Suitable Triangular Fuzzy Number has been defined and the selected data collection method was expert opinion. A total of eight industry experts from one company were involved in this research study to give their opinion on the Fuzzy Analytical Hierarchy Process pairwise comparison table. The expert opinions indicated that the main concern of industry is financial-related topic. The data collected have been analyzed using Fuzzy Analytical Hierarchy Process calculations and confirmed by the consistency check. Following the results, dominant barriers were accordingly identified and ranked in each category as well as overall. According to the results from expert opinions, the highest-ranking barrier is lack of financial resources, followed by lack of Life Cycle Assessment expertise in the additive manufacturing context, and the third rank is the lack of laws and directives for Life Cycle Assessment application in additive manufacturing. The findings may be useful to managers to develop suitable mitigation strategies and make more informed decisions with individual focus, level focus, or cluster focus. It may also contribute to the additive manufacturing literature by the weighted presentation of the barriers to implementing Life Cycle Assessment in additive manufacturing within the Malaysian automotive manufacturing industry. This study will contribute to a framework of roadmaps and strategies for sound and environmentally friendly additive manufacturing implementation in Malaysian automotive industry