Sajid Siraj

A heuristic method to rectify intransitive judgments in pairwise comparison matrices

This paper investigates the effects of intransitive judgments on the consistency of pairwise comparison matrices. Statistical evidence regarding the occurrence of intransitive judgements in pairwise matrices of acceptable consistency is gathered by using a Monte–Carlo simulation, which confirms that relatively high percentage of comparison matrices, satisfying Saaty’s CR criterion are ordinally inconsistent. It is also shown that ordinal inconsistency does not necessarily decrease in the group aggregation process, in contrast with cardinal inconsistency. A heuristic algorithm is proposed to improve ordinal consistency by identifying and eliminating intransitivities in pairwise comparison matrices. The proposed algorithm generates near-optimal solutions and outperforms other tested approaches with respect to computation time.

Contribution of individual judgments toward inconsistency in pairwise comparisons

Pairwise comparison (PC) is a well-established method to assist decision makers in estimating their preferences. In PCs, the acquired judgments are used to construct a PC matrix (PCM) that is used to check whether the inconsistency in judgments is acceptable or requires revision. The use of Consistency Ratio (CR)—a widely used measure for inconsistency—has been widely debated and the literature survey has identified a need for a more appropriate measure. Considering this need, a new measure, termed congruence, is proposed in this paper. The measure is shown to be useful in finding the contribution of individual judgments toward overall inconsistency of a PCM and, therefore, can be used to detect and correct cardinally inconsistent judgments. The proposed measure is applicable to incomplete sets of PC judgments without modification, unlike CR which requires a complete set of PC judgments. To address ordinal inconsistency, another measure termed dissonance, is proposed as a supplement to the congruence measure. The two measures appear useful in detecting both outliers and the phenomenon of consistency deadlock where all judgments equally contribute toward the overall inconsistency.

Enumerating all spanning trees for pairwise comparisons

Determining the most suitable prioritization method for pairwise comparisons remains an open problem. This paper proposes a method based on the generation of all possible preferences from a set of judgments in pairwise comparisons. A concept of pivotal combination is introduced using a graph-theoretic approach. A set of preferences is generated by enumerating all spanning trees. The mean of these preferences is proposed as a final priority vector, and variance gives a measure of inconsistency. The proposed method provides a way of ordering objects according to a voting scheme. The proposed method is also applicable to incomplete sets of pairwise comparisons without modification, unlike other popular methods which require intermediate steps to estimate missing judgments.

Preference Elicitation from Inconsistent Judgments using Multi-objective Optimization

Several decision-making techniques involve pairwise comparisons to elicit the preferences of a decision maker (DM). This paper proposes a new approach for prioritization from pairwise comparisons using the concept of indirect judgments. No method exists that simultaneously minimizes deviations from both direct and indirect judgments. In order to estimate preferences, it is sensible to consider both the acquired judgments and the other judgments latent in the DM’s mind. Hence, a technique is developed here to minimize the deviations from both types of judgments.

PRACB: A Novel Channel Bonding Algorithm for Cognitive Radio Sensor Networks

Wireless sensor networks (WSNs) can utilize the unlicensed industrial, scientific, and medical (ISM) band to communicate the sensed data. The ISM band has been already saturated due to the overlaid deployment of WSNs. To solve this problem, WSNs have been powered up by cognitive radio (CR) capability. By using CR capability, WSNs can utilize the spectrum holes opportunistically. The sensor nodes, which need large bandwidth to transmit their sensed data from source to destination require some scheme, which should be able to provide them a wide band channel whenever required. Channel bonding (CB) is a technique through which multiple contiguous channels can be combined to form a single wide band channel. By using CB technique, CR-based WSN nodes attempt to find and combine contiguous channels to avail larger bandwidth. In this paper, we show that by increasing the number of channels, the probability of finding contiguous channels decreases. Moreover, we then propose a primary-radio (PR) user-activity-aware CB algorithm and compare it with three state-of-the-art schemes: SWA, KNOWS, and AGILE. It has been demonstrated through extensive NS-2 simulations that intelligent CB decisions can reduce harmful interference to PR nodes. We find that CB in CR sensor networks attempts to provide greater bandwidth and utilizes the spectrum effectively.

The mathematical equivalence of the “spanning tree” and row geometric mean preference vectors and its implications for preference analysis

Pairwise comparison is a widely used approach to elicit comparative judgements from a decision maker (DM), and there are a number of methods that can be used to then subsequently derive a consistent preference vector from the DM’s judgements. While the most widely used method is the eigenvector method, the row geometric mean approach has gained popularity due to its mathematical properties and its ease of implementation. In this paper, we discuss a spanning tree method and prove the mathematical equivalence of its preference vector to that of the row geometric mean approach. This is an important finding due to the fact that it identifies an approach for generating a preference vector which has the mathematical properties of the row geometric mean preference vector, and yet, in its entirety, the spanning tree method has more to offer than the row geometric mean method, in that, it is inherently applicable to incomplete sets of pairwise comparison judgements, and also facilitates the use of statistical and visual techniques to gain insights into inconsistency in the DM’s judgements.

Spare parts classification in industrial manufacturing using the dominance-based rough set approach

Classification is one of the critical issues in the operations management of spare parts. The issue of managing spare parts involves multiple criteria to be taken into consideration, and therefore, a number of approaches exists that consider criteria such as criticality, price, demand, lead time, and obsolescence, to name a few. In this paper, we first review proposals to deal with inventory control. We then propose a three-phase multicriteria classification framework for spare parts management using the dominance-based rough set approach (DRSA). In the first phase, a set of ‘if–then’ decision rules is generated from historical data using the DRSA. The generated rules are then validated in the second phase by using both the automated and manual approaches, including cross-validation and feedback assessments by the decision maker. The third and final phase is to classify an unseen set of spare parts in a real setting. The proposed approach has been successfully applied to data collected from a manufacturing company in China. The proposed framework was practically tested on different spare parts and, based on the feedback received from the industry experts, 96% of the spare parts were correctly classified. Furthermore, the cross-validation results show that the proposed approach significantly outperforms other well-known classification methods. The proposed approach has several important characteristics that distinguish it from existing ones: (i) it is a learning-set based analysis approach; (ii) it uses a powerful multicriteria classification method, namely the DRSA; (iii) it validates the generated decision rules with multiple strategies; and (iv) it actively involves the decision maker during all the steps of the decision making process.

Priest: A Tool to Estimate Priorities from Inconsistent Judgments

Pair wise comparison (PC) is a well-established method to assist decision makers in estimating their preferences. This paper presents an open-source priority estimation tool (PriEsT) that has been developed to offer new features related to the PC method. PriEsT is able to assist decision makers (DMs) in revising their judgments based on different consistency measures and graphical aids. When inconsistency cannot be improved due to practical limitations, PriEsT offers a wide range of Pareto-optimal solutions based on multi-objective optimization, unlike other tools which offer only a single solution. DMs have the flexibility to select any of these non-dominated solutions according to their requirements. Using PriEsT, DMs can also perform Sensitivity Analysis to analyze how sensitive the solution is to changes in input data. The features of PriEsT have been demonstrated and evaluated via a real-world case study: an application to select the most appropriate Telecom infrastructure for rural areas. In the case study, the use of PriEsT has highlighted the presence of intransitive judgments in the acquired data. It has been found that correcting these judgments leads to a different ranking of the available alternatives. The generated solutions have also been tested for their sensitivity against small changes in the judgments.

A Framework to Select Edge Detection Method Using Multi-criteria Decision Making

In the fields of computer vision and image processing, edge detection refers to the identification and localization of significant changes in a digital image. This article presents a survey of widely-used edge detection techniques including linear approaches, morpohlogical operations, multi-resolution analysis, and machine learning methods. Since there exists no single method that is applicable in all situations, different methods are deployed for different applications. A hierarchical framework based on multiple criteria has been proposed here that can facilitate the process of selecting the most appropriate edge detection method in a given scenario. Use of the proposed framework has been explained through an example of medical images. Finally, possible areas for further exploration have been highlighted.

SURE: A method for decision-making under uncertainty

Abstract Managerial decision-making often involves the consideration of multiple criteria with high levels of uncertainty. Multi-attribute utility theory, a primary method proposed for decision-making under uncertainty, has been repeatedly shown to be difficult to use in practice. This paper presents a novel approach termed Simulated Uncertainty Range Evaluations (SURE) to aid decision makers in the presence of high levels of uncertainty. SURE has evolved from an existing method that has been applied extensively in the pharmaceutical and speciality chemical sectors involving uncertain decisions in whole process design. The new method utilises simulations based upon triangular distributions to create a plot which visualises the preferences and overlapping uncertainties of decision alternatives. It facilitates decision-makers to visualise the not-so-obvious uncertainties of decision alternatives. In a real-world case study for a large pharmaceutical company, SURE was compared to other widely-used methods for decision-making and was the only method that correctly identified the alternative eventually chosen by the company. The case study demonstrates that SURE can perform better than other existing methods for decision-making involving multiple criteria and uncertainty.