Pairwise Judgments Research Articles

Using a VGI and GIS-Based Multicriteria Approach for Assessing the Potential of Rural Tourism in Extremadura (Spain)

Extremadura (Spain), being one of the less-developed EU regions, is also eligible for European funds, including those related with the development of tourism activities in rural areas. To assess the spatial distribution of rural tourism potential (RTP), a methodological approach was followed by combining the synergetic use of geographic information systems (GIS) and the analytical hierarchical process (AHP). For the evaluation model, six factors were examined and hierarchized by a panel of eighteen experts: tourism accommodation offer, activities in natural areas, gastronomic offer, cultural activities, bath offer in natural environments, and activities in active tourism. These factors were then decomposed into thirty-two evaluation criteria and the relative importance of their weights was estimated using pairwise judgments. Using publicly available data and volunteered geographic information (VGI) platforms, the related spatial and non-spatial data were collected, collated, and standardized, employing appropriate tools developed with open-source GIS software. The results, represented by a series of intensity maps, indicate the RTP scores, highlight the strengths and weaknesses in each county, and could serve as a planning tool for public and/or private investments.

Transitivity in similarity judgments on German verbs

This paper investigates set-theoretical transitive and intransitive similarity relationships in triplets of verbs that can be deduced from raters’ similarity judgments on the pairs of verbs involved. We collected similarity judgments on pairs made up of 35 German verbs and found that the concept of transitivity adds to the information obtained from collecting pair-wise semantic similarity judgments. The concept of transitive similarity enables more complex relations to be revealed in triplets of verbs. To evaluate the outcomes that we obtained by analyzing transitive similarities we used two previously developed verb classifications of the same set of 35 verbs based on the analysis of large corpora (Richter & van Hout, 2016). We applied a modified form of weak stochastic transitivity (Block & Marschak, 1960; Luce & Suppes, 1965; Tversky, 1969) and found that (1), in contrast to Rips’ claim (2011), similarity relations in raters’ judgments systematically turn out to be transitive, and (2) transitivity discloses lexical and aspectual properties of verbs relevant in distinguishing verb classes.

Multi-criteria assessment of the benefits of a supply chain management training considering green issues

Green Supply Chain Management (GSCM) is an important issue for organizations that spend considerable amounts of investments on personnel training annually. Although these investments present positive effects, the manner to assess the effectiveness of the training is unclear. Training, whose characteristics are intangible, is sometimes difficult to be assessed. This research has carried out a multi-criteria training assessment for GSCM through the four top-level processes of Supply Chain Operations Reference Model (SCOR) i.e., Plan, Source, Make and Deliver. Analytic Hierarchy Process was applied in the training assessment. In the chemical industry where our study was performed, the SCOR top-level processes were considered criteria, whereas Individual and Organizational Benefits alternatives. The modeling considered pairwise judgments for criteria, and ratings or absolute measure for alternatives. The analysis revealed that training essentially contributes to the organization, resulting in 87% for Organizational Benefits, and 77% for Individual Benefits. Organizational Benefits focused on the use of the best practices in GSCM and on the common understanding of vocabulary and processes. In addition, Individual Benefits increased knowledge and skills in GSCM. This result, presented to managers of the company, was validated as consistent and feasible.

An examination of performance relations among selected consistency measures for simulated pairwise judgments

A review of contemporary literature devoted to decision making support systems draws attention to the Analytic Hierarchy Process (AHP). At the core of the AHP are various prioritization procedures which elicit priorities for alternative solutions for complex decisional problems. Certainly, the procedures coincide when decision makers’ preferences of alternative solutions are cardinally transitive, otherwise the results differ. This is why consistency measurement of human judgments is so important. It has been scientifically proven that a high inconsistency of decision makers’ preferences concerning alternative solutions of decisional problems may lead to fallacious choices. Research verifies the thesis that consistency measures derived from different prioritization procedures are interrelated. It turns out that one of the independent consistency measures is extremely closely related to the consistency index embedded in original approach of the AHP. The main objective of this study is realized through the novel and sophisticated simulation algorithm designed for the AHP and executed within its exemplary decisional framework for three levels. The outcome of the research proves that consistency can be measured in various ways, but recently devised concepts can indicate better solutions as a result of significantly improved methodology.

Entropy-optimal weight constraint elicitation with additive multi-attribute utility models

We consider the elicitation of incomplete preference information for the additive utility model in terms of linear constraints on the weights. Eliciting incomplete preferences using holistic pair-wise judgments is convenient for the decision maker, but selecting the best pair-wise comparison is difficult. We propose a framework for comparing holistic preference elicitation questions based on their expected information gain, and introduce a procedure for approximating the optimal question. We extend the basic approach to generate reference alternatives that differ on only a few attributes, and to determine when further preference information is unlikely to reduce decision uncertainty. We present results from computational experiments that assess the performance of the procedure and assess the impact of limiting the number of attributes on which the reference alternatives differ. The tests show that the proposed method performs well, and when implemented in a decision support system it may substantially improve on-line elicitation using pair-wise comparisons.

Hesitant fuzzy programming technique for multidimensional analysis of hesitant fuzzy preferences

The linear programming technique for multidimensional analysis of preferences (LINMAP) is the most representative method for handling the multiple criteria decision making (MCDM) problems with respect to the preference information over alternatives. This paper utilizes the main structure of LINMAP to develop a novel hesitant fuzzy mathematical programming technique to handle MCDM problems within the decision environment of hesitant fuzzy elements (HFEs). Considering the hesitancy of the decision maker, both the pair-wise comparison preference information over alternatives and the evaluation information of alternatives with criteria are represented by the HFEs. Based on the incomplete pair-wise preference judgments over alternatives, we propose the concepts of the hesitant fuzzy consistency and inconsistency indices. Furthermore, we construct a hesitant fuzzy mathematical programming model to derive the weights of criteria and the positive-ideal solution. In this hesitant fuzzy programming model both the objective function and partial constraints' coefficients take the form of HFEs, and an effective approach based on the ranking method of HFEs is further developed to solve the new derived model. To address the incomplete and inconsistent preference structures of criteria weights, we introduce several deviation variables and establish the bi-objective nonlinear programming model. At length, we employ a green supplier selection problem to illustrate the feasibility and applicability of the proposed technique and conduct a comparison analysis to validate its effectiveness.

A Fuzzy Analytic Hierarchy Process (FAHP) Approach for Optimal Selection of Low-carbon Energy Technologies

In process systems engineering, one may encounter design problems that require choosing one among the predefined set of alternatives in a complex decision making environment. In most cases, the selection process involves multiple conflicting criteria that can be either qualitative or quantitative in nature. The use of multiple attribute decision making (MADM) technique thus has been proven effective in providing a transparent, systematic and rational approach to problem solving. In this study, a variant of the widely used MADM technique known as the Analytic Hierarchy Process (AHP) has been developed and applied for the selection of low-carbon technologies. This approach enables the selection of optimal alternative by incorporating not only the judgment of domain experts but also their degree of confidence through the use of fuzzy numbers for the pairwise comparison ratios in the AHP decision framework. The proposed fuzzy AHP then determines a set of crisp weights that maximizes the degree of consistency of all judgments taken together. The said approach can also derive crisp weights from an incomplete fuzzy pairwise comparative judgment matrix (PCJM). To illustrate the technique, a case study involving comparison of electricity storage technologies for renewable energy systems is considered. This selection problem is important due to the intermittent nature of many forms of renewable energy, which thus require cost-effective auxiliary energy storage subsystems for successful deployment.

Uncertainty index based consistency measurement and priority generation with interval probabilities in the analytic hierarchy process

The pairwise judgments provided by a decision-maker are often inconsistent in the analytic hierarchy process. Dealing with inconsistency among the given judgments by uncertainty and interval probabilities has received more attention in recent years. In this paper, an interval multiplicative reciprocal matrix is constructed to capture inconsistency and the decision-maker’s judgments from a multiplicative reciprocal comparison matrix (MRCM). A geometric mean based uncertainty index is defined to measure the uncertainty level of the constructed interval matrix, and used to check acceptable consistency of MRCMs. The paper devises a parameterization approximate relation between the normalized interval probabilities and the constructed interval matrix. A two-stage procedure consisting of two optimization models is developed to generate interval probabilities from MRCMs. The first stage minimizes the power-sum of absolute deviations between the logarithms of the sides of the approximate relation. The second stage aims to seek the most suitable interval probability vector among the optimal solutions derived from the previous stage such that inconsistency of the original MRCM is reflected by interval probabilities as much as possible. An interval probability based algorithm is further put forward for solving multi-criteria decision making problems with MRCMs. Two numerical examples and comparison analyses are presented to demonstrate the performance and validity of the proposed models.

Logarithmic least squares prioritization and completion methods for interval fuzzy preference relations based on geometric transitivity

This article introduces the notion of geometric transitivity, which may be used to define consistent interval fuzzy preference relations. Some useful properties are presented for consistent interval fuzzy preference relations. A close investigation reveals that existing methods for determining the analogous property of consistency are not robust to permutations of the pairwise judgments and not able to reflect the hesitancy in the decision-maker’s preference. A parametric transformation formula is put forward to convert a normalized interval weight vector into a consistent interval fuzzy preference relation. By minimizing the squared difference between the logarithm of the ratio of the original judgment and the logarithm of the ratio of the converted consistent one, a logarithmic least squares model is developed to derive interval weights from any interval fuzzy preference relation. Based on geometric transitivity, a logarithmic least squares model is established to rectify inconsistency for complete and inconsistent interval fuzzy preference relations, and a logarithmic least squares completion approach is further developed to estimate missing values for incomplete interval fuzzy preference relations. Numerical examples are furnished to show the validity of the proposed models and compare with other existing methods.

Pleasures of Ambiguity: the Case of Piranesi’s Carceri

Are pictorial spaces evoked by intentionally ambiguous pictures internally coherent? If so, then we expect these to be idiosyncratic. We addressed this issue empirically. Three sheets from the second edition of Piranesi’s Carceri d’Inventione were selected for the experiment. These were compared with a conventional landscape drawing (after a Capriccio by Guardi) as a base line. The pictorial spaces were probed by way of pairwise depth-order judgments. In each image about fifty landmarks were selected, thus yielding over a thousand binary depth-order judgments per image. From such a full set of pairwise comparisons one obtains a linear depth order. This linear order again yields postdictions for the individual pairwise judgments. Actual judgments differ from these postdictions, thereby yielding a convenient handle on the coherence of the pictorial space. Since the Piranesi Carceri are generally considered to be ‘difficult’, ‘ambiguous’ or ‘labyrinthine’, whereas a conventional landscape as the Guardi is designed for its well-defined depth structure, it is expected that they will give rise to very distinct degrees of coherence. This is indeed what we find. We studied the variation of coherence over observers and images in detail. The pictorial locations that are heavily involved in incoherent responses were identified, and the reason for their ambiguous nature traced in the structure of the depth cues provided by the artist (Piranesi). We speculate that the Carceri manage to strike just the right level of ambiguity (between total chaos and obvious structure) so as to render them visually attractive.

A mathematical programming model for the fuzzy analytic network process—applications of international investment

Currently, the analytic network process (ANP) method is widely employed to consider the multiple criteria analysis problems with dependence and feedback effects. However, in order to extend the ANP to resolve the problem of uncertainty or human subjective judgment, the concepts of fuzzy numbers should be incorporated into the ANP to represent the subjective uncertain pairwise judgments. In this paper, therefore, we propose a novel fuzzy analytic network process (FANP) model by solving a mathematical programming problem. Unlike other FANPs, the proposed method does not require the reciprocity assumption of the weight ratios between criteria, and it can derive local and global weights simultaneously in a single model. Two numerical examples of international investment problems are used to demonstrate the proposed method.

Material selection for light-weight naval crafts using the modified digital logic method: dealing with ranking abnormalities

The modified digital logic (MDL) weighting technique along with the weighted-sum-method (WSM) is applied to a material selection problem for light-weight naval crafts. Both the standard linear and non-linear normalisation schemes have been applied on a selected set of material properties. A ranking abnormality analysis is conducted to examine the robustness of the selection process. It is believed that the MDL method can be effective in similar applications, owing to its simplicity in finding the criteria weights through pair-wise judgements by the designer. In order to make the selection method more robust, it is suggested to define a set of fixed scaling factors in normalising the material data, rather than using maximum or minimum values of each decision matrix. The implementation of the fixed scaling factors for normalisation can significantly reduce the abnormality in ranking results as shown in the performed case study.

A method to weight three categories of adaptive thermal comfort

The adaptive thermal comfort theory considers people as active rather than passive recipients in response to ambient physical thermal stimuli, in contrast with conventional, heat-balance-based, thermal comfort theory. Occupants actively interact with the environments they occupy by means of utilizing adaptations in terms of physiological, behavioural and psychological dimensions to achieve ‘real world’ thermal comfort. This paper introduces a method of quantifying the physiological, behavioural and psychological portions of the adaptation process by using the analytic hierarchy process (AHP) based on the case studies conducted in the UK and China. Apart from three categories of adaptations which are viewed as criteria, six possible alternatives are considered: physiological indices/health status, the indoor environment, the outdoor environment, personal physical factors, environmental control and thermal expectation. With the AHP technique, all the above-mentioned criteria, factors and corresponding elements are arranged in a hierarchy tree and quantified by using a series of pair-wise judgements. A sensitivity analysis is carried out to improve the quality of these results. The proposed quantitative weighting method provides researchers with opportunities to better understand the adaptive mechanisms and reveal the significance of each category for the achievement of adaptive thermal comfort.

Development of an AHP–CBR evaluation system for remanufacturing: end-of-life selection strategy

This paper presents our research works on developing an evaluation system for remanufacturing. This paper has two objectives. The first objective is to evaluate the product end-of-life (EOL) by integrating an analytical hierarchy process (AHP) with case-based reasoning (CBR). The nearest neighbourhood (NN) algorithm was used to retrieve a past case that is closest to the current case under consideration. The AHP, which allows the pair-wise comparison and consistency judgement, was used to determine the weight in NN. The second objective is to evaluate EOL of parts and components. The integration of an economical cost model and an environmental cost model was used to determine the EOL of parts and components. An example is presented and discussed. The predicted results of the complete method were compared with those of the previous study. The results showed that the integration of the AHP–CBR method has reached a good correspondence with the established methods.

An evaluation of maintenance strategy using risk based inspection

Risk based inspection (RBI) methodology was proposed to evaluate the maintenance strategy in industrial process which was constructed in one of the units of Fujian Oil Refinery ISOMAX unit. Using classic definition of risk, both the probability and consequence of accident or failure were investigated respectively under the support of risk-specific code. All equipment in this unit were evaluated and categorized into five risk zone based on the RBI result which covered five levels. In addition, an application of the analytical hierarchy process (AHP) to select the most practicable maintenance strategy for equipment which was located in each risk rating scale was described. To arrange the hierarchic structure and evaluation, four main criteria were defined for pairwise judgments. Finally, four possible alternative strategies were proposed for administrators on the site.

Decision‐making process of patients with gynecological cancer regarding their cancer treatment choices using the analytic hierarchy process

In order to support patients' decision-making regarding cancer treatments, it is important to clarify which criteria that cancer patients use to set priorities in their treatment choices. Using the analytic hierarchy process (AHP), a mathematical decision-making method, this article investigates the criteria and the priorities of patients with gynecological cancer. In the AHP, multiple and hierarchical criteria in the decision-making process were organized by a repeated pairwise judgment of the participants so as to serialize the alternatives along with the rational order of the priorities. For the alternatives "to receive treatment" and "to not receive treatment," the following five criteria were set: "anxiety about relapse and metastasis", "distress about side-effects", "advice of family", "advice of medical staff", and "economic burden". The participants determined a pairwise priority scale, as well as a priority scale between the alternatives for every criterion. The logical consistency of their answers was checked by a consistency index (CI). The participants were 31 patients with ovarian or endometrial cancer who were being followed up after undergoing surgery and adjuvant chemotherapy. Of the participants who answered the questionnaire, 17 satisfied the logical consistency. Of the five criteria for the treatment choices, "anxiety about relapse and metastasis" and "advice of medical staff" were found to be the important factors for treatment choice; however, the weight attached to the priority criteria differed much among the patients. The AHP made it possible to support patients' decision-making in order to clarify their priority criteria and to quantitatively present their decision-making process.

Effects of Training on the Acoustic–Phonetic Representation of Synthetic Speech

Investigate training-related changes in acoustic-phonetic representation of consonants produced by a text-to-speech (TTS) computer speech synthesizer. Forty-eight adult listeners were trained to better recognize words produced by a TTS system. Nine additional untrained participants served as controls. Before and after training, participants were tested on consonant recognition and made pairwise judgments of consonant dissimilarity for subsequent multidimensional scaling (MDS) analysis. Word recognition training significantly improved performance on consonant identification, although listeners never received specific training on phoneme recognition. Data from 31 participants showing clear evidence of learning (improvement>or=10 percentage points) were further investigated using MDS and analysis of confusion matrices. Results show that training altered listeners' treatment of particular acoustic cues, resulting in both increased within-class similarity and between-class distinctiveness. Some changes were consistent with current models of perceptual learning, but others were not. Training caused listeners to interpret the acoustic properties of synthetic speech more like those of natural speech, in a manner consistent with a flexible-feature model of perceptual learning. Further research is necessary to refine these conclusions and to investigate their applicability to other training-related changes in intelligibility (e.g., associated with learning to better understand dysarthric speech or foreign accents).

On the importance of distinguishing between within- and between-subject effects in intransitive intertemporal choice

Most probabilistic paired comparison models treat inconsistent choices as caused by independent and random errors in the pairwise judgments. In this paper, we argue that this assumption is too restrictive for the analysis of paired comparison data obtained from multiple judges when transitivity violations are systematic. We present a new framework that contains the random error assumption as a special case but also allows for systematic changes in an option's utility assessments over the pairwise comparisons. Accounting for both between- and within-judge sources of variability, we demonstrate in an application on intertemporal choice that the proposed framework can capture systematic transitivity violations as well as individual taste differences.

Time dependent decision-making; dynamic priorities in the AHP/ANP: Generalizing from points to functions and from real to complex variables

Because good decisions depend on the conditions of the future, and because conditions vary over time, to make a good decision requires judgments of what is more likely or more preferred over different time periods. There are at least three ways to deal with dynamic decisions. One is to include in the structure itself different factors that indicate change in time such as scenarios and different time periods and then carry out paired comparisons with respect to the time periods using the fundamental scale of the AHP. The second is to do paired comparisons as rates of relative change with respect to time. This is done at different points of time as representatives of intervals to which they belong. These intervals can have different lengths. For each representative point one needs to provide a pairwise judgment about the relative rate of change of one alternative over another and derive mathematical functions for that matrix of comparisons for one of the time periods. The third is to do what I proposed in my first book on the AHP and that is to use functions for the paired comparisons and derive functions from them. It is usually difficult to know what functions to use and what they mean. Ideas and examples are presented towards the development of a theory for dynamic decision making.

Backpropagation multi-layer perceptron for incomplete pairwise comparison matrices in analytic hierarchy process

Analytic hierarchy process (AHP) is a widely used decision making method in many areas such as management sciences. The performance ratings of multiple criteria and alternatives can be elicited from pairwise comparisons obtained by expressing the decision maker’s perceive. However, it may be difficult for the decision maker to prudently assign values to comparisons for large number of criteria or alternatives. Since there exist distinct relationships between any two elements in the real world, the relationship between the missing comparison and the assigned comparisons should be taken into account. The aim of this paper is to propose a novel method using a well-known regression tool, namely the backpropagation multi-layer perceptron (i.e., MLP) to realize the above implicit relationship so as to estimate a missing pairwise judgment from the other assigned entries. A computer simulation is employed to demonstrate that the proposed method can effectively find a missing entry of an incomplete pairwise matrix such that its consistency index is minimized.