Original Analytic Hierarchy Process Research Articles

A web-based software for group decision with analytic hierarchy process

The Analytic Hierarchy Process (AHP) is a multi-criteria decision support method and is widely applied in many areas. The original AHP method proposed by Thomas L. Saaty in the 1970s requires (n²-n)/2 comparisons. The number of required comparisons can make using this method challenging for maintaining consistent judgments in problems involving many criteria and/or alternatives. Furthermore, the available software is platform-dependent and generally does not support group decision-making. In this paper, we present software for AHP that demands n-1 comparisons. Additionally, the software supports group decision-making using individual aggregation of priorities with arithmetic and geometric means. The system is available at http://ahpweb.net/ and is accessible from any internet-connected device. It currently has more than 100 users and dozens of decision problems in various areas.•The original AHP formulation requires (n²-n)/2 comparisons per cluster which makes it difficult to make consistent judgments.•AHP avaliable software does not enable group decision making.•The proposed system AHP-WEB fills these gaps. The method demands n-1 comparisons per cluster without any inconsistency and allows group decision making on a web system.

Land Evaluation for Acacia (Acacia mangium × Acacia auriculiformis) Plantations in the Mountainous Regions of Central Vietnam

In recent years, both scientists and local governments have been giving serious attention to land evaluation, especially in regard to the use of agricultural land. This is with the intention of increasing the sustainability of agricultural production. In Vietnam, acacia plantations play an important role in the livelihoods of farmers in mountainous regions. Therefore, identifying suitable areas for acacia plantations is an important consideration within mountainous areas. This research was conducted in Nam Dong district, Central Vietnam, using six physical soil criteria for land evaluation by the Analytic Hierarchy Process (AHP) and also the Fuzzy Analytic Hierarchy Process (FAHP). The results have shown that the ranking of selected criteria in both methods was the same, but the weighting of each criterion was different. Among the six physical soil criteria, soil depth has the highest priority, followed by slope, soil organic carbon content, soil texture, soil pH, and soil type. The suitability maps for acacia plantations within the area studied have shown that 9344 ha were not suitable, and 99 ha had low suitability for acacia plantation by both methods. For the AHP approach, 928 hectares were in the range of moderate suitability, and 3080 hectares were in the high suitability class. In contrast, the FAHP method determined 905 hectares to be of the moderate suitability class and 3102 hectares to be of the high suitability class. Based on the observed acacia’s productivity and the scores of the two methods, it shows that the FAHP has a stronger correlation than the of AHP. Within the six selected criteria, the FAHP method can increase the accuracy of land evaluation results by 4.62% in comparison to the original AHP method. Therefore, the FAHP is the most suitable method for land evaluation, especially for agricultural land planning. Further studies should be integrated into more social and economic criteria for comprehensive land evaluation scenarios.

Multi-criteria selection of the mix of generating plants in local energy systems based on a modified analytic hierarchy process

This paper presents a modification of the analytic hierarchy process in order to increase its efficiency for a multi-criteria comparison of mixes of generating plants in local energy areas during their development. The multi-criteria problem of selecting the most effective ratio of rated capacities is considered for power plants representing a single mix of generating plants during the development of a local energy area in the Khabarovsk Krai. The energy sources are represented by thermal, solar, wind and diesel power plants. The following estimation criteria for alternative solutions were accepted: levelized cost of electricity, ecological effeciency estimation; estimation of public opinion about the consequences involved with the establishment of power plants. In order to solve the multi-criteria problem, the analytic hierarchy process (AHP) was used. When using the original AHP for the set problem, a large quantity of alternatives at the stage of pairwise comparisons were found to represent a perceptible load on a decision maker. Thus, already during the estimation of 10 alternatives according to 5 criteria, decision makers should conduct 225 pairwise comparisons, which may eventually result in an unacceptable consistency of the results. In addition, this requires a procedure accounting for the uncertainty of the decision maker's preferences. The proposed solution represents a method of forming matrices of pairwise comparisons upon criteria. This method consists in generating an interval or fuzzy model of the decision maker's preferences for evaluating pairs of estimates according to the criterion. The proposed method was verified using a numerical example of solving the set problem. The obtained optimum mix of power plants consists of thermal, solar and diesel plants with a power of 30, 35 and 39 mW, respectively. The proposed method ensures a high consistency of the results obtained during alternative pairwise comparisons. In addition, the modified analytic hierarchy process takes into account the non-linear nature of the decision maker's preferences for estimating alternatives according to criteria.

Research on the Development Support Strategy of Cultural Enterprises Based on Fish Swarm Algorithm under the Background of Public Health.

Under the background of public health events, the government needs to adopt reasonable support strategies to help cultural enterprises tide over the crisis. However, the original analytic hierarchy process cannot be comprehensive and accurate analysis, resulting in that the government support strategy cannot play a role. Fish swarm algorithm is a comprehensive intelligent algorithm, which can comprehensively analyze the factors affecting the formulation of supporting strategies for cultural enterprises, and has the advantages of simple operation and strong analysis ability. Under this background, this paper puts forward a fish swarm model; this method is a comprehensive intelligent analysis method, which can help the government find the best support strategy from the perspectives of politics, economy, and society. In order to verify the effectiveness of the fish school model, this paper uses MATLAB software for verification; the results show that, in the support strategy classification, selection accuracy, and selection time, fish school model is superior to the analytic hierarchy process. Therefore, the fish swarm model can help the government to better choose supporting policies and help cultural enterprises tide over the crisis and improve the accuracy of formulating supporting strategies for cultural enterprises.

Decision support system for selecting tourist attractions using fuzzy analytic hierarchy process

The selection of tourist attractions is a multi-criteria decision making problem, which requires time and careful consideration to make the right decision. The proper destination selection based on human needs in a particular moment affects satisfaction in traveling. This research aims to create a decision support system for selecting tourist attractions (a case study in Kupang City) using fuzzy analytic hierarchy process method. Users can input the priority scale of 9 human need attributes and then be directed to the system’s recommendations of tourist attractions. This paper also compares fuzzy analytic hierarchy process method with the original analytic hierarchy process calculations. The result shows that both methods can be a solution for multi-criteria decision making, but the fuzzy analytic hierarchy process method performs a more optimal solution for cases with uncertainty in comparisons between elements.

Risk assessment of geohazards along Cheng-Kun railway using fuzzy AHP incorporated into GIS

This article presents a case study on the risk assessment of geohazards along Cheng-Kun railway line. Cheng-Kun railway passes through a region of highly varied elevation and faults and the operation of Cheng-Kun railway has been frequently interrupted owing to geological disasters. A hybrid method via integrating triangular fuzzy number (TFN) and the analytic hierarchy process (AHP) (here after simply call TFN-AHP) into a geographic information system (GIS) is employed in this study to perform the geohazards assessment. The assessment results showed that TFN-AHP with GIS can effectively predict the distribution of geohazards risk in the study region within the last 10 years. The results also showed that the TFN-AHP method is more efficient in identifying high-risk areas compared with using original AHP. Based on the assessment results, prospective management measures to prevent risk are recommended.

Inundation risk assessment of metro system using AHP and TFN-AHP in Shenzhen

Metro system is a vital transportation infrastructure, which has been inundated frequently during flood season (from May to September) in Shenzhen, China. This study incorporates the original analytic hierarchy process (AHP) and triangular fuzzy number-based AHP (TFN-AHP) into a geographic information system (GIS) to assess the inundation risk of the metro system in Shenzhen. The assessed results are verified by the 11 flood locations in the flood event that happened on April 11, 2019 (hereafter called the “4.11 flood event”). The risk indicators of the 11 flood locations derived from the TFN-AHP are greater than those obtained from the AHP. Most of the metro lines of the higher-risk and highest-risk match the regions with high inundation risks. The percentages of the higher-risk and highest-risk levels of the metro system obtained from TFN-AHP are greater than those from the AHP. The comparative result indicates that the TFN-AHP method can assess the inundation risk more distinctively than the original AHP.

AN AHP-ISM APPROACH FOR CONSIDERING PUBLIC PREFERENCES IN A PUBLIC TRANSPORT DEVELOPMENT DECISION

Recently, there has been a transparent need to involve public in transport development decisions not only in the EU but also in other countries worldwide. Public involvement in decision-making, however, suffers from two critical issues: lack of expertise and lack of enthusiasm. This paper aims to overcome the first problem: how to amend passenger preferences related to public transport development with expert knowledge on transport systems. For this purpose, a new research methodology has been created which combines the well proven Analytic Hierarchy Process (AHP) and Interpretive Structural Modelling (ISM) methods in a novel way. ISM is used to reveal the non-hierarchical connections of the transport system elements and by this, AHP results are modified with the consideration of element interactions. The first stage of the three-stage-survey has been conducted in Yurihonjo (Japan), the second and third in an international workshop with the participation of experts. Results show that the original AHP scores – gained from passenger evaluations – are significantly modified by adding expert knowledge on factor interactions, thus new preference order is gained related to the importance of the development of public transport system elements. The introduced procedure can be applied for other public transport system improvement decision-making situations in which passenger involvement is required.

Comparison among Original AHP, Ideal AHP and Moderate AHP Models

Decisions always involve the getting the best solution, selecting the suitable experiments, most appropriate judgments, taking the quality results etc., using some techniques. Every decision making can be considered as the choice from the set of alternatives based on a set of criteria. The analytic hierarchy process (AHP) is a multi-criteria decision making and is dealing with decision making problems through pairwise comparisons. This paper is concerned with the moderate AHP decision model is always same as the original AHP decision model. It does not violate the rule itself.

AHP model for competitiveness analysis of selected countries

Competitiveness analysis of countries and regions stands in the foreground in recent years. Different methods as well as indicators are used to assess competitiveness, but no single procedure is considered to be the main one and it can hardly be stated, which of the measurement approaches is the most proper. The IMD World Competitiveness Online database represents one of such tools, containing the Overall Competitiveness ranking that evaluates 59 world countries by more than 300 individual indicators in 2012. The paper proposes an original Analytic Hierarchy Process (AHP) model for competitiveness ranking of selected countries. The model is based, due to the high number of indicators and countries, on absolute measurement and expert evaluation. The results given by the AHP model are compared to IMD competitiveness ranking. Differences of both results are analysed and discussed.

On the analytic hierarchy process and decision support based on fuzzy-linguistic preference structures

The Analytic Hierarchy Process (AHP) has received different fuzzy formulations, where two main lines of research can be identified in literature. The most popular one refers to the Extent Analysis Method, which has been subject of recent criticism, among other things, due to a number of misapplications that it may lead to. The other approach refers to the Logarithmic Least Squares Method (LLSM), which offers a constrained optimization approach for estimating fuzzy weights, but fails to generalize the original AHP proposal. The fact remains that the AHP uses linguistic evaluations as input data, where experts value pairs of alternatives/criteria with words, making it essentially fuzzy under the view that words can be represented by fuzzy sets for their respective computation. Hence, reasoning with fuzzy logic is justified by the analytical framework that it offers to design the meaning of words through membership functions and not assume a direct mapping between words and crisp numbers. In this paper we propose the fuzzy representation of linguistic preferences for the AHP, and examine its generalization by means of the fuzzy-linguistic AHP algorithm.

On-Board Power Simulation Training Evaluation Model Based on Improved Gray Analytic Hierarchy Process

We frist establish the evaluation index system according to the characteristics of the simulation training system through analysis, and second , we calculate the index weight use improved gray analytic hierarchy process which simplify the steps of the original analytic hierarchy process. Third we use the Delphi method to establish the membership degree of every evaluation index, and finally we use fuzzy comprehensive evaluation method to get the evaluation results of the simulation training system, the results show that the evaluation model is consistency to the expert assessment , meet the actual needs, is an effective method of power system simulation training assessment.

A Fuzzy Weights Representation for Inner Dependence AHP

The Analytic Hierarchy Process (AHP) proposed by T. L. Saaty has been widely used in decision making. Inner dependence method AHP is used for cases in which criteria are not independent enough. Using the original AHP or inner dependence AHP may cause results to lose reliability because the comparison matrix is not necessarily sufficiently consistent. In such cases, fuzzy representation for weighting criteria using results from sensitivity analysis is useful. We present weights of normal AHP criteria via fuzzy sets, then calculate modified fuzzy weights of inner dependence methods. We also get overall weights of alternatives based on certain assumptions. Results show the fuzziness of inner dependence AHP if the comparison matrix is not sufficiently consistent and individual criterion do not have enough independence.

Analytic Hierarchy Process and Expert Choice: Benefits and limitations

This article describes the original Analytic Hierarchy Process (AHP) as it is implemented in the software package Expert Choice. We demonstrate its application through a practical example. In particular, we discuss problem modelling, pairwise comparisons, judgement scales, derivation methods, consistency indices, synthesis of the weights and sensitivity analysis. Finally, the limitations of the original AHP along with the new proposed development are explained.

Value functions and trade-offs associated with the analytic hierarchy process composition law

In this article, we provide a fresh bridge between the original formulation of the analytic hierarchy process (AHP) and the more classical theory of value functions. We focus on the hierarchic composition law (HCL) as a device for aggregation. Multi-attribute value functions can be similarly described. We derive a class of fundamental functional equations which relate the priorities construct of the AHP to a particular value function. It is therefore possible to associate a class of trade-off or indifference curves to the HCL by this technique. Our results indicate that the number of alternatives being compared in the AHP is the main cause of rank reversal. We show that different numbers of alternatives determine different trade-off curve systems, and hence necessarily, different value functions. Two classical cases of rank reversal, on account of alternative addition and deletion, respectively, are reexamined for illustration. The rank reversal can be resolved in both cases by this methodology. The results obtained here establish a link between the original AHP formulation using the HCL and multi-attribute value function theory, with promise of more positive mutual benefit between the topics in the future. In particular, the value function class associated with the HCL has a number of desirable features.

Strategic management of new products development at technological conglomerate network using expert support systems

While Analytic Hierarchy Process (AHP), a popular Multi Criteria Decision-Making (MCDM) method, is able to deal with the strategic New Products Development (NPD) selection by synthesising subjective judgement, the judgement of experts is usually obscure. To deal with the vagueness in responses, an original AHP incorporated with sensitivity analysis instead of popular fuzzy AHP model is proposed and a firm can make a decisive evaluation by applying the new model more easily. In addition, the research finds that technological development keeps the network on leading technologies and diversified/differentiated development satisfies every customer's individual needs under industrialised Mass Customisation (MC) manufacturing network.

A FUZZY-BASED DECISION MAKING APPROACH FOR PRODUCT CONCEPT SELECTION

Selecting the best product concept is one of critical tasks in product development process. Making decisions at this stage becomes very difficult due to imprecise and uncertain product requirements. This paper presents the framework of product concept selection that integrates the fuzzy set theory and the analytic hierarchy process (AHP). In the proposed approach, the fuzzy membership function is employed in performing "pairwise comparison" between competing alternatives and a "reference" on each of the criteria. The use of a reference is due to the difficulty in consistently comparing concepts to one another. The comparisons are also used to obtain the relative importance of criteria with respect to the overall objective. Once pairwise comparisons are completed, vector aggregates are computed through the use of an original AHP method and fuzzy arithmetic operations. A numerical example is presented to illustrate the approach.

On multiplicative priority rating methods for the AHP

Recently, several alternative variants to the original Analytic Hierarchy Process (AHP) have been proposed. Most of these sought to resolve some of the theoretical problems associated with the original AHP, which uses an additive preference aggregation. In this paper, we take a close look at the multiplicative ratings method, which has recently received growing attention. The interest in the multiplicative AHP (MAHP) is motivated by the fact that, in contrast with the original AHP, it precludes certain types of rank reversals as the composite priority ratings continue to follow a ratio scale, even after normalization. The purpose of this paper is threefold. First, we derive and discuss several interesting properties of the MAHP that have eluded attention in previous studies. Second, we argue that these properties of the MAHP are interesting not only for mathematical reasons but also on behavioral grounds. We show how the MAHP offers a more flexible preference modeling framework, while still preserving the ratio scale property, by relaxing the “constant returns to scale” assumption made in previous research. Third, we use simulation experiments to explore the extent to which the theoretical differences between the original AHP (additive AHP) play out computationally for various different types of preference structures, enabling us to assess whether the MAHP is merely an interesting theoretical construct, or can in fact make a substantial difference in terms of the rankings and ratings of the alternatives and rank reversals between the alternatives.

Two new cases of rank reversals when the AHP and some of its additive variants are used that do not occur with the multiplicative AHP

AbstractMany researchers have long observed some cases in which certain ranking irregularities can occur when the original analytic hierarchy process (AHP), or some of its variants, are used. This paper presents two new categories of ranking irregularities which defy common intuition. These ranking irregularities occur when one decomposes a decision problem into a set of smaller problems each defined on two alternatives and the same criteria as the original problem. These irregularities are possible when the original AHP, or some of its additive variants, are used. Computational experiments on random test problems and an examination of some real‐life case studies suggest that these ranking irregularities are dramatically likely to occur. This paper also proves that these ranking irregularities are not possible when a multiplicative variant of the AHP is used. Copyright © 2001 John Wiley & Sons, Ltd.

A computational evaluation of the original and revised analytic hierarchy process

The Analytic Hierarchy Process (AHP) and its variants have long been used in numerous scientific and engineering applications. The present paper demonstrates that the original AHP and one of its variants have the potential to reach the wrong conclusion under certain circumstances. This paper examines the effectiveness of these two methods under the assumption that in reality the pairwise comparisons, which are used in these methods, take on continuous values. This assumption is made in order to capture the majority of the real world cases. The computational results in this paper demonstrate that when the above assumption is made, the AHP and the revised AHP might yield a different ranking of the alternatives than the ranking that would result if the actual relative importances were known. The same results also reveal a dramatic increase in the probability that an incorrect ranking occurs as the number of alternatives involved increases.