Multiplicative Analytic Hierarchy Process Research Articles

An integrated design concept evaluation model based on interval valued picture fuzzy set and improved GRP method.

The objective of this research is to enhance the precision and efficiency of design concept assessments during the initial stages of new product creation. Design concept evaluation, which occurs at the end of the conceptual design phase, is a critical step in product development. The outcome of this evaluation significantly impacts the product's eventual success, as flawed design concepts are difficult to remedy in later stages. However, the evaluation of new product concepts is a procedure that encompasses elements of subjectivity and ambiguity. In order to deal with the problem, a novel decision-making method for choosing more logical new product concepts is introduced. Basically, the evaluation process is outlined in three main phases: the construction of evaluation index system for design concept alternatives, the calculation of weights for evaluation criteria and decision-makers, the selection of the best design concept alternatives. These stages are composed of a hybrid method based on kano model, multiplicative analytic hierarchy process (AHP) method, the entropy of IVPFS and improved grey relational projection (GRP) under interval-valued picture fuzzy set (IVPFS). The novel approach integrates the strength of interval-valued picture fuzzy number in handling vagueness, the advantage of multiplicative AHP and the merit of improved GRP method in modelling multi-criteria decision-making. In final, the effectiveness of the proposed model is validated through comparisons with other models. The potential applications of this study include but are not limited to product development, industrial design, and innovation management, providing decision-makers with a more accurate and comprehensive design concept evaluation tool.

Vulnerability Assessment of Prefabricated Component Suppliers in Prefabricated Buildings Based on the Controlled Interval and Memory Method Extended under the Probability Language Terminology Set

Accurately evaluating the vulnerability of prefabricated components in prefabricated buildings is the basis of scientific management of its supply chain. Thus, a novel vulnerability evaluation method for the suppliers of prefabricated components in the context of prefabricated buildings was proposed in this study. First, a vulnerability evaluation index system was identified and constructed by the pressure–state–response (PSR) model. With the clear logic and strong applicability of PSR, this system, including 18 indexes, was easy to understand and exhibited strong practicability. The weights were then determined via the multiplicative analytic hierarchy process with the expansion of a probabilistic language terminology set (PLTS). PLTS could describe decision information more comprehensively, so the evaluation result is more scientific. Subsequently, the probability of the vulnerability level was superimposed in a parallel bottom-to-top method via the controlled interval and memory (CIM) models, and these were extended by the PLTS. This set handled the uncertain information in the decision-making process more efficiently and accurately, and finally determined the vulnerability distribution. Ultimately, the probability of each vulnerability level was determined by combining the weight information. The reconstruction and resettlement housing construction project of urban shanty towns in the Taohua South Road Community in Xihu District, Nanchang City, was selected as a case study. The case study proves the effectiveness of this method, which has higher resolution and is more convenient for managers to make decisions.

Comprehensive extraction technology of key quality characteristics of meta-action unit for CNC machine tools design

The QCs (quality characteristics) of MAU (meta-action unit) determine the quality of CNC (computer numerical control) machine tools. For improving the accuracy of MAU QCs analysis, and solving the problems that the current methods either only have subjective analysis, or only have objective analysis, or the analysis process that includes both subjective and objective analysis methods is relatively complex, a comprehensive identification method of MAU QCs according to the improved MAHP (multiplicative analytic hierarchy process) method and Shannon entropy is proposed in this paper. Firstly, the QCs of the MAU are divided into quality layer and index layer. Secondly, the expert evaluation weight is introduced to improve the MAHP, then the sub quality layer of the meta-action unit was subjectively analyzed. Thirdly, the index layer of the MAU is objectively analyzed by the Shannon entropy. Finally, the results obtained by WMAHP (weighted multiplication analytic hierarchy process) method and Shannon entropy method are synthesized, and the Pareto principle is adopted to extract the key QCs of the MAU. The proposed method combines the advantages of both subjective and objective analysis, and it can reduce the fluctuation of the analysis results caused by data changes. Meanwhile, the analysis process is relatively simple. Its applicability and superiority have also been confirmed by an experiment and comparisons with various methods. The proposed method is of great significance to improve the quality of CNC machine tools.

A conceptual model of decision-making support of thevolunteer team in conditions of dynamic changes

The paper examines the problem of decision-making by a team of volunteers in transport logistics tasks under conditions of dynamic changes in the external environment. Transport logistics is a system of organizing cargo delivery to the place of need along a certain route. The task of transport logistics, during dynamic changes in the external environment, is a task of multi-criteria selection due to consideration of various criteria. Solving the problems of transport logistics requires the construction of aconceptual model of decision-making support, regarding the choice of the best route, taking into account all the factors that influence decision-making, and the choice of the decision-making method. The multi-criteria decision-making methodswhich are used in the transport sector are analyzed. A conceptual model of decision-making support for choosing the optimal route in the transport logistics problem is proposed. Verification of the proposed model was carried out, for which the task of choosing the bestroute of cargo transportation in the transport logistics problem was set and solved. When finding a solution, the multi-criteria decision-making methods were used: Analytic Hierarchy Process method, Multiplicative Analytic Hierarchy Process method, SimpleMulti-Attribute Rating Technique method, improved Simple Multi-Attribute Rating Technique method. The criteria used to evaluate alternative routes for cargo transportation were identified based on volunteer surveys. In order to evaluate the alternatives according to the established criteria, volunteer experts were involved, since during dynamic changes in the conditions of cargo transportation, the involvement of professional experts is a difficult task. To establish the reliability of the evaluations of alternatives according to the criteria obtained from volunteer experts, the Kendall and Spearman correlation coefficients were calculated. Analytic Hierarchy Process method, Multiplicative Analytic Hierarchy Process method, and the improved Simple Multi-Attribute Rating Technique method are found to provide the most reliable results, but the Analytic Hierarchy Process method and Multiplicative Analytic Hierarchy Process methods are more time-consuming during data inputthan the improved Smart method

A novel integrated MADM method for design concept evaluation

Design concept evaluation plays a significant role in new product development. Rough set based methods are regarded as effective evaluation techniques when facing a vague and uncertain environment and are widely used in product research and development. This paper proposed an improved rough-TOPSIS method, which aims to reduce the imprecision of design concept evaluation in two ways. First, the expert group for design concept evaluation is classified into three clusters: designers, manufacturers, and customers. The cluster weight is determined by roles in the assessment using a Multiplicative Analytic Hierarchy Process method. Second, the raw information collection method is improved with a 3-step process, and both design values and expert linguistic preferences are integrated into the rough decision matrix. The alternatives are then ranked with a rough-TOPSIS method with entropy criteria weight. A practical example is shown to demonstrate the method’s viability. The findings suggest that the proposed decision-making process is effective in product concept design evaluation.

Selection of Khadi fabrics for optimal comfort properties using multi-criteria decision-making technique

PurposeKhadi fabrics are known for their unique comfort properties which are attributed to their unique structural and functional properties. For getting optimal comfort from a collection of available Khadi fabrics, further exploration is needed. Ranking the Khadi fabrics from a competitive lot for optimal comfort is a challenging job, which has not been addressed so far by any researcher. The purpose of this study is to present one such selection problem using the multi-criteria decision-making (MCDM) technique, a popular branch of operations research, which can handle almost any decision problem involving a finite number of alternatives and multiple decision criteria.Design/methodology/approachTwo widely popular methods/exponents of MCDM, namely, analytic hierarchy process (AHP) and multiplicative analytic hierarchy process (MAHP) have been deployed in this study for ranking a competitive lot of 15 Khadi fabrics and selecting the best alternative for optimal summer comfort based on three comfort attributes, namely, drape coefficient, thermal insulation value and air permeability.FindingsBoth the approaches yield a similar ranking pattern with Spearman’s rank correlation coefficient of 0.9857, Khadi fabric K1 achieving Rank 1 (best in terms of optimal comfort) and sample K6 acquiring Rank 15 (worst choice). Two-phase sensitivity analyses were performed subsequently to demonstrate the stability of the two approaches: sensitivity analysis by changing weightage levels of the criteria and sensitivity analysis in dynamic decision conditions by changing the elements of the initial decision matrix. During sensitivity analyses, no occurrence of rank reversal is observed for the best and worst alternatives in either of the two approaches. This corroborates the robustness of the two models.Practical implicationsKhadi fabrics are widely acclaimed for their intrinsic comfort properties for both summer and winter. Although the popularity of Khadi fabrics is increasing day by day, this domain is under-researched, and hence, needs to be explored further. The present approach demonstrates how the MCDM technique can serve as a useful tool for ranking the available Khadi fabrics in terms of optimal comfort in summer. The same approach can be extended to other domains of the textile industry, in general, as well.Originality/valueThis study is the first-ever theoretical approach/research on the selection of Khadi fabrics for optimal summer comfort using the MCDM tool. Another novelty of the present study is that the efficacy of AHP and MAHP approaches, in this study, has been validated through a two-phase sensitivity analysis. This validation part has been ignored in most of the hitherto published applications of AHP and MAHP in other domains.

A new case of rank reversal in analytic hierarchy process due to aggregation of cost and benefit criteria

Rank reversal in Analytic Hierarchy Process (AHP) due to introduction or removal of a new alternative is well documented in literature. However, rank reversal due to the aggregation of benefit and cost criteria has not been addressed with requisite rigour. This paper demonstrates a new type of rank reversal in AHP which can arise due to the method (ratio or difference) and approach (sum 1 or sum 2) used to aggregate the benefit and cost criteria. Numerical examples, mathematical analyses and computer simulations have been used for demonstration of results. It is found that considering the benefit and cost criteria separately (sum 2 approach) while aggregating them can yield irrational ranking. It is also demonstrated that ratio method of aggregation is untenable in additive variants of AHP as it yields identical ranking in sum 1 and sum 2 approaches. Difference method of aggregation considering the benefit and cost criteria together (sum 1 approach) is most logical and sound in additive variants of AHP. The results also counter the notion that multiplicative AHP is immune to rank reversal between ratio and difference methods of aggregation. Besides, sum 1 and sum 2 approaches produce different raking of alternatives in multiplicative AHP irrespective of the method of aggregation. Outcome of this research will be helpful while choosing the appropriate method and approach for aggregation of benefit and cost criteria in different variants of AHP.

A heuristic method to rank the alternatives in the AHP synthesis

This paper proposes a heuristic method (Bayesian cosine maximization method (BCCM)) to rank the alternatives in the Analytic Hierarchy Process (AHP) synthesis, based on the multiplicative AHP model, which focuses on the revision of the pair-wise comparison matrices (PCMs) and derivation of the priority vectors from the PCMs in whole hierarchy, considering both the consistency of the PCMs and total consistency. An Eight-step algorithm for the AHP synthesis is developed to how to revise the PCMs in the uncertainty context and generate the final priority vector of the alternatives, which obtains more accurate estimates of the priority vectors and provides a global AHP framework based on the multiplicative AHP model. Finally, two numerical examples and corresponding comparison with several other methods are implemented to illustrate the application and efficiency of the proposed BCCM.

Score function based on concentration degree for probabilistic linguistic term sets: An application to TOPSIS and VIKOR

Probabilistic linguistic term sets (PLTSs) can express the qualitative information of decision makers more accurately in the complicated linguistic setting. However, the existing comparison methods for PLTSs cannot compare some special PLTSs. To tackle this problem, a novel score function based on the concentration degree of an PLTS, called ScoreC-PLTS, is proposed. Additionally, the existing distance measures may distort the original information and lead to unreasonable results. Therefore, a novel probability splitting algorithm is proposed to preprocess PLTSs, based on which, a novel generalized hybrid distance is proposed for PLTSs. Moreover, a novel multiplicative analytic hierarchy process (MAHP) based on ScoreC-PLTS is proposed to determine the weight vector of attributes. Based on the generalized hybrid distance and MAHP, two novel TOPSIS-ScoreC-PLTS and VIKOR-ScoreC-PLTS methods are put forward to handle multi-attribute decision-making problems with PLTSs. Afterwards, an illustrative example concerning the selection of children English educational organization is solved using the proposed TOPSIS-ScoreC-PLTS and VIKOR-ScoreC-PLTS methods. In this example, four indicators are developed and the superiority of our studies is verified by comparing with the previous TOPSIS and VIKOR methods.

Multi-criteria decision-making approach to material selection in tribological application

This paper presents application of various multi-criteria decision-making (MCDM) techniques to material selection in tribological application. The alternative materials considered for ranking are variants of AISI 4140 which is nitrided and then coated with various low-friction surface coating materials. This study analyses and discusses the priority settings on the basis of constructed model which compares the ranking outcomes among simple additive weighting (SAW), multiplicative analytic hierarchy process (MAHP), technique for order preference by similarity to ideal solution (TOPSIS), modified-TOPSIS (M-TOPSIS) and compromise ranking method (VIKOR). Attribute weights obtained by analytic hierarchy process (AHP), are used as the inputs and outputs are materials' rankings on the basis of material selection index (MSI), which help designers and engineers to reach a consensus on materials selection for a specific application. The ranks obtained by various methods are compared. Results indicate that suggested method can effectively be applied to similar problems.

Multi-criteria decision-making approach to material selection in tribological application

This paper presents application of various multi-criteria decision-making (MCDM) techniques to material selection in tribological application. The alternative materials considered for ranking are variants of AISI 4140 which is nitrided and then coated with various low-friction surface coating materials. This study analyses and discusses the priority settings on the basis of constructed model which compares the ranking outcomes among simple additive weighting (SAW), multiplicative analytic hierarchy process (MAHP), technique for order preference by similarity to ideal solution (TOPSIS), modified-TOPSIS (M-TOPSIS) and compromise ranking method (VIKOR). Attribute weights obtained by analytic hierarchy process (AHP), are used as the inputs and outputs are materials' rankings on the basis of material selection index (MSI), which help designers and engineers to reach a consensus on materials selection for a specific application. The ranks obtained by various methods are compared. Results indicate that suggested method can effectively be applied to similar problems.

National Car Development in Indonesia with Multiplicative Analytic Hierarchy Process

National Car Development in Indonesia with Multiplicative Analytic Hierarchy Process

Development of a meta-model for the determination of technological value of cotton fiber using design of experiments and the TOPSIS method

ABSTRACTTo meet the requirements of the cotton spinning industry and achieve the best quality of ring-spun yarn, it becomes an imperative task to determine the technological values of cotton fibers. The availability of High Volume Instrument (HIV) data now makes it possible to evaluate the quality of cotton fiber with respect to some of its major physical properties. The fiber quality index (FQI), the spinning consistency index (SCI), and the multiplicative analytic hierarchy process (MAHP) are some of the popular approaches adopted by the spinning industry personnel to determine the quality values of cotton fibers. In this paper, while integrating the design of experiments (DoE) and the technique for order preference by similarity to ideal solution (TOPSIS), a regression meta-model is developed for determining the technological value of cotton fiber with respect to the TOPSIS score. This model identifies the statistically significant fiber properties and their interactions affecting the estimated TOPSIS score while fitting a polynomial to the experimental data in multiple linear regression analysis. It is observed that the uniformity index has no importance in quality value evaluation of the cotton fiber, although its interactions with other properties are statistically significant. A validation analysis shows an excellent degree of congruence of this meta-model with the existing models for cotton fiber quality determination.

Intuitionistic Multiplicative Group Analytic Hierarchy Process and Its Use in Multicriteria Group Decision-Making

As an extension of multiplicative preference relations (MPRs), intuitionistic MPRs (IMPRs) reflect experts' hesitant quantitative judgments. This paper presents an intuitionistic multiplicative preference information-based group analytic hierarchy process (AHP) and develops an intuitionistic multiplicative group AHP (IMGAHP), which addresses multicriteria group decision-making (MCGDM) that uses IMPRs to capture experts' preference judgments. First, we introduce a consistency index to gauge the consistency of IMPRs and describe the concept of acceptably consistent IMPRs. Second, we propose an algorithm for repairing an inconsistent IMPR to an acceptable level. Third, we propose an aggregation operator to integrate acceptably consistent IMPRs into a collective IMPR with acceptable consistency. We also propose an approach to derive an intuitionistic multiplicative priority weight vector from an acceptably consistent IMPR. An IMGAHP method is then described as a means of solving an MCGDM process with IMPRs. Finally, a practical example and comparative analysis are presented.

Intuitionistic multiplicative analytic hierarchy process in group decision making

Analytic Hierarchy Process (AHP), which analyzes complex decisions by organizing the problems into a multilayer hierarchic structure, is a simple yet popular decision technique used extensively in every decision field. But it is inadequate to handle the uncertain decision making problems. Taking advantage of intuitionistic multiplicative information in portraying the vagueness of problems with Saaty’s 1/9–9 scale, in this paper, we extend the intuitionistic multiplicative information into AHP to enhance the ability of AHP in tackling various decision making problems. We first verify that the intuitionistic multiplicative weighted geometric aggregation (IMWGA) operator has desirable characteristics to guarantee that the overall intuitionistic multiplicative preference relation (IMPR) is consistent when all individual IMPRs are consistent. Then, we provide a whole procedure of intuitionistic multiplicative analytic hierarchy process for solving group decision making problems, including adjusting the individual IMPRs, aggregating the individual IMPRs and deriving the priorities from the overall IMPR. Finally, we present an example concerning the performance assessments of the hydropower stations to illustrate the effectiveness and applicability of the group intuitionistic multiplicative analytic hierarchy process.

An approach for green supplier selection in the automobile manufacturing industry

Purpose – The purpose of this paper is to study a modified multiplicative analytic hierarchy process (MMAHP) method, which is combined with multi-criteria decision making (MCDM) and applied MMAHP model for solving green supplier selection problem. Design/methodology/approach – Supplier selection is typically a MCDM problem including both qualitative and quantitative factors that has to be taken into consideration. To select the best green suppliers with the highest potential for meeting a firm’s needs consistently, the MMAHP is utilized in this study. Then a green supplier selection problem of a well-known automobile manufacturing company in Qingdao is investigated. The authors also make a comparison of the results with that of the traditional AHP, during which the authors observe that the MMAHP is an effective approach for the considered problem and potential rank reversals can be avoided, that is, when a new supplier is added, the ranking of suppliers does not change and maintains its original relative ratio. Findings – A numerical example of green supplier selection is utilized to verify the proposed approach. The results show that the MMAHP is an effective approach for the considered problem and potential rank reversals can be avoided. Practical implications – The proposed approach can be used to solving green supplier selection problems and can avoid the rank reversal. Originality/value – The paper introduces the MMAHP method to help researchers to choose more effective approach for green supplier selection.

Modeling Group Perceptions Using Stochastic Simulation: Scaling Issues in the Multiplicative AHP

This paper proposes a new decision support approach for applying stochastic simulation to the multiplicative analytic hierarchy process (AHP) in order to deal with issues concerning the scale parameter. The paper suggests a new approach that captures the influence from the scale parameter by making use of probability distributions. Herein, the uncertainty both with regard to the scale and the inherent randomness from the parameter is captured by probabilistic input and output distributions. Provided that each alternative and criteria under consideration are independent it is assumed that the embedded uncertainty from the progression factors remains the same. The result is then an interval estimate for each alternative’s final scores. This can lead to overlapping intervals of scores which may be interpreted as possible rank reversals. Thus, the decision support approach makes it possible to calculate the probability of overlapping for any given set of pairwise comparisons.

Effects of Cropping System (Organic and Conventional) on the Fiber Quality Index, Spinning Consistency Index and Multiplicative Analytic Hierarchy Process of Cotton (<i>Gossypium hirsutum</i> L.)

Markets for organically produced high quality cotton (Gossypium hirsutum L.) are projected to increase. Field experiments were conducted in Palamas, Karditsa in Central Greece, to compare the effects of two cropping systems on fiber quality of three cotton cultivars. The experiments, conducted during three years, were laid out in a split plot design with four replicates, two main plots (organic and conventional system) and three sub-plots (cotton cultivars). Findings suggest that fiber quality index (FQI), spinning consistency index (SCI) and multiplicative analytic hierarchy process (MAHP) are three indices that could be integrated in a useful protocol for the evaluation of different cropping systems for cotton cultivation. In particular, our results indicate that in general there was not any superiority of conventional compared to the organic cropping system regarding fiber quality as shown by the above mentioned indices. Regarding the length of the cotton fiber, this was positively correlated with micronair and the uniformity index of the cotton fiber. The organic system resulted to higher values of SCI than the ones of the conventional (1547.9 and 1522.3, respectively). The present 3-years study shows that organic cultivation of cotton can ensure high fiber quality and this was clearly confirmed by means of the several important indices.

Bayesian revision of the individual pair-wise comparison matrices under consensus in AHP–GDM

Analytic hierarchy process (AHP) has been widely used in group decision making (GDM). There are two traditional aggregation methods for the synthesis of group priorities in AHP–GDM: aggregation of the individual judgments (AIJ) and aggregation of the individual priorities (AIP). However, AIJ and AIP may be less reliable because of inconsistency of the individual pair-wise comparison matrices (PCMs) and deviation among decision makers. Based on multiplicative AHP model with lognormal errors, we propose a Bayesian revision method for improving the individual PCMs under the assumption that the consensus exists among decision makers, which is considered an aid to AIJ and AIP. In order to effectively deal with decision making involving multiple actors when using AHP as the methodological support, we revise the individual PCMs using the Bayesian revision method before using AIJ and AIP for the synthesis of group priorities. The Bayesian revision method not only makes full use of the prior distribution for parameters and sample information while complying with the Pareto principal of social choice theory, but also provides the reliable individual Bayesian PCMs for AIJ and AIP. Finally two numerical examples are examined to illustrate the applications and advantages of the Bayesian revision method.

Selection of Handloom Fabrics for Summer Clothing Using Multi-Criteria Decision Making Techniques

Ranking and selection of textile fabrics for a particular end-use requirement is a complex task. In this article, an attempt has been made to develop a simple index of handloom fabric quality, which can be used for selecting fabrics for a specified end use. The Analytic Hierarchy Process (AHP) and Multiplicative Analytic Hierarchy Process (MAHP) of multi-criteria decision making (MCDM) have been used for ranking 25 handloom cotton fabrics in terms of their overall quality value considering their applicability as summer clothing materials. The rank correlation between the rankings elicited from two MCDM methods was found to be 0.926 which implies that the rankings given by AHP and MAHP are in high degree of agreement with each other and any of the two methods can be chosen for ranking of fabrics.