基于TOPSIS方法改进的多属性决策模型:最小化偏好反转

针对多属性决策方法(MCDM)中出现的偏好反转问题,提出一种基于TOPSIS方法改进的MCDM模型.该模型用MAX法代替矢量法对数据进行标准化处理,并根据备选方案的相似距离衡量每个选项的优劣性.这种基于距离计算的综合属性评价方法不仅计算简单,而且可以较好地测度选项间的差异,增强决策结果的准确性.同时,将该模型计算的结果与SAW、AHP、TOPSIS、VIKOR方法进行对比分析,发现只存在原选项时,所提出的模型与SAW、AHP方法的排序结果一致,而当添加或删除某个选项时,SAW、AHP、TOPSIS、VIKOR方法均会产生不同程度的偏好反转现象,而所提出的基于TOPSIS改进的模型可以保持选项的相对顺序不变,表明所提出的模型是有效的,且在避免偏好反转问题时较SAW、AHP、TOPSIS、VIKOR方法具有一定的优越性和可靠性.     

A Model for Decision Making with Missing,Imprecise, and Uncertain Evaluations of Multiple Criteria

In real‐life multicriteria decision making (MCDM) problems, the evaluations against some criteria are often missing, inaccurate, and even uncertain, but the existing theories and models cannot handle such evaluations well. To address the issue, this paper extends the Dempster–Shafer (DS)/analytic hierarchy process (DS/AHP) approach of MCDM to handle three types of ambiguous evaluations: missing, interval‐valued, and ambiguous lottery evaluations. In our extension, the aggregation of criteria's evaluation takes the following six steps: (i) calculate the expected evaluation interval and the ambiguity degree of each group of decision alternatives regarding each criterion, (ii) from them to obtain the preference degree of each group of decision alternatives, (iii) apply the DS/AHP method to obtain the mass function distribution of each group of decision alternatives, (iv) use the Dempster's rule of combination to get the overall mass function of each group of decision alternatives with respect to all criteria, (v) according to the overall mass function to count the belief function and the plausibility function of each decision alternative, and (vi) set the overall preference ordering of decision alternatives by our regret‐avoid ambiguous principle and then find the optimal solution. Finally, we give an example of real estate investment to illustrate how our approach is employed to deal with real‐life MCDM problems.     

TOPSIS with belief structure for group belief multiple criteria decision making

The technique for order performance by similarity to ideal solution(TOPSIS)is one of the major techniques in dealing with multiple criteria decision making(MCDM)problems, and the belief structure(BS)model has been used successfully for uncertain MCDM with incompleteness, impreciseness or ignorance. In this paper, the TOPSIS method with BS model is proposed to solve group belief MCDM problems. Firstly, the group belief MCDM problem is structured as a belief decision matrix in which the judgments of each decision maker are described as BS models, and then the evidential reasoning approach is used for aggregating the multiple decision makers' judgments. Subsequently, the positive and negative ideal belief solutions are defined with the principle of TOPSIS. To measure the separation from ideal solutions, the concept and algorithm of belief distance measure are defined, which can be used for comparing the difference between BS models. Finally, the relative closeness and ranking index are calculated for ranking the alternatives. A numerical example is given to illustrate the proposed method.     

TOPSIS with fuzzy belief structure for group belief multiple criteria decision making

TOPSIS is one of the major techniques in dealing with multiple criteria decision making (MCDM) problems, and Belief Structure (BS) model and Fuzzy BS model have been used successfully for uncertain MCDM with incompleteness, impreciseness or ignorance. In this paper, the TOPSIS method with Fuzzy BS model is proposed to solve Group Belief MCDM problems. Firstly, the Group Belief MCDM problem is structured as a fuzzy belief decision matrix in which the judgments of each decision maker are described as Fuzzy BS models, and then the Evidential Reasoning approach is used for aggregating the multiple decision makers’ judgments. Subsequently, the positive and negative ideal belief solutions are defined with the principle of TOPSIS. In order to measure the separation from the ideal belief solutions, the concept and algorithm of Belief Distance Measure are introduced to compare the difference between Fuzzy BS models. Using the Belief Distance Measure, the relative closeness and ranking index can be calculated for ranking the alternatives. A numerical example is finally given to illustrate the proposed method.     

The use of improved TOPSIS method based on experimental design and Chebyshev regression in solving MCDM problems

Decision makers today are faced with a wide range of alternative options and a large set of conflicting criteria. How to make trade-off between these conflicting attributes and make a scientific decision is always a difficult task. Although a lot of multiple criteria decision making (MCDM) methods are available to deal with selection applications, it’s observed that in most of these methods the ranking results are very sensitive to the changes in the attribute weights. The calculation process is also ineffective when a new alternative is added or removed from the MCDM problem. This paper presents an improved TOPSIS method based on experimental design and Chebyshev orthogonal polynomial regression. A feature of this method is that it employs the experimental design technique to assign the attribute weights and uses Chebyshev regression to build a regression model. This model can help and guide a decision maker to make a reasonable judgment easily. The proposed methodology is particularized through an equipment selection problem in manufacturing environment. Two more illustrative examples are conducted to demonstrate the applicability of the proposed method. In all the cases, the results obtained using the proposed method almost corroborate with those derived by the earlier researchers which proves the validity, capability and potentiality of this method in solving real-life MCDM problems.     

Comparative study of multiple criteria decision making methods for building design

In this paper, multiple criteria decision making methods are studied in the context of building design. The approach is to compare the functionality and the results provided by different methods on three test problems that represent various design situations. The number of criteria in the test problems are two, three and four. Multicriteria optimization is applied to generate the alternatives, among which a preferred solution is to be searched by the decision making methods. Six methods have been selected for comparison: the weighted sum method, the weighted product method, VIKOR, TOPSIS, PROMETHEE II, and a procedure based on the PEG-theorem. The numerical study on the test problems indicate that in most cases, the methods provide different solutions. The PEG-procedure tends to find a well-balanced solution, where none of the criteria is emphasized. While the “best” MCDM method is not discovered in the study, information about the performance of the methods in building design problems is presented.     

Evaluation of suitable locations for the installation of solar thermoelectric power plants

The aim of the present paper is to determine the best location to host a solar thermoelectric power plant. We will seek to show how Geographic Information Systems (GIS) and Multi Criteria Decision Making (MCDM) such as the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS method) and Analytic Hierarchy Process (AHP), are an excellent combination to solve complex locations problems. The coast of the Region of Murcia in the southeast of Spain has been chosen as the study area to carry out this evaluation.The GIS will be shown to be a very useful tool, since GIS are able to generate a database which serves as a starting point for conducting any decision support system. The posed problem will be resolved using restrictions to reduce the area of study, and the criteria that will influence the decision-making. These criteria will be of different natures; with quantitative criteria (numerical values) coexisting with qualitative criteria (labels and linguistic variables). In this article, AHP will be used to obtain the weights of the criteria, and the fuzzy TOPSIS method for the evaluation of the alternatives. In order to compare the results obtained with TOPSIS, the ELECTRE-TRI methodology will be applied.     

A new flexible and reliable interval valued fuzzy VIKOR method based on uncertainty risk reduction in decision making process: An application for determining a suitable location for digging some pits for municipal wet waste landfill

Facility location selection problem is one of the challenging and famous kinds of MCDM problems including both quantitative and qualitative criteria. For each Multiple Criteria Decision Making (MCDM) problem, when the ratings of alternatives with respect to the criteria and/or the values of criteria’s weights are presented by Interval Valued Fuzzy Numbers (IVFNs), the conventional fuzzy MCDM methods (Type-1 fuzzy MCDM methods) tend to be less effective. Therefore, the IVF-MCDM (Interval Valued Fuzzy MCDM) methods should be applied for solving such fuzzy MCDM problems. In this paper, we propose an IVF-VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) method based on uncertainty risk reduction in decision making process. By using such method, the reliability of the captured decisions in an IVF decision making problem is significantly increased. The proposed method is applied for solving two numerical examples that the former of which is a real application problem related to selecting a suitable location for digging some pits for municipal wet waste landfill in one of the largest cities in Iran. The second numerical example is presented with an aim of comparing our method with the two other IVF-MCDM methods. As a result, we found out the proposed method is reliable and practical for the facility location selection problems and other MCDM problems. Moreover, the proposed method has a considerable accuracy and is flexible and easy to use.     

The evaluation of hospital service quality by fuzzy MCDM

This study applies the Multiple Criteria Decision Making (MCDM) to evaluate the service quality of some Turkish hospitals. In general the service quality has abstract properties, which mean that using the previously known measurement approach is insufficient. It is for this reason that the fuzzy set theory is adopted as a research template. In Istanbul, Turkey, there are four B class hospitals classed as private hospitals that are covered by the Social Security Institution (SSI) and for which we propose to represent the service performance measurement using triangular fuzzy numbers. In this study, importance weights of performance criteria are found with AHP. Then, the Multiple Criteria Decision Making methods TOPSIS and Yager's min-max approach are applied to find and rank the crisp performance values. In a second step, an aggregation of performance criteria with OWA and Compensatory AND operators are looked at instead of the TOPSIS method and min-max approach. Thereby numerical applications are supplied by the four methods and the obtained results are compared.     

Development of expert decision model to monitor precision of solar silicon wafer machine line

In this study, we develop a two-stage decision model for managing uncertainty and imprecision of solar silicon wafer slicing evaluations during a wafer manufacturing process. Stage 1 is the evaluation process, which is performed by a procedure based on a combination of the fuzzy analytic hierarchy process (AHP) and the TOPSIS method. Stage 2 is the verification process, in which process capability indices are calculated to verify the feasibility and effectiveness of the proposed methods.     

Development of expert decision model to monitor precision of solar silicon wafer machine line

In this study, we develop a two-stage decision model for managing uncertainty and imprecision of solar silicon wafer slicing evaluations during a wafer manufacturing process. Stage 1 is the evaluation process, which is performed by a procedure based on a combination of the fuzzy analytic hierarchy process (AHP) and the TOPSIS method. Stage 2 is the verification process, in which process capability indices are calculated to verify the feasibility and effectiveness of the proposed methods.     

Simple additive weighting—A metamodel for multiple criteria decision analysis methods

Multiple Criteria Decision Analysis (MCDA) methods, such as ELECTRE, PROMETEE, AHP, TOPSIS, VIKOR, have been applied to solving numerous real-life decision making problems in business and management. However, the mechanics of those methods is not easily understandable and it is often seen by users without much formal training as a kind of “scientific witchcraft”.In order to make those popular MCDA methods more transparent, we provide a simple framework for interpretations of rankings they produce. The framework builds on the classical results of MCDA, in particular on the preference capture mechanism proposed by Zionts and Wallenius in seventies of the last century, based on Simple Additive Weighting.The essence and the potential impact of our contribution is that given a ranking produced by an MCDA method, we show how to derive weights for the Simple Additive Weighting which yield the same ranking as the given method. In that way we establish a common framework for almost no–cost posterior analysis, interpretation and comparison of rankings produced by MCDA methods in the expert systems environment. We show the working of the concept taking the TOPSIS method in focus, but it applies in the same way to any other MCDM method.We illustrate our reasoning with numerical examples taken from literature.     

Rank B2C e-commerce websites in e-alliance based on AHP and fuzzy TOPSIS

E-alliance is the union of e-commerce and its success and efficiency is related to comprehensive quality of e-commerce. Thus, ranking e-commerce websites in e-alliance is of importance, which is a multi-criteria decision-making (MCDM) problem. This paper proposes an evaluation model based on analytic hierarchy process (AHP), fuzzy sets and technique for order performance by similarity to ideal solution (TOPSIS), to tackle the issue in fuzzy environment. The AHP is applied to analyze the structure of ranking problem and to determine weights of the criteria, fuzzy sets is utilized to present ambiguity and subjectivity with linguistic values parameterized by triangular fuzzy numbers, and TOPSIS method is used to obtain final ranking. Case analysis is conducted to illustrate the utilization of the model for the problem. It demonstrates the effectiveness and feasibility of the proposed model.     

产品族创新策略选择的多属性决策方法

针对产品族演进过程中产品族创新策略选择问题,提出了FAHP-TOPSIS集成方法的产品族创新策略的多属性决策模型。在界定3种产品族创新策略类型和特点的基础上,构建产品族创新策略的评价指标体系及产品族创新策略的多属性决策模型。为了消除决策过程中的主观不确定性和模糊性,将FAHP和TOPSIS有机结合起来进行定性和定量综合评价产品族创新策略方案的优劣。通过具体实例,验证了该方法的有效性,这为解决产品族创新演进过程中策略决策问题提供了一种新的分析途径。     

A web-based high-performance multicriteria decision support system for medical diagnosis

Multicriteria decision making (MCDM) methods can be powerful aids for evaluating patients' medical information in medical diagnostic systems. Technique ordered preference by similarity to the ideal solution (TOPSIS) is one of the more widely used MCDM methods in decision support systems. For the purpose of this work, the TOPSIS method is modified into a more suitable form and used for the implementation of a web-based medical diagnostic system. In our modified TOPSIS method, we have utilized fuzzy logic so that users can more accurately describe their symptoms. The data given to the modified TOPSIS method are often massive in proportions and may take a considerable amount of time to generate a ranking of alternatives. TOPSIS lends itself to parallel computation because it is virtually a combination of matrix computations. Therefore, computer parallelism is implemented so that a large amount of input data can be handled simultaneously, hence decreasing overall execution time. In addition, to make our MCDM system more accessible, we have designed our system to be web based. The web-based medical diagnosis system includes a dynamically generated web-based user interface, while the parallel implementation of the modified TOPSIS component, in conjunction with the Common Gateway Interface, forms the back end of the system. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 1083–1099, 2007.     

Weapon selection using the AHP and TOPSIS methods under fuzzy environment

The weapon selection problem is a strategic issue and has a significant impact on the efficiency of defense systems. On the other hand, selecting the optimal weapon among many alternatives is a multi-criteria decision-making (MCDM) problem. This paper develops an evaluation model based on the analytic hierarchy process (AHP) and the technique for order performance by similarity to ideal solution (TOPSIS), to help the actors in defence industries for the selection of optimal weapon in a fuzzy environment where the vagueness and subjectivity are handled with linguistic values parameterized by triangular fuzzy numbers. The AHP is used to analyze the structure of the weapon selection problem and to determine weights of the criteria, and fuzzy TOPSIS method is used to obtain final ranking. A real world application is conducted to illustrate the utilization of the model for the weapon selection problem. The application could be interpreted as demonstrating the effectiveness and feasibility of the proposed model.     

一种基于理想目标法的决策方法研究

通过对比几种典型的多目标决策方法,提出了一种逼近理想解方法和层次分析法相结合的理想目标法,通过验证,该方法在目标要害判定过程中具有较强的科学性和准确性。     

Group multi-criteria design concept evaluation using combined rough set theory and fuzzy set theory

Design concept evaluation is a critical stage in the product development which has significant impact on the downstream process in product development thus on success of new product. Design concept evaluation is widely recognized as a complex multi-criteria decision-making (MCDM) problem involving various decision criteria and large amount of data which are usually imprecise and subjective. This paper proposes a new decision-making method to evaluate product design concepts based on the distance between interval vectors each alternative and positive and negative ideal reference vectors. Rank of design concepts is obtained by calculating interval-based relative closeness index for each alternative. In this method, to deal with uncertainty and vagueness of data in the primary phases of product design, performance of design concepts with respect to quantitative and qualitative criteria are concurrently evaluated using rough set and fuzzy set. The weights of criteria used in the evaluation are obtained using the extent analysis method on fuzzy AHP. The efficacy of the method is demonstrated with a numerical example and the results are compared to TOPSIS method. In final, the conclusions of our method are represented and some future directions are proposed to improve the model.     

Multicriteria Decision Making with Cognitive Limitations: A DS/AHP‐Based Approach

In real life, sometimes multicriteria decision making (MCDM) problems are dealt with inevitably under cognitive limitations of human's minds. However, few existing models can directly solve MCDM problems of this kind. Thus, to address the issue, this paper proposes a novel approach, which can: (i) handle the cognitive limitations in MCDM problems by distinguishing the case of complete criteria (i.e., there are no hidden cognitive factors that can deviate rational decisions) from the case of incomplete criteria (i.e., there are some hidden cognitive factors that can deviate rational decisions); (ii) differentiate incomplete and complete relative ranking of the groups of decision alternatives (DAs) over a criterion; and (iii) solve the imprecise and uncertain evaluation of criterion weight as well as the ambiguous evaluations of the groups of DAs regarding a given criterion. Hence, we give a measure to consider the influence of cognitive limitations and give two methods to reduce the influence of cognitive limitations when a decision making needs more rational. Moreover, we illustrate our approach by solving a real‐life problem of estate investment. Finally, we give some experimental results about the reduction of the required number of knowledge judgments in our method compared with the previous methods.