Identify the most critical criteria is which of the following steps in multi-criteria analysis?

Abstract:

Multi-criteria decision making (MCDM) is a branch of operations research (OR). Decision making often involves imprecision and vagueness which can be effectively handled by fuzzy sets and fuzzy decision making techniques. In recent years, a great deal of research has been carried out on the theoretical and application aspects of MCDM and fuzzy MCDM. This chapter provides an outline of decision making in general and fuzzy MCDM in particular. The algorithms of the popular MCDM processes (AHP and TOPSIS) are explained and their applications in cotton fibre grading and selection are discussed. Subsequently, fuzzy MCDM techniques (fuzzy AHP and fuzzy TOPSIS) are introduced and their applications are explained with some simplified examples of cotton fibre selection.

4.4 Justification for applying MCDM in materials selection

Most real-life decision-making problems have several conflicting criteria and objectives to be considered simultaneously. For example, the compromises required to strike a balance between the performance and cost of a motor car, or between health and the pleasure of eating rich foods. Similar conflicts arise between material properties and performance metrics in the choice of materials (Sirisalee et al., 2004). Among the many fields where MCDM applied (computer software selection, project selection, and system selection), materials selection is certainly one of the most crucial. Searching for suitable materials is a key part of the engineering design process, and is a multi-dimensional problem with many “boxes ticked” at the same time. Changing the materials set in an established technology is a rare event and can be considered as a revolution (Curtarolo et al., 2013). Furthermore, materials selection is the prerequisite for a chain of different engineering selection problems, such as process selection, machine selection, tools selection, material handling equipment selection, supplier selection, and personnel selection (Jahan and Edwards, 2015). Traditionally, choosing a new material or replacing an existing material with another material whose characteristics provide better performance, is usually carried out by applying “trial-and-error” methods and/or by using previous experience. This may or may not result in an optimum design solution but the adoption of MCDM methods will help to avoid the use of inappropriate materials and make sure costs are kept to a minimum.

MCDM address the need for a numerate structure (Charles et al., 1997) in the materials selection process. MCDM provides a foundation for selecting, sorting, and prioritizing materials and help in the overall assessment. The use of MCDM is particularly important when:

The application is complex or advanced.

The materials and/or application are new.

The use of leading edge technology is involved, such as aerospace, electronics, nuclear, and biomedical applications, where product differentiation and competitive advantage are often achievable with just small gains in material performance.

Due to considerable disagreement among members of the engineering design community as to the extent that engineering design involves decision-making and to which classical decision theory applies to engineering, design engineers have not adopted the formalisms of decision theory, despite its long history and wide acceptance in other communities. Therefore, many well accepted methods in engineering design clearly produce questionable results (Hazelrigg, 2003).

Unlike the exact sciences, where there is usually only one single correct solution to a problem, materials selection and substitution decisions require the simultaneous consideration of conflicting advantages and limitations, necessitating compromises and trade-offs; as a consequence, different satisfactory solutions are possible (Farag, 2002). Suppose you need to choose a material for an economic lightweight design from the hypothetical materials shown in Table 4.3. Should the cheapest material or the lightest material be chosen? If Materials A and B are compared, it cannot be determined that either is superior without knowing the relative importance of weight versus price. However, comparing Materials B and C shows that Material C is better than Material B for both objectives, and as a consequence Material C “dominates” Material B. Therefore, as long as Material C is a feasible option, there is no reason that B should be chosen. To conclude the comparisons, it can also be seen that Material D is dominated by Material E. The rest of the material options (Materials A, C and E) have a trade-off associated with weight versus price, so none is clearly superior to the others. This is called the “nondominated” set of solutions because none of the solutions are dominated. Usually, solutions of this type form a typical shape as shown in Fig. 4.6.

Table 4.3. Hypothetical data for materials selection of a lightweight design

Solutions that lie along the line are nondominated solutions while those that lie inside the line are dominated because there is always another solution on the line that has at least one objective that is better. The line is called the “Pareto-front” and solutions on it are called “Pareto-optimal.” All Pareto-optimal solutions are nondominated. Thus, it is important to find the solutions as close as possible to the Pareto-front, as far along it as possible. This is more challenging in MOO problems with constraints that have many solutions in the feasible region. One way of finding points on the Pareto-front is converting all but one into constraints in the modeling phase or invent weightings for the criteria and optimize the weighted sum but this simplifies the consideration and loses information (Miettinen, 1999). There are different methods used in practice for both MADM and MODM problems. In MOO, one method is to use a genetic algorithm (Awad et al., 2012; Cui et al., 2008) to enumerate points along the Pareto-front over several iterations, then use a method to rank the quality of the trade-offs based on the particular application being modeled. Solving MOO problems requires a correct and proper formulation of the problem. In most of the practical optimization problems inaccuracy and uncertainty is present and a clear formulation of the problem may be given after the problem is solved (Miettinen, 1999).

It is observed that there has been a growth in the study of the material evaluation and selection problems using the MCDM approaches from 2006 (Jahan et al., 2010). It is expected that this will keep increasing in the coming years, because in materials selection there are often several solutions for a particular application and materials affect many aspects of a product design, that is, shape, manufacturing process, and product performance, so a more precise approach is required. The “Ashby” materials selection chart method discussed in Chapter 3 does allow a cost-based approach. The method also has the versatility of being able to examine many materials at a glance and allow competing materials to be quickly identified. However, it cannot be guaranteed that the selected material is the best because of the limit of only being able to consider two or three criteria simultaneously, as discussed in the previous section.

Abstract

Multi-Criteria Decision-making (MCDM) has the potential for improving all areas of decision-making in engineering, from design to manufacture, but is especially beneficial for applications in high technology market sectors, where product differentiation and competitive advantage are often achieved by just very small gains in material performance. The full capability of MCDM methods are realized by their ability to simultaneously consider material, process, and shape for complex materials selection problems. It is essential therefore to expand the scope of MCDM methods to a wide range of engineering applications and feedback the experience to improve materials selection. The need to handle uncertainty and make compromises are recurring practical design issues and the effective manipulation of data ranges is critical to more effective use of MCDM in materials selection and design. The selection of more advanced materials, and materials with tailored properties, particularly composites and multi-functional materials, is a significant area that is beginning to take advantage of MCDM. With the current emphasis on materials design and modeling, it is desirable in future versions of computer simulation software to include multi-criteria analysis capability.

2.2 Decision making for risk management

Multi-criteria decision-making in general follows six steps including, (1) problem formulation, (2) identify the requirements, (3) set goals, (4) identify various alternatives, (5) develop criteria, and (6) identify and apply decision-making technique (Sabaei, Erkoyuncu, & Roy, 2015). Various mathematical techniques can be used for this process, and the choice of techniques is made based on the nature of the problem and the level of complexity assigned to the decision-making process. All methods have their own pros and cons.

In risk management, risk should be prioritized and analyzed through the decision-making concepts (Ayyub, 2014). Risk prioritization aids managers in identifying and assessing high-risk sources, essential control strategies, and adjustment techniques for the control strategies (Behraftar, Hossaini, & Bakhtavar, 2017). Risk prioritization and assessment should be performed based on the triple main risk factors concept including, occurrence probability (O), severity (S), and detection probability (D) as addressed in the concept of failure mode and effects analysis (FMEA) method (Bakhtavar & Yousefi, 2019). FMEA is a method which can be used to identify the causes and consequences of failure events (Sharif et al., 2017). FMEA was first introduced within an aerospace agency in the 1960s. Later, the technique was adopted in many sectors particularly addressing the issues of quality and safety. FMEA is a powerful and one of the most widely-applied techniques for identifying and assessing risks (Liu, Chen, Duan, & Wang, 2019). It considers the triple risk factors of occurrence, severity, and detectability simultaneously in ranking the risks by assigning a risk priority number (RPN) (Rah, Manger, Yock, & Kim, 2016).

In this type of analysis, the failure modes (what can go wrong?), the causes of failure (the factors that contribute to the failure), and the detections or control mechanisms (what are the mechanisms to prevent or identify the failures?) are investigated for a given system. Numerical values are assigned to the severity of the impacts of failure, the probability (or frequency) of occurrence, and the ease of detection. Based on the above value, the RPN is calculated for each combination of failure modes.

RPN=severity×occurence×detection

The FMEA technique holds an important position in the operations research sector. Moreover, the term “risk” is very common in operations research. Hence, it is important to discuss the risk management from the context of FMEA.

FMEA is unable to assign different importance weights to the triple risk factors, separating failure modes with different severities but having similar risk priority number (RPN) and fully prioritizing (Bakhtavar & Yousefi, 2019). The literature on FMEA is steadily growing and covering many sectors, along with some modifications and applications. Determining the risk ranking of failure modes in FMEA is a multifaceted challenge that needs a multi-criteria decision making (MCDM) analysis (Liu, Chen, et al., 2019). Therefore, FMEA can be viewed as a MCDM problem because of the involvement of multiple risk factors, which includes prioritization and assessing the failure modes based on the triple risk factors. Several comprehensive studies have overviewed the application of MCDM techniques in different fields including but not limited to; energy, environment, and sustainability; supply chain management; materials; quality management; construction and project management; safety and risk management; operation research and soft computing, etc. However, it was observed that operation research and soft computing has a relatively higher application of MCDM (Mardani et al., 2015).

MCDM considers the importance of the risk factors, deconstructs the risk assessment process into distinct phases, and prioritizes failure modes through mathematical models (Liu, Chen, et al., 2019). According to a recent literature review by Liu, Chen, et al. (2019), there were more than 150 research articles published in the last two decades showing the application of MCDM in the context of FMEA under different scenarios. At a broader level, the common MCDM techniques applied in FMEA includes but not limited to distance-based techniques, outranking techniques, compromised techniques, pairwise comparison techniques etc. In addition, various hybrid and multiple factor-based techniques have been developed to address the FMEA.

In a MCDM problem, the basic ingredients are the criteria and alternatives. Different alternatives evaluated against set criteria to formulate a comparison of alternatives. The results can be improved further by assigning weights to different criteria, as the importance can vary extremely from one decision-maker to another. Hence, for selected criteria, there can be a different level of importance from the perspective of different decision-makers (Sabaei et al., 2015). It important to evaluate the assign weights to each criterion from different decision-makers to ensure the reliability of results.

The selection of the MCDM technique for a solving a particular problem can vary depending on the context, which emphasizes the need to understand decision-making classifications. The MCDM techniques are categorized based on (1) compensatory and non-compensatory, (2) discrete and continuous, and (3) individual and group decision-making. Classification of MCDM based on discrete and continuous data is the most commonly applied ones (Sabaei et al., 2015). From the perspective of discrete and continuous data, the MCDM is divided into multi-attribute decision making (MADM) and multi-objective decision making (MODM) (Zavadskas, Antucheviciene, & Kar, 2019). MADM considers the problems under an inherent discrete decision space (Triantaphyllou, 2000). MODM is based on mathematical theory and deals with the problems under continuous decision space.

5.5.2.4 Criteria importance through intercriteria correlation

MCDM involves determining the optimal alternative among multiple, conflicting, and interactive criteria (Chen et al., 1992). In MCDM, many of the criteria are often highly correlated (Ramík and Perzina, 2010; Angilella et al., 2004), and the incorporation of several interdependent criteria could yield misleading results, while the arbitrary omission of some criteria entails the removal of more or less useful information sources (Diakoulaki et al., 1995). Furthermore, an attribute cannot often be considered separately because of the complementarities between them. For example, in the case of steel, there is a common relationship between the Brinell hardness number (BHN) and the Ultimate Tensile Strength (UTS). Similar relationships can be shown for brass, aluminum, and cast irons. These kinds of relationships have been reported widely in materials engineering for different mechanical properties (Durst et al., 2008; Jiang et al., 2006). Moreover, in the conceptual design stage, when designers are more interested in sensorial aspects of materials (Karana et al., 2008; Karana et al., 2009), the interdependency would be more significant because the technical and sensorial properties of materials have to be considered simultaneously and these two have an obvious relationship. For instance, both sensorial criteria of transparency and smoothness are used for conveying the meaning of sexy in a product (Karana et al., 2009), while there are relationships between these two aspects and mechanical properties. Considering these interdependencies may reduce the risk of the wrong selection when there are a lot of materials with very similar performances. One way to address this issue is to obtain the relationship among criteria and then to derive the final weightings by considering the influences between them. An objective weighting method of Criteria Importance Through Intercriteria Correlation (CRITIC) based on the SD method was proposed by Diakoulaki et al. (1995).

6.4.1 Weighting method

In multi-criteria decision-making problem, the weights of the criteria can be determined by using various methods, including subjective methods (Saaty, 1987; Lee et al., 2014; Ocampo et al., 2018; Meesapawong et al., 2014; Ren et al., 2015a,b; Somsuk and Laosirihongthong, 2014; Tadic et al., 2014), objective methods (Bazzazi et al., 2011), and combined methods. The CRITIC is an objective weighting method on the basis of standard deviation and correlation. In this study, the CRITIC is employed to objectively determine the sustainability assessment criteria weights for urban sewage treatment.

4.3.2 Multi-criteria decision making

Multi-criteria decision making (MCDM) also referred to as multiple criteria decision analysis (MCDA), is a research area that involves the analysis of various available choices in a situation or research area which spans daily life, social sciences, engineering, medicine, and many other areas. MCDM is one of the most popular decision-making tools utilized in various fields [12–22].

MCDM analyses the criteria to determine whether each criterion is a favorable or unfavorable choice for a particular application. It also attempts to compare this criterion, based on the selected criteria, against every other available option in an attempt to assist the decision maker in selecting an option with the minimal compromise and maximum advantages. The criteria used in the analyses of these criteria can be either qualitative or quantitative criteria.

Division of MCDM can be made into two categories based on the method used to determine the weight of each alternative.

Compensatory decision making: Involves the evaluation of the criteria, of the criteria including the weak points and strong points of the criteria and allows the strong points of each criteria to compensate for the weak points, thereby putting all the criteria of the criteria into consideration. An example of a compensatory decision-making tool is the analytical hierarchy process (AHP)—a technique used mostly when the environment for the analysis is complex. It is used in the comparison of criteria that are difficult to quantify.

Outranking decision making: This method compares the criteria of the criteria in couples in order to determine which criteria ranks higher than the others based on the comparisons. A popular example of an outranking decision-making method is elimination and choice expressing reality (ELECTRE), a method that is used to choose, rank, and sort alternatives to solve a problem.

1.1 Introduction

Application of multi-criteria decision-making (MCDM) theory is the use of computational methods that incorporate several criteria and order of preference in evaluating and selecting the best option among many alternatives based on the desired outcome. It is applied to different fields to obtain an optimum solution to a problem where there are many parameters to consider that cannot be decided by the users’ experiences. The application gives a ranking result based on the selected criteria, their corresponding values, and assigned weights. The application of MCDM theory in biomedical engineering and healthcare is a new approach that can be enormously helpful for patients, doctors, hospital managers, engineers, etc. Whether it is improving healthcare delivery or making a sound and safe decision for the benefit of the patient, healthcare professionals and other decision makers are always entangled with decision-making dilemmas. In real-life problems, there are many critical parameters (criteria) that can directly or indirectly affect the consequences of different decisions. Stakes are always high whenever human life is in danger, so it is always important to make the right decisions. When deciding whether to use a particular medication, treatment, or medical equipment, not only are the problems with multiple criteria very complex, but multiple parties are also deeply affected by the effects.

There are many methods available for solving MCDM problems. However, the MCDM methods discussed in this textbook are the Analytic Hierarchy Process (AHP), Technique for Order of Preference by Similarities to Ideal Solution (TOPSIS), Elimination Et Choix Traduisant la Realité (ELECTRE), Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE), ViseKriterijumska Optimizcija i Kaompromisno Resenje (VIKOR), and Data Envelopment Analysis (DEA). AHP is based on mathematics and psychology. Rather than recommending the best alternative, AHP encourages decision makers to find a solution that better suits their goal and perception of the problem. It offers a comprehensive and rationally oriented context in which the decision problem can be organized, quantified, and evaluated. TOPSIS is a very useful MCDM method. This is an alternative approach that measures weights for each parameter, normalizes scores for each criterion, and determines the numerical difference for each alternative and the optimal alternative, which is the best score for every criteria. ELECTRE is another popular MCDM method used to eliminate any unacceptable alternatives. PROMETHEE is suitable when groups of people are working on complex issues, particularly those with various parameters that require several views and viewpoints that have long-term consequences in their decisions. This provides unique advantages when it is difficult to quantify or compare important elements in the decision, or when cooperation between departments or team members is limited by their different requirements or expectations. Other multicriteria decision-making MCDM methods that will be discussed include VIKOR, fuzzy logic–based MCDM methods, and DEA.

8.4.2 Technique for order of preference by similarity to ideal solution (TOPSIS)

TOPSIS is a multi-criteria decision-making method that uses the basic mathematical approach to find the optimal alternative [32]. The guideline utilized in TOPSIS is that the chosen elective must have the nearest separate from the positive ideal solution and farthest from the negative ideal solution by incorporating the Euclidean distance to determine the relative proximity geometrically. The positive ideal solution (X+) is represented as the total of all best-obtained values for each alternative. In contrast, the negative ideal solution (X−) includes all the worst attainable values for each alternative considered. Both the solutions are hypothetical and are obtained within the process. This method does so by calculating the proximity related to the positive ideal solution. As per the relative comparison and calculations, we choose an alternative priority (Y). This MCDM method is widely used for solving real-life problems. With efficient computation and the caliber to calculate the relative performance of decision options, it is a straightforward technique.

3.3 Materials and methodology

Fuzzt PROMETHEE is a multi-criteria decision-making method used across many disciplines of research. In fuzzy PROMETHEE, the input data are treated as fuzzy numbers, with the purpose of considering the uncertainty contained in the data [8]. This decision-making tool aids the decision maker in identifying the best alternative from a group of options according to his/her goals and their own understanding of the problem.

This method is particularly important to give clarity on decisions that are difficult to quantify or compare, especially if two or more individuals have different perspectives as in this study. A patient, physician, researcher, or a medical device company has different perspectives on the elements that make a treatment technique the most or the least favorable.

In order to evaluate the brain cancer treatment alternatives, we collected the main criteria of the alternatives, including the radiation dose, side effects, success rate, recovery time, session duration, cost of the treatments, and cost of the machine (Table 3.1). Because of the treatment alternatives’ vague criteria, we defined the criteria with a triangular fuzzy linguistic scale, as seen in Table 3.2. In addition, we used the same fuzzy linguistic scale to calculate the importance degree of the criteria. Then, we applied the Yager index to defuzzify the fuzzy data of the criteria and, lastly, we applied the visual PROMETHEE decision lab software to obtain the results.

Table 3.1. Treatment alternatives, common criteria, and their corresponsing values.

VH: Very high; H: High; M: Medium; L: Low; VL: Very low

Table 3.2. Linguistic scale of importance.

The linguistic scale of importance shows the sets of triangular fuzzy numbers. Each fuzzy set is given a scale for evaluation (graded), depending on how the set will define the criteria investigated. The seven criteria investigated in this study have been assigned an importance rating from VH to VL in relation to a corresponding fuzzy set. The specific criteria for each fuzzy set are selected based on how criteria make a specific therapy technique superior to others, e.g. success rate is of paramount importance since it is the goal of any treatment technique, so it is given a fuzzy set with the highest grading, which in this case is VH. Other criteria are also assigned to their fuzzy sets in a similar way. Furthermore, a Gaussian preference function was used for the comparison of the alternatives corresponding to their parameter. Visual PROMETHEE decision lab program was then applied and the results are presented in the next section.