COMMENTS ON “MULTIPLE CRITERIA DECISION MAKING (MCDM) METHODS IN ECONOMICS: AN OVERVIEW”

. This paper offers comments on a previously published paper, titled “Multiple criteria decision making (MCDM) methods in economics: an overview,” by Zavadskas and Turskis (2011). The paper’s authors made great efforts to summarize MCDM methods but may have failed to consider several important new concepts and trends in the MCDM field for solving actual problems. First, the traditional model assumes the criteria are independently and hierarchically structured; however, in reality, problems are often characterized by interdependent criteria and dimensions and may even exhibit feedback-like effects. Second, relatively good solutions from the existing alternatives are replaced by aspiration levels to fit today’s competitive markets. Third, the emphasis in the field has shifted from ranking and selection when determining the most preferable approaches to performance improvement of existing methods. Fourth, information fusion techniques, including the fuzzy integral method, have been developed to aggregate the performances. Finally, the original fixed resources in multi-objective programming are divided such that both decision and objective spaces are changeable. In this paper, we add new concepts and provide comments that could be thought of as an attempt to complete the original paper.


Introduction
Zavadskas and Turskis' (2011) work, titled "Multiple criteria decision making (MCDM) methods in economics: an overview, " has made a considerable contribution to the field. These researchers present a panorama of decision making methods in economics, summarizing the most important results and applications over the last five years. These authors present a thorough historical review and classify and illustrate the primary steps of MCDM methods. The authors go on to discuss several opportunities for future research. The methods illustrated were, however, mostly developed in the 1980s and 1990s but have recently been applied to new fields. We feel that important research into new methods and current trends was not adequately addressed in the paper.
For example, a new hybrid dynamic multiple-criteria decision making (HDMCDM) method for problem-solving in interdependent and feedback situations in the fields of economics and business has been proposed Ho et al. 2011). For multiple-objective decision making (MODM) problems, several researchers developed a new changeable space including decision space and objective space (CDOS) method that incorporates many of the realities of a dynamic and changing environment. Tzeng and Huang (2012a) applied the De Novo method of optimization in the objective space, given constraints in the decision space, to determine the aspiration levels for all objectives (Huang, Tzeng 2007). With regard to nontraditional MCDM methods, Greco et al. (2010) developed a decision rule approach based on the dominance-based rough set theory. Deb et al. (2002Deb et al. ( , 2011) applied a genetic algorithm to solve MODM problems. In this paper, not only we discuss the Zavadskas and Turskis paper, but also provide more reference material for greater completeness. This supplemental material could help readers understand the complete scope of MCDM and demonstrate the benefits of MCDM in economics and business. Fig. 1 illustrates the basic concepts of problem solving. Through either data collection or investigation of objectives, the responses and social and personal attributes of the objectives may be represented as a data set (e.g., crisp, fuzzy or rough set). These data can be further analyzed using data processing techniques (e.g., data mining, statistical/multivariate analysis, neural networks or logic reasoning) or forecasting models (e.g., regression, fuzzy regression, grey forecasting or Bayesian regression). The data could also be analyzed using MCDM. MCDM can be roughly separated into MODM (Multi-Objective Decision Making) and MADM (Multi-Attribute Decision Making) components. MODM includes goal programming (GP), multiple objective programming (MOP) and compromise solution methods. These problems can be solved using many methods including single level, fuzzy, multi-stage and dynamic methods. MADM includes structure relation methods (e.g., interpretive structural modeling (ISM), Decision Making Trial and Evaluation Laboratory (DEMATEL) or fuzzy cognitive map), weight analysis (e.g., Analytic Hierarchy Process (AHP), Analytic Network Process (ANP) or entropy measure) and performance aggregated methods (e.g., simple additive weight (SAW), Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS), ELECTRE or grey relation for additive types and fuzzy integral for non-additive types). Data envelopment analysis (DEA) is a method to investigate problems with multiple inputs and outputs. DEA is comprised of various methods including fuzzy DEA, network DEA and multi-objective programming (MOP) DEA. Fig. 2 compares the traditional approach with other methods for knowledge economy. Data mining techniques may be used to process the data to support meaningful conclusions and generate useful knowledge. With the current focus on technology in business, two of the most important questions organizations must answer are how to increase market share and how to incorporate new technologies into products. Marketing efforts can be enhanced through knowledge discovering and technology can be improved through innovation and creativity in intelligent systems. MCDM could help decision-makers when faced with multiple-objective or multiple-attribute problems.
The rest of this paper is structured as follows. In Section 2, we provide supplementary material about the development of MCDM and note the differences between Multiple Objective Decision Making (MODM) and Multiple Attribute Decision Making (MADM). Important new concepts and methodologies ignored in Zavadskas and Turskis's (2011) work are discussed in Section 3. We offer concluding arguments in Section 4.

Supplementary history and classification of MCDM
MCDM refers to methods for decision making in realistic and common scenarios in which multiple, often conflicting criteria (i.e., multiple attributes or objectives) must be taken into consideration. Many such problems are related to the measurement, design, evalua-  tion, ranking, selection, and improvement of organizational initiatives. In this study, we will illustrate several important aspects of and new trends in MCDM that have not been adequately addressed.
(1) Planning/Design in MODM ( Fig. 3): One of the primary functions of MODM is to analyze planning and design problems with multiple objectives and criteria based on a changeable decision-space in a dynamic environment (as opposed to traditional assumptions of unchangeable constraint conditions) and to bring objectives closer to their aspiration levels. One way to accomplish this is to maximize the extent of goal achievement (this is called fuzzy multi-objective programming and includes fuzzy goals, fuzzy parameters, and fuzzy variables). Alternatively, one may also redesign a decision space to achieve the desired aspiration level. This approach is called De Novo programming and is related to changeable decision-space improvement to achieve the aspiration level in objective-space (concept further explained in Appendix III). This method could be applied both in theory and practice, to real decisionmaking cases in planning or design, including changeable space (decision space and objective space). In addition to the methods described above, several other important methods have been developed since the 1990s including disaggregation methods (Zopounidis et al. 1999), preference programming (Liesiö et al. 2007) and stochastic multi-objective acceptability analysis (SMAA) (Kangas et al. 2006). The development of MODM is illustrated in Fig. 3. It is worth noting that this list is not exhaustive and is composed of only a few important authors and trends that appeared after the 1990s.  (Zadeh 1965) DM in fuzzy environment (Bellman, Zadeh 1970) Grey eory (Deng 1982) Fuzzy Combinatorial MODM with GA (Sakawa et al . 1994) GA in search, Opt. and Machine Learning (Goldberg 1989) GA + Data Structure = Evolutionary Programming (Michalewicz , Schoenauer 1996) Vector Optimization (Kuhn, Tucker 1951) (Koopmans 1951) (Yu 1973;Yu, Zeleny 1975) Habitual Domain (HD) Multistage Multiobjective (Yu 1980) Fuzzy + HD Multiobjective Game (Sakawa , Nishizaki 1992) De Novo Programming (Zeleny 1986(Zeleny , 1990 Goal Programming (Charnes et al. 1955) Data Envelopment Analysis, DEA (Charnes et al. 1978) Multiple Criteria Multiple Constraints Level (MC 2 ) (Yu, Seiford 1979)

Some trends a er 1990s (Combined models)
Fuzzy De Novo (Li, Lee 1990) Fuzzy MC 2 (Shi, Liu 1993) Fuzzy DEA (Kahraman 1998;Guo, Tanaka 2001) Fuzzy Multi-objective for DEA (Chiang, Tzeng 2000) Network DEA (Fare, Grosskopt 2000) Fuzzy + HD + Dynamic + Multistage + Multi-level Multi-objective Decision Making (Yu, Chen 2010, Concepts on changeable space) TOPSIS for MODM (Lai et al. 1994) Fuzzy Multiobjective Programming (Zimmermann 1978;Sakawa 1983) In the Future GA for MODM (Deb et al. 2002) (2) Evaluation/Improvement/Selection in MADM ( Fig. 4): One of the trends within MADM is to analyze gaps between objectives and associated aspiration levels. The Influential Network Relation Map (INRM) could help decision makers understand the relationships among dimensions and criteria and thus enable them to propose sound strategies for improvement. This goal could be accomplished with additive or super-additive (non-additive) strategies based on the DEMATEL technique. A new hybrid MCDM method (Liu et al. 2012) has been developed using the DEMATEL technique and DANP (DEMATEL-based ANP, called DANP). Several methods based on the INRM can be used to evaluate problems and enhance aspiration level achievement, including additive (e.g., VIKOR (ViseKriterijumska Optimizacija I KOmpromisno Rešenje in Serbian translates as Multicriteria Optimization and Compromise Solution method) and grey relation method) and non-additive (also referred to as superadditive e.g., Fuzzy Integrals)    (Lin et al. 2010), and Formal Concept Analysis (FCA) (Fang et al. 2012). Current MADM-related trends are toward the determination of how to establish strategic systems to reduce the gaps between existing performance values and aspiration levels for each criterion. Additional points of interest include the improvement and selection of the best option for decision making in new theories (e.g., DANP) and the application of these hybrid MADM methods to real problems. Furthermore, new methods, such as COPRAS (Zavadskas et al. 2007), MULTIMOORA (Brauers, Zavadskas 2010) and LINMAP (Li 2008) have been developed or extended for solving recent economic problems.

Current developments in MCDM
In this section, we will outline several important concepts that were not considered by Zavadskas and Turskis (2011) including (1) interdependent modeling, (2) aspiration levels, (3) improvement (in addition to ranking and selection), (4) information fusion (non-additive models), and (5) changeable space in the decision and objective spaces.

Interdependence and network structure
Zavadskas and Turskis listed many MCDM methods, but assumed independent criteria in a hierarchical structure (such as additive modeling and weighting by AHP). In reality, the evaluation criteria are seldom independent, and the relationships between them are frequently characterized by a degree of interactivity, interdependence and feedback effects. Saaty (1996) proposed using the Analytic Network Process (ANP), which relaxes the hierarchical structure restriction. However, two questions related to the ANP model warrant attention: how to generate the influential network relationship and how to evaluate the degree of influence (Liou 2012 (Benayoun et al. 1966;Roy 1968) ELECTRE I (Roy 1971) ELECTRE II (Roy, Bertiet 1973) ELECTRE III , IV (Roy 1976(Roy , 1978Roy, Vincke 1981;Roy 1991;Figueira et al. 2005) TOPSIS (Hwang, Yoon 1981) TOPSIS for MODM (Lai et al. 1994) FMADM (Seo, Sakawa 1985) Fuzzy neural network Dynamic MADM (Hashiyama et al. 1995) AHP (Saaty 1971(Saaty , 1977 Dynamic Weights AHP (Saaty 1992) Non-independent ANP (Saaty 1996) Rough Sets eory (RST) (Pawlak 1982) Grey (Deng 1982) Fuzzy Set (Zadeh 1965) DM in fuzzy environment (Bellman, Zadeh 1970) Choquet Integral (Choquet 1953) Habitual Domain (Yu 1980 (Greco et al. 2001) Dominance-based Rough Set Approach (DRSA ) (Greco et al. 2010) Zero-sum Game (Nash 1951) ELECTRE TRI (Wei 1992;Mousseau & Slowinski 1998) are subsequently incorporated into the traditional ANP to create the new DANP method that yields more realistic weights for the respective dimensions and criteria. These weights could also be combined with other MCDM methods, such as additive types of VIKOR (Kuan et al. 2012), the grey relation  or non-additive types of fuzzy integrals (Larbani et al. 2011), to evaluate the performance criteria of various options and the extent to which the option achieve the desired aspiration level.

Replacement of the relatively good existing alternatives by aspiration levels
The traditional MADM ranks alternatives to select the best solution. However, Simon, who was awarded the Nobel Prize in economics in 1978, claimed that decision making does not obey the postulates of the "rational man. " Humans do not solve problems by maximizing utility, but are "satisfiers" who set aspiration levels that a solution must satisfy. If humans are able to identify a solution that satisfies the stated aspiration levels, they accept the solution. A metaphor can be used to illustrate this difference. In the traditional method (which focuses only on ranking alternatives and selecting the overall best among them), we could pick one apple to be the benchmark from a basket of inferior apples; the benchmark is still an inferior apple. With the new concept, the decision maker sets an aspiration level as the benchmark, an alternative which might not exist in the current basket of apples, but decision-makers will understand the gaps between each alternative and the aspiration level. Decision-makers can therefore devise and implement a strategy to reduce the gaps. The current trend is toward improvement of the traditional decision-making concept, which is to choose the best from among inferior choices. The new concept is that decision makers should set an aspiration level as the benchmark and change the process to avoid this problem Liu et al. 2012).

Improving but not ranking alternatives
The development of MCDM has shifted the focus from ranking and selecting alternatives to improving their performance. The old models can only identify the gaps between competing alternatives. A new trend is to reduce the gap to achieve an aspiration level in a more realistic strategy. For example, if measures for scaling the performance value are from zero to ten (0, 1, 2,…, 10), we can set zero (0) to be the worst value and ten (10) to be the aspiration level. We can thus examine alternatives to reduce the gap based on an influential network relation map. This newly developed model helps decision-makers realize the gaps between current performance and aspiration levels and enhances competitiveness. Several researchers have proposed an improvement technique to lessen the gaps for each criterion obtained from VIKOR (Ou Yang et al. 2009). This technique is based on an influential relation map created by DEMATEL which is used to reduce gaps between current performance and aspiration levels. This approach can improve the traditional decision-making basic concept for alternatives ranking and selection only. It should be noted that another notably popular MCDM model, TOPSIS, has proven shortcomings with regard to ranking alternatives (Opricovic, Tzeng 2004).

Information fusion techniques
Many methods based on multiple attribute utility theory (MAUT) have been proposed (e.g., the weighted sum and the weighted product methods in an additive model) to deal with MADM problems. The concept of MAUT is to aggregate all criteria to a specific dimension (the utility function) to evaluate alternatives. The main issue is to find a rational and suitable aggregation operator that represents the decision maker's preferences. Although the aggregation operator of MAUT has often been discussed (Fishburn 1970), the primary remaining challenge is the assumption of preferential independence (Hillier 2001;Grabisch 1995).
Preferential independence can be described as the preferential outcome of one criterion over another that is not influenced by the remaining criteria. However, in practical MADM application, the criteria are sometimes interactive. For example, in supplier selection, the cost, risk and quality are often interdependent. To overcome the problem of non-additivity, the Choquet integral was proposed (Choquet 1953;Sugeno 1974). The Choquet integral can represent a certain kind of interaction between criteria using the concept of redundancy and synergy and has been applied in many fields Chu et al. 2007). Another fusion approach can be seen in Peng et al. (2011aPeng et al. ( , 2011b.

Changeable decision space
In the original iteration of the MODM, it was assumed that the decision space was fixed and that the decision-maker can only choose solutions from an existing region. Zeleny (1986Zeleny ( , 1990 proposed De Novo programming to redesign the feasible region to maximize the achievement levels of objectives to ideal solutions or aspiration levels (concept described in more detail in Appendix III). Tzeng applied the De Novo method of optimization in the objective space given constraints in the decision space (relaxing assumptions) to achieve the aspiration levels for all objectives (Huang et al. 2006). Tzeng also focused on applications of the new hybrid dynamic multiple-criteria decision making (HDMCDM) and changeable space, including decision space and objective space (CDOS) methods, in a wide range of industries in the fields of economics and business as a way to solve practical problems in management, create value in innovation and increase win-win competitiveness. The new concept is illustrated in Fig. 5. The traditional method looks for a solution from the Pareto solutions in the existing feasible decision space. De Novo programming pursues the ideal solution and redesigns the original decision space. The new concept has decision makers setting an aspiration level, though it may not be reachable using current resources, or simply redesigning the decision space. However, the aspiration level could be attained by expanding employees' competence set (e.g., training) or adding or changing new resources (e.g., through strategy alliance, innovation or creativity) to expand the original decision space.

Conclusions
This paper discusses several important concepts that were not addressed in Zavadskas and Turskis' (2011) work. We provide a historical review of MCDM with supplementary material and note several of the key authors in each stage (see Figs 3 and 4). Several significant concepts, such as building interrelationships (dependence and feedback) among criteria and improvement of criteria in general to achieve the aspiration level, are introduced. We also offer some techniques to integrate performance (information fusion) in super-additive/nonadditive value function situations. Finally, we present ways in which the decision space may be modified to achieve aspiration level of the objective space in changeable space situations. These concepts are designed to solve real problems encountered using traditional methods. This supplemental paper can be viewed as a companion to the original work and could contribute to a more comprehensive understanding of the MCDM framework and enhance the available set of techniques available for economic problem solving.
In addition to identifying new trends in MCDM, we illustrate the future outlook. The current MCDM methods depend on a decision-maker or a group of decision-makers, which group could be replaced by all stakeholders. Comparisons between statistical methods (regression or structural equation modeling (SEM)) and MCDM techniques are welcome. Future research could include the examination of more effective ways, e.g., linguistic variables or fuzzy logic, to reflect decision-makers opinions combined with new MCDM techniques. A direct relation matrix is produced for each respondent, and an average matrix A is subsequently derived from the mean of the same perspectives and criteria in the respective direct matrices for all respondents. The average matrix A is given by: Step 2. Calculate the initial direct influence matrix. The initial direct influence matrix X can be obtained by normalizing the average matrix A. In addition, the matrix X can be obtained through equations (2) and (3), in which all principal diagonal criteria are equal to zero. Step where the superscript ' denotes transpose; ri denotes the row sum of the ith row of matrix T and shows the sum of the direct and indirect effects of perspective or criterion i on the other perspectives and criteria. Similarly, s j denotes the column sum of the jth column of matrix T and shows the sum of direct and indirect effects that perspective or criterion j has received from the other perspectives and criteria. In addition, when i = j (i.e., the sum of the row and column aggregates) r i + s i provides an index of the strength of influence given and received, that is, r i + s i illustrates the extent to which criterion i plays a central role in the problem. If r i -s i is positive, then criterion i affects other criteria, and if r i -s i is negative, then criterion i is influenced by other criteria. Based on the total influence matrix, the INRM can be draw as Fig. A1. VIKOR method for reducing performance gaps to improve the alternatives Opricovic and Tzeng (2004) proposed the compromise ranking method (VIKOR) as one applicable technique to implement within MCDM. Suppose that the feasible alternatives are represented by V 1 , V 2 ,…, V k ,…,V m . The performance scores of alternative V k and the jth criterion is denoted by f kj . w j is the influential weight (relative importance) of the jth criterion, where j = 1, 2,…, n and n is the number of criteria. Development of the VIKOR method began with the following form of the L p -metric: -A simple production problem involving two products: suits and dresses in quantities 1 x and 2 x , with each of them consuming five different resources (unit market prices of resources are given). According to De Novo programming, the Maximum levels of two products can be calculated by mathematical programming:

Ax b
The data are summarized as follows:  (2) He is a member of IEEE, IAEE, ISMCDM, World Transport, the Operations Research Society of Japan, the Society of Instrument and Control Engineers Society of Japan, the City Planning Institute of Japan, the Behaviormetric Society of Japan, the Japan Society for Fuzzy Theory and Systems; and participating many Society of Taiwan. He is editors-in-Chief of International Journal of Information Systems for Logistics and Management, and so on.