|Gwo-Hshiung Tzeng New Concepts and Trends of Hybrid MCDM for Tomorrow||
According to the defined upper and lower approximations and the boundary regions, RST may help reduce the required attributes (i.e., CORE attributes; the related discussion is provided in Subsection 1.6) to discern the target attribute (also termed decision attribute), which may support the minimal and representative attributes (criteria) for MADM models. 1.6 Emerging Trend in Multiple Rules-Based Decision-Making (MRDM) Extended from the classical RST, DRSA (Greco et al. 1999, 2002a, 2002b, 2005) was proposed to consider the preferential characteristics in attributes and the “dominance” relationships among alternatives (with respect to certain attributes in the system for classification). The idea of preference regarding criteria is crucial in decision-making. For example, in a stock selection problem, the alternative with higher profitability (which is a criterion) should be preferred. Thus, the potential usefulness of DRSA in resolving MCDM problems has been recognized since the late 1990s (Greco et al. 2001, 2005, 2008; Slowinski 2008). A new trend in MCDM has also emerged since then and may be termed multiple rule-based decision-making (MRDM); one of the key advantages of DRSA is that it can generate a set of decision rules to denote the rough knowledge in data. The basic ideas of DRSA are briefly discussed as follows. DRSA may begin with organizing data in IS in the form of a table, with the attributes and objects (alternatives) arranged in rows and columns, respectively. The table of DRSA is a 4-tuple IS, i.e.,
The high potential of DRSA as a decision aid in MCDM, for ranking or selection, has been noticed since the works of Greco et al. (1999, 2001, 2005), which has emerged as a new research field in MCDM. The original idea was based on collecting a certain preference order (i.e., partial preorder of the available alternatives in which a DM has confidence) and forming a pairwise comparison table (PCT), introduced by Greco et al. (1997, 1999). Subsequently, the dominance principle, stated as multigraded dominance by Slowinski et al. (2005) or as the dominance relation D2 by Szelag et al. (2013) is defined on pairs of objects, such as: if objects a, b, c, d ∈ U , (a, b) and (c, d) are defined as pairs over set H , pair (a, b) is regarded as D2 dominance (c, d) with respect to criteria P ⊆ C (where C is the aforementioned condition attribute set in DRSA, and P is a partial set of C ), iff Vi(a)- Vi(b) ≧ Vi(c) – Vi(d) for each criterion I ∈ P (in here, Vi(a) denotes the value of alternative a on criterion i). In the next, on the basis of the essential ideas of DRSA, decision rules were adopted for capturing the rough knowledge from the aforementioned PCT. The obtained decision rules are thus applied to the other alternatives (objects), and to certain exploitation methods, such as the net flow score of Greco et al. (1999). This can be adopted to give rankings for the whole set of alternatives. This approach enables ranking by collecting a set of reference objects to denote the preference structure of a DM. The obtained DRSA decision-rule-based exploitations are to be calculated for the preference order of all alternatives. It may be regarded as the multidisciplinary integration of diverse fields: soft computing, machine learning, and the outranking approach. The brilliant contributions of Greco et al. (1997, 1999, 2001, 2002a, 2002b, 2005), Slowinski et al. (2005), and Szelag et al. (2013) on this emerging field have inspired us to propose new hybrid MCDM models to resolve practical problems, especially regarding improvement planning. The proposed framework of the new hybrid MCDM models is discussed in Subsection 2.3.
1.7 Outline of the Book
Aside from this background of MCDM research and certain computational intelligence techniques for problem solving, the remainder of this book comprises two parts; the first part introduces the essential concepts and theories of relevant methods and techniques, and certain real-world applications, mainly in financial and IT industries, are illustrated in the second part. Although the cases discussed in this book mainly fall in the category of business, the proposed hybrid approach for problem solving is not limited to this field; numerous types of real-world problems, in fields like economics, business, psychology, social welfare, engineering, transportation planning, new product development, and national policy formation, can be addressed using these methods. In addition, the three pillars—MRDM, MADM, and MODM—may be regarded as three types of methods for solving different types of problems, and the combination or integration of the techniques from those three fields should be based on the problems that are addressed. The details of the new hybrid approach are discussed in the following chapters. We hope that interested readers may find it helpful to apply the new hybrid MCDM models for solving real-world problems in various fields, thus bridging the gap between academia and practice.
NEW CONCEPTS AND TRENDS IN MCDM
Multiple Attribute Decision Making: Methods and Application
By Gwo-Hshiung Tzeng & Jih-Jeng Huang (2011), CRC Press, Taylor & Francis Group, A Chapman & Hall Book.
Part I Concepts and Theory of MADM
Analytic Hierarchy Process; Analytic Network Process and Fuzzy Analytic Network Process; Simple Additive Weighting Method; TOPSIS and VIKOR; ELECTRE Method; PROMETHEE Method; Gray Relational Model; Fuzzy Integral Technique; Rough Sets; Structural Model (Interpretive Structural Modeling (ISM) Method, DEMATEL Method, Fuzzy Cognition Maps).
Part II Applications of MADM
AHP: An Application; VIKOR Technique with Applications Based on DEMATEL and ANP; TOPSIS and VIKOR: An Application; ELECTRE: An Application; PROMETHEE: An Application; Fuzzy Integral and Gray Relation: An Application; Fuzzy Integral: An Application; Rough Sets: An Application.
Fuzzy Multiple Objective Decision Making
By Gwo-Hshiung Tzeng & Jih-Jeng Huang (2013), CRC Press, Taylor & Francis Group, A Chapman & Hall Book.
Section I Concepts and Theory of Multi-Objective Decision Making
Multi-Objective Evolutionary Algorithms; Goal Programming; Compromise Solution and TOPSIS; De Novo Programming and Changeable Parameters (including Decision Space and Objective Space, called Changeable Spaces); Multi-Stage Programming; Multi-Level Multi-Objective Programming; Data Envelopment Analysis.
Section II Applications of Multi-Objective Decision Making
Motivation and Resource Allocation for Strategic Alliances; Choosing Best Alliance Partners and Allocating Optimal Alliance Resources Using Fuzzy Multi-Objective Dummy Programming Model; Multi-Objective Planning for Supply Chain Production and Distribution Mode: Bicycle Manufacturer; Fuzzy interdependent Multi-Objective Programming; Novel Algorithm for Uncertain Portfolio Selection; Multi-objective Optimal Planning for Designing Relief Delivery Systems; Comparative Productivity Efficiency for Global Telecoms; Fuzzy Multiple Objective Programming in Interval Piecewise Regression Model.
New MCDM Books (MADM & MODM)
Gwo-Hshiung Tzeng, Jih-Jeng Huang (2012). Multiple Attribute Decision Making: Methods and Applications, CRC Press, Taylor & Francis Group, 2011, 349 pages.
Gwo-Hshiung Tzeng, Jih-Jeng Huang (2013). Fuzzy Multiple Objective Decision Making, CRC Press, Taylor & Francis Group, 2013, 313 pages
Gwo-Hshiung Tzeng, Kao-Yi Shen (2016). New Concepts and Trends of Hybrid Multiple Criteria Decision Making, CRC Press, Taylor & Francis Group, In Press.
Tzeng, G.H.; Kao-Yi Shen, K.Y. New Concepts and Trends of Hybrid Multiple Criteria Decision Making, CRC Press, Taylor & Francis Group, 2016, In Press.
New Concepts and Trends of Hybrid Multiple Criteria Decision Making including three parts: (1) Hybrid MRDM (Multiple Rule/Rough-based Decision Making), (2) Hybrid MADM (Multiple Attribute Decision Making, (3) Hybrid MODM (Multiple Objective Decision Making). The features and contributions of this new book are shown as followings:
In Hybrid MRDM (Multiple Rule/Rough-based Decision Making),
First, for avoiding "Statistics and Economics are unrealistic in assumptions/ hypotheses: How can be easy to understand and control from “Big-Data” to extract the “CORE Attribute” for decision-makers in making decision through/combining MADM and MODM; Tzeng’s research group using logical thinking and reasoning based on basic concept of “Rough Set Theory (RST)” to construct the core attributes in if-then rules” from “Big Data”. Furthermore, this book uses the “DRSA (dominance-based rough set approach) or VC-DRSA” to build “Flow Graph” in “if-then rule-based” combining DEMATEL technique to construct the cause-effect in “if-then Rule/Rough-based Decision-Making” (called Multiple Rule/Rough-based Decision Making, MRDM) as influential relationship flow, called MRDM. These results can make decision-makers or users easy to understand and grasp the problems in the causal-effect relationship combining DEMATEL technique. So we also can combine the "new hybrid MCDM model”, can more obtain effectively to provide the decision-makers for solving the real world problems-improving.
In Hybrid MADM (Multiple Attribute Decision Making), Second-Fifth items),
Second, how can find the influence relation matrix in the key "aspects and criteria" to establish the Influential Network Relation Map (INRM) and find the influential weights of DANP (DEMATEL-based ANP) in dependence and feedback problems by cause-effect via interrelationship in the practical situations;”?. The traditional model assumes the criteria are independent and hierarchical in structure; the previous studies that mainly rely on statistical models (e.g., regressions and time series models) to examine the relationship based on independence, linear, correlation, etc. However, in real-world problems, the interrelationships between the criteria or aspects (or called dimensions) are usually interdependent and sometimes even exert feedback effects; So we adopt DEMATEL method to construct influential network relation map (INRM) and to find the influential weights of DANP using basic concept of ANP (Saaty, 1996) based on influence relation matrix of DEMATEL technique (Ou Yang et al., 2008, 2013; Peng and Tzeng, 2013; Shen et al., 2014; Hu et al., 2014) for solving the inter-dependence and feedback (interrelationship problems) of criteria (or called attributes) aspects (or called dimensions) in the real world problem to avoid “unrealistic assumptions in Statistics and Economics”.
Third, how fulfill “problem-solving and improvement (Adopting “aspired-worst” to replace traditional “max-min” as benchmark)” for the overall consideration “aspects and criteria” can be all towards for reaching “aspiration level”? The relative good solution from the existing alternatives is replaced by the aspiration levels to fit today’s competitive markets; so we modified VIKOR method (Opricovic and Tzeng, 2004, 2007), SAW, Grey Relation Analysis (Chiu et al., 2014, Liou et al., 2015), PROMETHEE (Tsui et sl., 2015), ELECTRE to correct traditional Max-Min as ideal point and negative ideal point into aspiration level and the worst value. The relatively good solution from existing alternatives based on “max-min” as goal/target (benchmark) is replaced by aspiration level and worst value (“aspired-worst” as benchmark) for avoiding “Choosing the best among inferior options/alternatives”, i.e. for avoiding “pick the best apple among a barrel of rotten apples”. Simon incorporated the basic concept of the “aspiration level” in his work, receiving the Nobel Prize in Economics in 1978. HA Simon - Decision and organization, 1972 - innovbfa.viabloga.com ... The Scottish word "satisficing" (=satisfying) has been revived to denote problem solving and decision making that sets an aspiration level, searches until an alternative is found that is satisfactory by the aspiration level criterion, and selects that alternative (Simon (1957), Part IV ... (Simon, 1978, Nobel Prize). For example, the performance value of each criterion can be obtained by using questionnaires with a scale ranging from 0 points (complete dissatisfaction/bad) to 10 points (the best satisfaction/good). Then in this case, we can set the aspiration level as ten (10) and the worst value as zero (0) j=1,2,…,n, called “aspired-worst” as benchmark. In contrast to the traditional approach, which sets the best and the worst value in each criterion j as maximal and minimal performance for all alternatives k=1,2,…K respectively, called “max-min” as benchmark.
Fourth, how can build the integrity (overall-view) of improvement strategies by systematics based on INRM? The new hybrid MADM analytical tools are not only used in ranking and selection, but also can be used in the performance gaps improvement among criteria and its corresponding aspects (or dimensions); So the emphasis in the field has shifted from ranking and selection when determining the most preferable approaches to performance improvement of existing methods based on INRM, because "we need a systematic approach to problem-solving; instead of addressing the systems of the problem, i.e., we need to identify the sources of the problem in performance improvement based on INRM, because “we need a systematic approach to problem-solving; instead of addressing the systems of the problem, we, to avoid “stop-gap piecemeal”.
Fifth, how can build the integrity (overall-view) of improvement strategies by systematics based on INRM? Kahneman and Tversky (Kahneman received the Nobel Prize in Economics in 2002), they, in results of many their studies during 1960s, found consumers in products-selecting of multi-attribute preference value are almost different from traditional multi-attribute utility (value-function aggregation in multi-attribute) by using additive model. , i.e., almost all the results are inconsistent with the real actual problems, when they mistakenly thought preference people have problems Until 1974, Sugeno completed his Doctoral thesis “Theory of fuzzy integrals and its applications” in Tokyo Institute of Technology; fuzzy integrals are, namely, “non-additive model” or so-called “super-additive model”, as a value-function integrated model. So Kahneman based on above basic concept proposed “Prospect Theory” in 1978.
In Hybrid MODM (Multiple Objective Decision Making),
Sixth, based on above points five we can be systematically how find overall thinking the problem-improving for achieving or toward “aspiration levels, the resolve of implementing improvement-strategies in enforcement, how can enforce it? Classical MODM (Multiple Objectives Decision Making) in thinking of plan/design is based on a fixed set conditions or resources (fixed conditions or resources, this is called “Decision Space”, in feasible space to be fixed (i.e., fixed feasible region, this is called “Objective Space”) how we can find the Pareto optimal solution? We will propose a new thinking of “MODM models with changeable spaces” to implement and enforce for improvement in solving MADM problems for enhancing the performance values toward achieving the aspiration levels in criteria, dimensions, and overall through innovation and creativity. This new thinking in changeable spaces programming not only can help decision-makers to reach win-win planning or design, but also can be forward achieving the desired point (aspiration level), which is better than pursuing the Pareto optimal solutions or ideal point.