A study of high-level managerial decision processes, with implications for MCDM research

We study six real-world major strategic decisions and discuss the role that analytic Multiple Criteria Decision Making (MCDM) models could play in helping decision makers structure and solve such problems. We have interviewed successful and well-educated managers who had access to quantitative decision models, but did not use them as part of their decision process. Our approach is a clinical one that takes a close look at the decision processes. We believe that the normative MCDM framework is oversimplified and does not always fit well with complex, real-world organizational decision processes. This may be one reason why decision tools are not used more widely for solving high-level decision problems. We believe that it would be worthwhile to revise some of the MCDM mainstream postulates and practices to make existing models and tools more suitable for practical purposes. The MCDM mainstream research has until today focused on the choice among alternatives. One should realize that MCDM models could also be used in creating alternatives, in assessing the importance of criteria, in providing the decision makers with “post-commitment support”, and as part of a devil's advocate approach.     

An Experimental Evaluation of Interactive MCDM Methods and the Decision Making Process

Increasingly, it is becoming recognized that interactive solution methods should provide not only a solution to a multiple criteria decision making (MCDM) problem, but also the opportunity for decision makers to learn about their own preferences. In this paper, we describe an experiment that examines three MCDM solution methods and the process of converging on a final solution. Twenty-four management students participated in the experiment and were required to solve two completely different MCDM problems. Within this experimental framework, we examined the use of a two-stage approach to decision making. Both quantitative and qualitative results are presented. Preferences among the different solution methods vary significantly. Several conclusions are drawn concerning the desirable features of interactive MCDM solution methods.     

Modeling subjective evaluation for fuzzy group multicriteria decision making

This paper presents a new fuzzy multicriteria decision making (MCDM) approach for evaluating decision alternatives involving subjective judgements made by a group of decision makers. A pairwise comparison process is used to help individual decision makers make comparative judgements, and a linguistic rating method is used for making absolute judgements. A hierarchical weighting method is developed to assess the weights of a large number of evaluation criteria by pairwise comparisons. To reflect the inherent imprecision of subjective judgements, individual assessments are aggregated as a group assessment using triangular fuzzy numbers. To obtain a cardinal preference value for each decision alternative, a new fuzzy MCDM algorithm is developed by extending the concept of the degree of optimality to incorporate criteria weights in the distance measurement. An empirical study of aircraft selection is presented to illustrate the effectiveness of the approach.     

A new decision support model in multi-criteria decision making with intuitionistic fuzzy sets based on risk preferences and criteria reduction

In this paper, we propose a new model for decision support to address the ‘large decision table’ (eg, many criteria) challenge in intuitionistic fuzzy sets (IFSs) multi-criteria decision-making (MCDM) problems. This new model involves risk preferences of decision makers (DMs) based on the prospect theory and criteria reduction. First, we build three relationship models based on different types of DMs’ risk preferences. By building different discernibility matrices according to relationship models, we find useful criteria for IFS MCDM problems. Second, we propose a technique to obtain weights through discernibility matrix. Third, we also propose a new method to rank and select the most desirable choice(s) according to weighted combinatorial advantage values of alternatives. Finally, we use a realistic voting example to demonstrate the practicality and effectiveness of the proposed method and construct a new decision support model for IFS MCDM problems.     

Kernel-based learning methods for preference aggregation

The mathematical representation of human preferences has been a subject of study for researchers in different fields. In multi-criteria decision making (MCDM) and fuzzy modeling, preference models are typically constructed by interacting with the human decision maker (DM). However, it is known that a DM often has difficulties to specify precise values for certain parameters of the model. He/she instead feels more comfortable to give holistic judgements for some of the alternatives. Inference and elicitation procedures then assist the DM to find a satisfactory model and to assess unjudged alternatives. In a related but more statistical way, machine learning algorithms can also infer preference models with similar setups and purposes, but here less interaction with the DM is required/allowed. In this article we discuss the main differences between both types of inference and, in particular, we present a hybrid approach that combines the best of both worlds. This approach consists of a very general kernel-based framework for constructing and inferring preference models. Additive models, for which interpretability is preserved, and utility models can be considered as special cases. Besides generality, important benefits of this approach are its robustness to noise and good scalability. We show in detail how this framework can be utilized to aggregate single-criterion outranking relations, resulting in a flexible class of preference models for which domain knowledge can be specified by a DM.      

On redundancy in multi criteria decision making

The concept of redundancy is accepted in Operations Research and Information Theory. In Linear Programming, a constraint is said to be redundant if the feasible decision space is identical with or without the constraint. In Information Theory, redundancy is used as a measure of the stability against noise in transmission. Analogies with Multi Criteria Decision Making (MCDM) are indicated and it is argued that the redundancy concept should be used as a regular feature in conditioning and analysis of Multi Criteria Programs. Properties of a proposed conflict-based characterisation are stated and some existence results are derived. Redundancy is here intended for interactive methods, when the efficient set is progressively explored. A new redundancy test for the linear case is formulated from the framework. A probabilistic method based on correlation is proposed and tested for the non-linear case. Finally, some general guidelines are given concerning the redundancy problem.     

A fuzzy-stochastic OWA model for robust multi-criteria decision making

All realistic Multi-Criteria Decision Making (MCDM) problems face various kinds of uncertainty. Since the evaluations of alternatives with respect to the criteria are uncertain they will be assumed to have stochastic nature. To obtain the uncertain optimism degree of the decision maker fuzzy linguistic quantifiers will be used. Then a new approach for fuzzy-stochastic modeling of MCDM problems will be introduced by merging the stochastic and fuzzy approaches into the OWA operator. The results of the new approach, entitled FSOWA, give the expected value and the variance of the combined goodness measure for each alternative. Robust decision depends on the combined goodness measures of alternatives and also on the variations of these measures under uncertainty. In order to combine these two characteristics a composite goodness measure will be defined. The theoretical results will be illustrated in a watershed management problem. By using this measure will give more sensitive decisions to the stakeholders whose optimism degrees are different than that of the decision maker. FSOWA can be used for robust decision making on the competitive alternatives under uncertainty.     

Finding the most preferred alliance structure between banks and insurance companies

In this paper we have studied alternative alliances between banks and insurance companies. First we defined six different possible structure models for such alliances, and nine criteria used to evaluate the models. The models and the criteria were introduced together with bank and insurance experts. The experts are representatives of the top management of Finnish banks and insurance companies. Searching for the most preferred alliance model is a multiple criteria decision making (MCDM) problem. To solve the problem, we used an expert panel and the Analytic Hierarchy Process (AHP). Based on the evaluations of the panel, the alternatives Financial Conglomerate and Cross-Selling Agreement, no Overlapping Service Channels are most preferred. Which one is chosen, depends on how risk is emphasized.     

Interactive outranking approaches for multicriteria decision-making problems with imprecise information

PROMETHEE is a powerful method, which can solve many multiple criteria decision making (MCDM) problems. It involves sophisticated preference modelling techniques but requires too much a priori precise information about parameter values (such as criterion weights and thresholds). In this paper, we consider a MCDM problem where alternatives are evaluated on several conflicting criteria, and the criterion weights and/or thresholds are imprecise or unknown to the decision maker (DM). We build robust outranking relations among the alternatives in order to help the DM to rank the alternatives and select the best alternative. We propose interactive approaches based on PROMETHEE method. We develop a decision aid tool called INTOUR, which implements the developed approaches.     

Selection of technology acquisition mode using the analytic network process

Selecting the appropriate acquisition mode for a required technology, is one of the critical strategic decisions in formulating a technology strategy. Although a number of factors were found to be influential in the choice of technology acquisition mode, it still remains a void in the literature how to make a strategic decision, based on a huge set of those factors with the help of a systematic approach. This study deals with the selection of technology acquisition mode as a multiple criteria decision making (MCDM) problem. The proposed solution to the problem in this study, is the analytic network process (ANP) approach. Since the ANP is a MCDM method that can accommodate interdependency among decision attributes, it is capable of providing priorities of alternatives with consideration of interrelationships among strategic factors. The 21 influential factors identified from the empirical studies are included as sub-criteria in the ANP model, and they are grouped into five criteria: capability, strategy, technology, market, and environment. The final decision can be made based on the resulting priorities of the alternative acquisition modes. The proposed approach is expected to effectively aid decision making on which mode is adopted for acquisition of required technologies. A case of a software company is presented for the illustration of the proposed approach.     

A multiple criteria ranking method based on game cross-evaluation approach

The application of Data Envelopment Analysis (DEA) as an alternative multiple criteria decision making (MCDM) tool has been gaining more attentions in the literatures. Doyle (Organ. Behav. Hum. Decis. Process. 62(1):87?C100, 1995) presents a method of multi-attribute choice based on an application of DEA. In the first part of his method, the straightforward DEA is considered as an idealized process of self-evaluation in which each alternative weighs the attributes in order to maximize its own score (or desirability) relative to the other alternatives. Then, in the second step, each alternative applies its own DEA-derived best weights to each of the other alternatives (i.e., cross-evaluation), then the average of the cross-evaluations that get placed on an alternative is taken as an index of its overall score. In some cases of multiple criteria decision making, direct or indirect competitions exist among the alternatives, while the factor of competition is usually ignored in most of MCDM settings. This paper proposes an approach to evaluate and rank alternatives in MCDM via an extension of DEA method, namely DEA game cross-efficiency model in Liang, Wu, Cook and Zhu (Oper. Res. 56(5):1278?C1288, 2008b), in which each alternative is viewed as a player who seeks to maximize its own score (or desirability), under the condition that the cross-evaluation scores of each of other alternatives does not deteriorate. The game cross-evaluation score is obtained when the alternative??s own maximized scores are averaged. The obtained game cross-evaluation scores are unique and constitute a Nash equilibrium point. Therefore, the results and rankings based upon game cross-evaluation score analysis are more reliable and will benefit the decision makers.     

Graph-based multi-agent decision making

In lots of practical multi-criteria decision making (MCDM) problems, there exist various and changeable relations among the criteria which cannot be handled well by means of the existing methods. Considering that graphic or netlike structures can be used to describe the relationships among several individuals, we first introduce the graphic structure into MCDM and formalize the relations among criteria. Then, we develop a new tool, called graph-based multi-agent decision making (GMADM) model, to deal with a kind of MCDM problems with the interrelated criteria. In the model, the graphic structure is paid sufficient attention to in two main aspects: (1) how the graphic structure has influence on the benefits of agents (or the criteria values); and (2) the relation between the graphic structure and the importance weights of agents (criteria). In this case, we can select the best plan(s) (or alternative(s)) according to the overall benefits (the overall criteria values) resulting from the model. Moreover, a fuzzy graph-based multi-agent decision making (FGMADM) method is developed to solve a common kind of situations where the graphic structure of agents is uncertain (confidential or false). Three examples are used to illustrate the feasibility of these two developed methods.     

Nonessential objectives within network approaches for MCDM

In Gal and Hanne [Eur. J. Oper. Res. 119 (1999) 373] the problem of using several methods to solve a multiple criteria decision making (MCDM) problem with linear objective functions after dropping nonessential objectives is analyzed. It turned out that the solution does not need be the same when using various methods for solving the system containing the nonessential objectives or not. In this paper we consider the application of network approaches for multicriteria decision making such as neural networks and an approach for combining MCDM methods (called MCDM networks). We discuss questions of comparing the results obtained with several methods as applied to the problem with or without nonessential objectives. Especially, we argue for considering redundancies such as nonessential objectives as a native feature in complex information processing. In contrast to previous results on nonessential objectives, the current paper focuses on discrete MCDM problems which are also denoted as multiple attribute decision making (MADM).     

Mathematical programming and the sensitivity of multi-criteria decisions

We report on the current state of a project whose aim is to implement a framework for sensitivity analysis in Multi-Criteria Decision Making (MCDM). The framework is largely based on mathematical programming. Due to the potentially large number and nature of the mathematical programmes, it is far from trivial to provide solutions to all of them in acceptable computing times. The challenge is even greater when we recognize that much decision analysis is performed in the context of decision conferences where any sensitivity analysis needs to be conducted in near real time (preferably) on a PC. We present a parallel processing approach to this challenge and point to some of the difficulties still to be resolved. Preliminary results obtained on a network of transputers are discussed.     

Preference ranking global frequencies in multicriterion analysis (Pragma)

This paper presents an MCDM method, known as Pragma, which provides the ranking frequencies of feasible actions. The method is based on the comparison of the partial profiles of each alternative with reference to all the possible pairs of criteria considered. The global frequencies are obtained as the weighted sum of the corresponding partial ranking frequencies. The information supplied by this method is valuable in solving discrete multiple criteria choice problems and, in particular, in building complete and partial preoders of feasible actions. Pragma is a useful complement to the Mappac method, being instrumentally based on the same fundamental preference indices.     

Extension of VIKOR method for decision making problem based on hesitant fuzzy set

The multiple criteria decision making (MCDM) methods VIKOR and TOPSIS are all based on an aggregating function representing “closeness to the ideal”, which originated in the compromise programming method. The VIKOR method of compromise ranking determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum of an “individual regret” for the “opponent”, which is an effective tool in multi-criteria decision making, particularly in a situation where the decision maker is not able, or does not know to express his/her preference at the beginning of system design. The TOPSIS method determines a solution with the shortest distance to the ideal solution and the greatest distance from the negative-ideal solution, but it does not consider the relative importance of these distances. And, the hesitant fuzzy set is a very useful tool to deal with uncertainty, which can be accurately and perfectly described in terms of the opinions of decision makers. In this paper, we develop the E-VIKOR method and TOPSIS method to solve the MCDM problems with hesitant fuzzy set information. Firstly, the hesitant fuzzy set information and corresponding concepts are described, and the basic essential of the VIKOR method is introduced. Then, the problem on multiple attribute decision marking is described, and the principles and steps of the proposed E-VIKOR method and TOPSIS method are presented. Finally, a numerical example illustrates an application of the E-VIKOR method, and the result by the TOPSIS method is compared.     

Fractional Minmax Goal Programming: A Unified Approach to Priority Estimation and Preference Analysis in MCDM

A special minmax goal programming model with fractional goals is formulated and then used as the basis for developing two specific MCDM methods: (1) a method to derive priorities for decision elements from pairwise comparison matrices in the AHP framework; (2) a method to assess an additive value function by analysing some preference information expressed over the set of alternatives on a ratio scale. For both methods a common iterative solution procedure is proposed by using a linear programming formulation.     

Research on AHP with interval-valued intuitionistic fuzzy sets and its application in multi-criteria decision making problems

This paper investigates an approach for multi-criterion decision making (MCDM) problems with interval-valued intuitionistic fuzzy preference relations (IVIFPRs). Based on the novel interval score function, some extended concepts associated with IVIFPRs are defined, including the score matrix, the approximate optimal transfer matrix and the possibility degree matrix. By using these new matrixes, a prioritization method for IVIFPRs is proposed. Then, we investigate an interval-valued intuitionistic fuzzy AHP method for multi-criteria decision making (MCDM) problems. In the end, a numerical example is provided to illustrate the application of the proposed approach.     

基于犹豫毕达哥拉斯模糊环境下的TODIM方法

在决策过程中TODIM方法能有效的捕捉决策者的心理行为。犹豫毕达哥拉斯模糊集不但能反映正反两个方面的不确定性,而且能反映决策者的犹豫程度。本文将TODIM方法扩展到犹豫毕达哥拉斯模糊集。首先定义了犹豫毕达哥拉斯模糊环境下的测量函数,用于比较两个犹豫毕达哥拉斯模糊数的大小,其次计算每个备选方案相对其它备选方案的相对优势度,然后根据相对优势度选出最佳方案。最后,用航空公司服务质量的评估来说明本文给出方法的可行性和有效性。     

An improved method for ranking alternatives in multiple criteria decision analysis

Scoring rules are an important disputable subject in data envelopment analysis (DEA). Various organizations use voting systems whose main object is to rank alternatives. In these methods, the ranks of alternatives are obtained by their associated weights. The method for determining the ranks of alternatives by their weights is an important issue. This problem has been the subject at hand of some authors. We suggest a three-stage method for the ranking of alternatives. In the first stage, the rank position of each alternative is computed based on the best and worst weights in the optimistic and pessimistic cases, respectively. The vector of weights obtained in the first stage is not a singleton. Hence, to deal with this problem, a secondary goal is used in the second stage. In the third stage of our method, the ranks of the alternatives approach the optimistic or pessimistic case. It is mentionable that the model proposed in the third stage is a multi-criteria decision making (MCDM) model and there are several methods for solving it; we use the weighted sum method in this paper. The model is solved by mixed integer programming. Also, we obtain an interval for the rank of each alternative. We present two models on the basis of the average of ranks in the optimistic and pessimistic cases. The aim of these models is to compute the rank by common weights.