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.     

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.     

Phased multicriteria preference finding

This paper considers the implications of a tendency of multicriteria decision-makers to use screening, ordering and choosing phases to find a preference as they reduce the set of their candidate alternatives. This corresponds with increasing levels of effort and willingness to use sophisticated cognitive processes. It suggests that appropriate corresponding types of measurement are those using attributes, utilities and relative scores of alternatives, for which standard methods are SMART, MAUT and AHP. Theory on the decision processes of the mind is incorporated, which shows how to structure criteria trees and that relatively measured weights and scores should be synthesised using a power function. Tests of revised utility and relative MCDM methods and of software incorporating these ideas are reviewed. They facilitate interactive refinement of scores at all points of the criteria tree and easy reduction in the number of alternatives. Two alternative screening phases are considered, one based on scoring all the attributes together, the other scoring the attributes in clusters in the structured criteria tree. Empirical tests confirm the value of the three phase approach, but leave slightly open the question about which type of first phase is preferable.     

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.     

Extensions of the multicriteria analysis with pairwise comparison under a fuzzy environment

Multicriteria decision-making (MCDM) problems often involve a complex decision process in which multiple requirements and fuzzy conditions have to be taken into consideration simultaneously. The existing approaches for solving this problem in a fuzzy environment are complex. Combining the concepts of grey relation and pairwise comparison, a new fuzzy MCDM method is proposed. First, the fuzzy analytic hierarchy process (AHP) is used to construct fuzzy weights of all criteria. Then, linguistic terms characterized by L–R triangular fuzzy numbers are used to denote the evaluation values of all alternatives versus subjective and objective criteria. Finally, the aggregation fuzzy assessments of different alternatives are ranked to determine the best selection. Furthermore, this paper uses a numerical example of location selection to demonstrate the applicability of the proposed method. The study results show that this method is an effective means for tackling MCDM problems in a fuzzy environment.     

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.     

Some issues in mathematical modelling of multiple criteria decision-making problems

Models for analyzing and solving multiple criteria decision-making (MCDM) problems are difficult to evaluate and compare, because they are intended for diverse orderings of a set of feasible alternatives. These models are based on a variety of assumptions about the decision maker's preferences and use different types of preference information. In this paper, a conceptual framework is developed for evaluating and comparing discrete alternative MCDM models available for a given decision situation. The procedure employed in the framework guides the user through an analysis of the decision situation making it possible for a decision maker or analyst to select the most appropriate MCDM model from among several alternative feasible models.     

Using DEA as a tool for MCDM: some remarks

The purpose of this paper is to study proposals to use Data Envelopment Analysis (DEA) as a tool for Multiple Criteria Decision Making (MCDM). We first recall, using a simple model, the equivalence between the concept of ‘efficiency’ in DEA and that of ‘convex efficiency’ in MCDM. Examples are then used to show that various techniques that have been proposed in the DEA literature to deal with MCDM problems violate simple normative properties that are commonly accepted. We conclude with some remarks on the possible areas of interaction between DEA and MCDM.     

The aspiration level interactive method (AIM) reconsidered: Robustness of solutions

In this paper we explore theory and practice for the aspiration-level interactive model (AIM), a useful decision tool that takes advantage of the concepts of satisficing as well as other concepts of multiple criteria decision making (MCDM). We examine the relationship between aspiration levels and their mapped-to solutions in the MCDM context using AIM.We extend the concept of robustness in decision making, by defining a solution to be robust if many (suitably defined) aspiration levels map to it. We use simulation to help explore robustness, by generating three groups of random test problems. Each problem has twenty alternatives. For each group of problems, the top 5 (most-mapped-to) alternatives out of 20 are mapped to by at least 50% of the aspiration levels. We also relate the concept of robustness in decision making to the ideas of simply ranking alternatives using equal weights. There is a strong correlation between the robustness ranking and the equal-weights ranking. Based on our analyses, we then randomly generate additional problems to explore certain other factors. We also discuss practical aspects of robustness.     

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.     

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.     

Some Theory and an Approach to Solving Sequential Multiple-Criteria Decision Problems

This paper examines a sequential multiple-criteria decision problem. The problem arises when a decision-maker is unable to consider all possible decision alternatives simultaneously. The decision-maker evaluates only a subset of all decision alternatives, from which he chooses the most preferred solution. Obviously, this solution is not necessarily ‘globally’ best. An interesting question is: how good is the most preferred solution and what are the chances of finding a better solution by considering additional alternatives? A unified approach to solving this problem based on probability theory is presented and illustrated with numerical examples.     

Integrating expert weighting and multi-criteria decision making into eco-efficiency analysis: the case of US manufacturing

In this paper, the effect of weighting strategies on sustainability performance assessment is addressed. Eco-efficiency is used as the main metric for sustainability performance evaluation. An integrated input-output life cycle assessment (LCA) and multi criteria decision making (MCDM) approach is employed. The US manufacturing sectors’ LCA results are used in conjunction with the proposed MCDM framework to perform the eco-efficiency evaluation of 276 US manufacturing sectors. Five environmental impact categories are considered as the negative factors, namely: greenhouse gas emissions, energy use, water withdrawal, hazardous waste generation and toxic releases into air and the economic output of each manufacturing sector is considered to be the positive output. To study the overall impact of different weighting strategies; twenty weighting scenarios are designed. Five pairs of weights considered for the overall economic versus environmental impacts along with four specific weighting strategies based on Harvard, SAB, EPP and Equal weighting for each pair. According to the results of the statistical analysis, it is concluded that the weighing strategies applied to the overall environmental impacts and economic outputs cause statistically significant differences in the eco-efficiency scores.     

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.     

Extended VIKOR method in comparison with outranking methods

The VIKOR method was developed to solve MCDM problems with conflicting and noncommensurable (different units) criteria, assuming that compromising is acceptable for conflict resolution, the decision maker wants a solution that is the closest to the ideal, and the alternatives are evaluated according to all established criteria. This method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria, and on proposing compromise solution (one or more). The VIKOR method is extended with a stability analysis determining the weight stability intervals and with trade-offs analysis. The extended VIKOR method is compared with three multicriteria decision making methods: TOPSIS, PROMETHEE, and ELECTRE. A numerical example illustrates an application of the VIKOR method, and the results by all four considered methods are compared.     

Classifying efficient alternatives in SMAA using cross confidence factors

Stochastic multicriteria acceptability analysis (SMAA) is a family of methods for aiding multicriteria group decision making. These methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one. The main results of the analysis are rank acceptability indices, central weight vectors and confidence factors for different alternatives. The rank acceptability indices describe the variety of different preferences resulting in a certain rank for an alternative; the central weight vectors represent the typical preferences favouring each alternative; and the confidence factors measure whether the criteria data are sufficiently accurate for making an informed decision.In some cases, when the problem involves a large number of efficient alternatives, the analysis may fail to discriminate between them. This situation is revealed by low confidence factors. In this paper we develop cross confidence factors, which are based on computing confidence factors for alternatives using each other’s central weight vectors. The cross confidence factors can be used for classifying efficient alternatives into sets of similar and competing alternatives. These sets are related to the concept of reference sets in Data Envelopment Analysis (DEA), but generalized for stochastic models. Forming these sets is useful when trying to identify one or more most preferred alternatives, or suitable compromise alternatives. The reference sets can also be used for evaluating whether criteria need to be measured more accurately, and at which alternatives the measurements should be focused. This may cause considerable savings in measurement costs. We demonstrate the use of the cross confidence factors and reference sets using a real-life example.     

A method for stochastic multiple criteria decision making based on pairwise comparisons of alternatives with random evaluations

This paper proposes a method for solving stochastic multiple criteria decision making (MCDM) problems, where evaluations of alternatives on considered criteria are random variables with known probability density functions or probability mass functions. Probabilities on all possible results of pairwise comparisons of alternatives are first calculated using Probability Theory. Then, all possible results of pairwise comparisons are classified into superior, indifferent and inferior ones using a predefined identification rule. Consequently, the probabilities on all possible results of pairwise comparisons are partitioned into superior, indifferent and inferior probabilities. Furthermore, based on the derived probabilities, an algorithm is developed to rank the alternatives. Finally, a numerical example is used to illustrate the feasibility and validity of the proposed method.     

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.     

Learning multicriteria classification models from examples: Decision rules in continuous space

The classification problem statement of multicriteria decision analysis is to model the classification of the alternatives/actions according to the decision maker's preferences. These models are based on outranking relations, utility functions or (linear) discriminant functions. Model parameters can be given explicitly or learnt from a preclassified set of alternatives/actions.In this paper we propose a novel approach, the Continuous Decision (CD) method, to learn parameters of a discriminant function, and we also introduce its extension, the Continuous Decision Tree (CDT) method, which describes the classification more accurately.The proposed methods are results of integration of Machine Learning methods in Decision Analysis. From a Machine Learning point of view, the CDT method can be considered as an extension of the C4.5 decision tree building algorithm that handles only numeric criteria but applies more complex tests in the inner nodes of the tree. For the sake of easier interpretation, the decision trees are transformed to rules.     

Multiobjective Q-analysis with concordance and discordance concepts

A multicriterion decision-making (MCDM) technique with possibly nonnumerical criteria, called Multicriteria Q-Analysis I (MCQA-I), developed earlier on the basis of only a concordance analysis, is extended to include a measure of discordance. This new version, labeled MCQA-II, reduces an MCDM problem to the tradeoff between three conflicting indices calculated for each project or alternative. The indices are respectively a value or utility-type index PSI, and two outranking-type indices PCI and PDI. The example of selecting a project to alleviate pollution problems in the lower San Francisco Bay area illustrates the application of both versions of MCQA. A sensitivity analysis performed on the slicing-level set tends to show that MCQA-II leads to a more stable ranking than MCQA-I; in either case, application of the technique leads to selection of the project preferred in practice.