Using the fuzzy majority approach for GIS-based multicriteria group decision-making

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Abstract

This paper is concerned with developing a framework for GIS-based multicriteria group decision-making using the fuzzy majority approach. The procedure for solving a spatial group decision-making problem involves two stages. First, each decision-maker solves the problem individually. Second, the individual solutions are aggregated to obtain a group solution. The first stage is operationalized by a linguistic quantifier-guided ordered weighted averaging (OWA) procedure to create individual decision-maker’s solution maps. Then the individual maps are combined using the fuzzy majority procedure to generate the group solution map which synthesizes the majority of the decision-makers’ preferences. The paper provides an illustrative example of the fuzzy majority method for a land suitability problem. It also demonstrates the implementation of the framework within the ArcGIS environment.

Introduction

GIS-based multicriteria decision analysis (GIS–MCDA) can be defined as a process that transforms and combines geographical data (map criteria) and value judgments (decision-makers’ preferences and uncertainties) to obtain appropriate and useful information for decision-making. The chief rationale behind integrating GIS and MCDA is that these two distinct areas of research can complement each other. While GIS is commonly recognized as a powerful and integrated tool with unique capabilities for storing, manipulating, analyzing and visualizing spatial data for decision-making, MCDA provides a rich collection of procedures and algorithms for structuring decision problems, designing, evaluating and prioritizing alternative decisions. It is in the context of the synergetic capabilities of GIS and MCDA that one can observe the benefits for advancing theoretical and applied research on the integration of GIS and MCDA (Malczewski, 1999, Malczewski, 2006a).

It has been argued that the GIS–MCDA systems can potentially enhance group decision-making processes by providing a flexible problem-solving framework where participants can explore, understand and redefine a decision problem (Feick and Hall, 1999; Jankowski and Nyerges, 2001a; Kyem, 2004, Malczewski, 2006a, Malczewski et al., 2006b). The GIS–MCDA methods provide a framework which can handle different views on the identification of the elements of a complex decision problem, organize the elements into a hierarchical structure, and study the relationships among components of the problem. In this setting, GIS–MCDA for group decision-making takes the format of aggregating individual judgments into a group preference in a way whereby the best compromise (the preferred alternative) can be identified (Malczewski, 2006a, Malczewski et al., 2006b).

Although the GIS–MCDA approaches have traditionally focused on the MCDA algorithms for individual decision-making, significant efforts have recently been made to integrate MCDA with GIS for group decision-making settings (Malczewski, 1996; Jankowski et al., 1997; Nyerges et al., 1997; Bennett et al., 1999; Feick and Hall, 1999; Jankowski and Nyerges, 2001a, Jankowski and Nyerges, 2001b; Kyem, 2004). In a survey of GIS–MCDA systems for collaborative decision-making, Malczewski (2006b) noted that the voting methods (social choice functions) are the most popular approach for generating a group solution in a GIS-based multicriteria group decision-making.

The voting schemes are rank-order methods (Hwang and Lin, 1987). They involve two steps: (i) the individual judgments are converted into a ranking of the alternatives (conversion from ratio scale to ordinal scale), and (ii) the individual rankings are combined into a group ranking or group solution. Therefore, each decision-maker can generate a solution map using an MCDA decision rule, at which point the solution maps can be translated into maps of ranked alternatives that can be aggregated using a voting method to generate the solution map of the group preference (e.g., Malczewski, 1996; Jankowski et al., 1997; Feick and Hall, 1999, Feick and Hall, 2004; Jankowski and Nyerges, 2001b).

The conversion of the individual preferences from ratio to ordinal scale simplifies the multicriteria decision modeling, which in turn may result in the trivialization of the decision-making process and increase the possibility of overlooking essential information about the decision-making process (Carver, 1999). Moreover, voting systems are subject to a number of conceptual and theoretical difficulties such as intransitivity as well as Arrow's impossibility theorem (Arrow, 1951; Hwang and Lin, 1987; Malczewski, 1999, Malczewski et al., 2006b). The intransitivity problem can be avoided if alternatives are not compared simultaneously but rather one-by-one and sequentially, though it can be demonstrated that the order of comparison has a direct effect on the ranking of the alternatives (Hwang and Lin, 1987). Arrow (1951) demonstrated in his impossibility theorem that there is no acceptable mechanism for aggregating ordinal preferences that would conform to social choice axioms. Given the limitations of the voting systems, some researchers suggest that these methods should be used as techniques for facilitating discussion rather than as a prescriptive measure (e.g., Meeks and Dasgupta, 2004; Rosmuller and Beroggi, 2004).

Pasi and Yager (2006) proposed a fuzzy majority approach to model the concept of majority opinion in group decision-making problems. Using a linguistic quantifier, the fuzzy majority concept can generate a group solution that corresponds to the majority of the decision-makers’ preferences. The linguistic quantifier guides the aggregation process of the individual judgments in such a way that there would be no need for rankings of the alternatives of individual solutions. Accordingly, the approach addresses the abovementioned difficulties encountered by the voting schemes in relation to the combination process. However, there still has been no implementation of the fuzzy majority approach for spatial group decision-making in GIS solutions.

There are two objectives of this paper: (1) to propose a new methodology by adapting the fuzzy majority approach for GIS-based multicriteria group decision-making when the decision-makers express their preferences using linguistic terms, and (2) to demonstrate an implementation of the fuzzy majority as an extension in ArcGIS environment. The remainder of this paper is organized as follows. Section 2 defines the structure of a GIS-based group decision-making problem. Section 3 provides an introduction to fuzzy criterion weighting where the decision-makers express their judgments about the importances of the criteria using linguistic labels. Section 4 offers a procedure for generating individual preferences: we use quantifier-guided ordered weighted averaging (OWA) procedure to create individual decision-maker's maps. Section 5 presents the fuzzy majority approach for aggregating the individual solution maps in the spatial group decision-making situation. Section 6 provides an illustrative example of the fuzzy majority approach using a hypothetical spatial multicriteria group decision-making problem. In Section 7, we demonstrate the implementation of the fuzzy majority approach in ArcGIS 9.2 environment. The last section provides concluding remarks.

Section snippets

Structure

The GIS-based multicriteria group decision-making procedure involves a set of geographically defined alternatives (e.g., land parcels), a set of evaluation criteria on the basis of which the alternatives are evaluated, and a group of decision-makers (e.g., planners, experts, stakeholders). In GIS–MCDA problems, an alternative is represented as a cell (raster) or as a polygon, a line or a point (vector GIS). An alternative is denoted by Ai for i=1, 2, …, m. The alternatives are to be evaluated with

Fuzzy criterion weighting

Spatial decision-making problems typically involve criteria that vary in significance to decision-makers. In light of this, the information regarding the importance of the criteria should be gathered in criterion weighting procedure. The purpose of criterion weighting is to assign a weight that indicates the importance of each criterion relative to the other criteria under consideration. In a group decision-making setting, the set of weights can be defined as W=[w1, w2, …, wn], wj∈[0, 1] and j=1nwj

MCDA decision rule

Central to GIS–MCDA is the concept of decision rules or evaluation algorithms. A decision (or combination) rule can be defined as a procedure that enables the decision-maker to order and select one or more alternatives from a set of available alternatives (see Starr and Zeleny, 1977; Malczewski, 1999). Over the last 20 years or so there have been a number of multicriteria decision rules implemented in the GIS environment including the weighted linear combination (WLC) or weighted

Collective choice rule

Collective choice rules are functions which aggregate individual solutions or preferences into a group solution. In spatial multicriteria group decision-making, these aggregations can be defined as function F:(SM1, SM2, SMq)→SMG. This function associates the preference profiles (set of solution maps) to the group solution, SMG, in such a way that there is one and only one group solution relation for a set of preference profiles (Hwang and Lin, 1987; Malczewski, 1996; Jankowski et al., 1997; Feick

Illustrative example

To illustrate the fuzzy majority approach using IOWA for spatial group decision-making, we consider a hypothetical land suitability problem. The problem involves a group of six decision-makers (e.g., planners, developers) who are evaluating five land parcels (alternatives) for housing development on the basis of a set of five criteria. The evaluation criteria include: (i) price, (ii) slope, (iii) view, (iv) impact on the environment, and (v) distance to wetlands. Fig. 6 shows the standardized

Implementing fuzzy majority approach for group decision-making in ArcGIS

The fuzzy majority approach has been implemented within ArcGIS 9.2 as ‘MultiCriteria Group Analyst’ extension.2 ArcGIS extensions are typically a grouped package of associated GIS functions which perform specific tasks. Extensions are components that implement the IExtension and IExtensionConfig interface of Arcobjects in ArcGIS development platform.3

Conclusion

In this paper, we have presented the fuzzy majority approach using IOWA procedure for GIS-based multicriteria decision-making and its implementation in the ArcGIS environment. The implementation of the fuzzy majority in ArcGIS extends the existing GIS–MCDA modules by offering the capabilities for analyzing group decision-making. It also addresses the concerns surrounding voting methods that have often been used in GIS environments for spatial group decision analysis. We have argued that owing

Acknowledgment

This research was supported by the GEOIDE Network (Project: HSS-DSS-17) of the Canadian Network of Centers of Excellence. The authors would like to thank anonymous reviewers for their constructive comments on an earlier version of this paper.

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