Group aggregation of pairwise comparisons using multi-objective optimization

AbstractIn group decision making, multiple decision makers (DMs) aim to reach a consensus ranking of alternatives in a decision problem. The differing expertise, experience and, potentially conflicting, interests of the DMs will result in the need for some form of conciliation to achieve consensus. Pairwise comparisons are commonly used to elicit values of preference of a DM. The aggregation of the preferences of multiple DMs must additionally consider potential conflict between DMs and how these conflicts may result in a need for compromise to reach group consensus.We present an approach to aggregating the preferences of multiple DMs, utilizing multi-objective optimization, to derive and highlight underlying conflict between the DMs when seeking to achieve consensus. Extracting knowledge of conflict facilitates both traceability and transparency of the trade-offs involved when reaching a group consensus.Further, the approach incorporates inconsistency reduction during the aggregation process to seek to diminish adverse effects upon decision outcomes. The approach can determine a single final solution based on either global compromise information or through utilizing weights of importance of the DMs.Within multi-criteria decision making, we present a case study within the Analytical Hierarchy Process from which we derive a richer final ranking of the decision alternatives

A Fuzzy Group Prioritization Method for Deriving Weights and its Software Implementation

Several Multi-Criteria Decision Making (MCDM) methods involve pairwise comparisons to obtain the preferences of decision makers (DMs). This paper proposes a fuzzy group prioritization method for deriving group priorities/weights from fuzzy pairwise comparison matrices. The proposed method extends the Fuzzy Preferences Programming Method (FPP) by considering the different importance weights of multiple DMs . The elements of the group pairwise comparison matrices are presented as fuzzy numbers rather than exact numerical values, in order to model the uncertainty and imprecision in the DMs’ judgments. Unlike the known fuzzy prioritization techniques, the proposed method is able to derive crisp weights from incomplete and fuzzy set of comparison judgments and does not require additional aggregation procedures. A prototype of a decision tool is developed to assist DMs to implement the proposed method for solving fuzzy group prioritization problems in MATLAB. Detailed numerical examples are used to illustrate the proposed approach

Rural Telecommunications Infrastructure Selection Using the Analytic Network Process, Journal of Telecommunications and Information Technology, 2010, nr 2

The decisions involved in rural settings are of complex nature, with some aspects compounded by the presence of intangible criteria. Hence, a suitable approach is needed that can produce effective solutions. This paper describes the applicability of a multicriteria decision-making method, specifically the analytic network process (ANP), to model the selection of an appropriate telecommunications infrastructure technology, capable of deploying e-services in rural areas of developing countries. It aims to raise awareness among telecommunication planners about the availability of ANP, and to demonstrate its suitability to enhance the selection process. The proposed model is constructed based on concerned experts’ views of relevant selection criteria and potential technology alternatives. Its network structure caters for all possible dependencies and interactions among criteria and alternatives

Important Facts and Observations about Pairwise Comparisons

This study has been inspired by numerous requests from researcherswho often confuse Saaty's AHP with the Pairwise Comparisons (PC)method, taking AHP as the only representation of PC. Most formal results of this survey article are based on a recently published work byauthors. This article should be regarded as an interpretation and clarication of future theoretical investigations of PC.In addition, this article presents a general PC research at ahigher level of abstraction: the philosophy of science. It delves intothe foundations and implications of pairwise comparisons. Finally,open problems have also been reported for future research

Evaluation of Services Using a Fuzzy Analytic Hierarchy Process

This paper proposes a new approach for tackling the uncertainty and imprecision of the service evaluation process. Identifying suitable service offers, evaluating the offers and choosing the best alternatives are activities that set the scene for the consequent stages in negotiations and influence in a unique manner the following deliberations. The pre-negotiation problem in negotiations over services is regarded as decision-making under uncertainty, based on multiple criteria of quantitative and qualitative nature, where the imprecise decision-maker’s judgements are represented as fuzzy numbers. A new fuzzy modification of the analytic hierarchy process is applied as an evaluation technique. The proposed fuzzy prioritisation method uses fuzzy pairwise comparison judgements rather than exact numerical values of the comparison ratios and transforms the initial fuzzy prioritisation problem into a non-linear program. Unlike the known fuzzy prioritisation techniques, the proposed method derives crisp weights from consistent and inconsistent fuzzy comparison matrices, which eliminates the need of additional aggregation and ranking procedures. A detailed numerical example, illustrating the application of our approach to service evaluation is given

Reasoning Under Uncertainty During Pre-Negotiations Using Fuzzy AHP

uncertainty and imprecision of the reasoning process while using decision support tools during prenegotiations. The pre-negotiation problem is regarded as decision making under uncertainty, based on multiple criteria of quantitative and qualitative nature, where the imprecise decision-maker’s judgments are represented as fuzzy numbers. A new fuzzy modification of the Analytic Hierarchy Process is applied as an evaluation technique. The proposed fuzzy prioritization method uses fuzzy pairwise comparison judgments rather than exact numerical values of the comparison ratios and transforms the initial fuzzy prioritization problem into a non-linear program. Unlike the known fuzzy prioritization techniques, the proposed metod derives crisp weights from consistent and inconsistent fuzzy comparison matrices, which eliminates the need of additional aggregation and ranking procedures. A detailed numerical example, illustrating the application of the approach to services evaluation is given