On consistency of the weighted arithmetical mean complex judgement matrix

The weighted arithmetical mean complex judgement matrix （WAMCJM） is the most common method for aggregating group opinions, but it has a shortcoming, namely the WAMCJM of the perfectly consistent judgement matrices given by experts canot guarantee its perfect consistency. An upper bound of the WAMCJM＇s consistency is presented. Simultaneously, a compatibility index of judging the aggregating extent of group opinions is also introduced. The WAMCJM is of acceptable consistency and is proved provided the compatibilities of all judgement matrices given by experts are smaller than the threshold value of acceptable consistency. These conclusions are important to group decision making.

A Comparison of Three Surrogacy Agreement Cases Using AHP

This paper builds on the previous work of Knott, Ninassi and Eisenhardt＇s 2009 paper, ＂Using the Analytic Hierarchy Process （AHP） to Look at the Tradeoffs Among Stakeholders in the Case of Surrogacy, when the Initial Intention of the Parties Involved Change After the Pregnancy Has Ensued＂. This paper proposes a new methodology for analyzing cases involving stakeholders in disputed surrogacy arrangement. The methodology utilized is the Analytic Hierarchy Process, which allows users to weigh different criteria based on their own opinions and background. Three case studies involved a surrogacy arrangement among three stakeholders： the biological mother, the biological father and the surrogate mother. The base for the model was that all parties had entered into an agreement, and that after the agreement had been made, a situation changed, such that a decision as to who had parental rights over the fetus became an issue. The criteria used in the decision making process in the three case studies were legal, health and ethical. The criteria differed based upon each stakeholder＇s point of view. In this paper, the three models were developed using the AI-tP methodology and judgments were gathered for each of the three cases to derive the priorities for the criteria in each model. Each author took the role of one of the three stakeholders.

The Generalized Mixed Least Square Methodsfor the Estimation of Weights in AHP

This paper proposes a class of generalized mixed least square methods(GMLSM) forthe estimation of weights in the analytic hierarchy process and studies their good properties such asinvariance under transpose, invariance under change of scale, and also gives a simple convergent iterativealgorithm and some numerical examples. The well-known eigenvector method(EM) is then compared.Theoretical analysis and the numerical results show that the iterative times of the GMLSM are generallyfewer than that of the MLSM, and the GMLSM are preferable to the EM in several important respects.

Research on Consistency of the Complex Interval Judgement Matrix in AHP

The weighted geometric mean method(WGMM) has been the most commonly used method in the analytic hierarchy process(AHP) for combining individual opinions to form a group opinion. In this paper, we study the consistency of the WGMM in group decision and prove that the weighted geometric mean complex interval judgement matrix (WGMIM) is of acceptable consistency under the condition that all interval matrices for the same decision\|making problem are of acceptable consistency. Thus, research on consistency of group decision in AHP is further developed and a theory basis for the application of the WGMM is also made.

On the Ordinal Consistency of a Judgement Matrix in AHP

We discuss the properties of an ordinal consistency matrix on the base of its directed graph, which benefit deriving the ranking of the compared alternatives.