Aggregation of Priorities in Multi-Criteria Decision Analysis (MCDA): Connecting Decision Spaces in the Cognitive Space

Abstract

In Multi-Criteria Decision Analysis, the well-known weighted sum method for aggregating normalised relative priorities ignores the unit of scale that may vary across the criteria and thus causes rank reversals. A new aggregation rule that explicitly includes the norms of priority vectors is derived and shown as a remedy for it. An algorithmic procedure is presented to demonstrate how it can as well be used in the Analytic Hierarchy Process when norms of priority vectors are not readily available. Also, recursion relations connecting two decision spaces with added or deleted alternatives give an opportunity to extend the idea of connectivity to a new concept of cognitive space. Expanded analytic modelling embracing multiple decision spaces or scenarios may assist in detecting deficiencies in analytic models and also grasping the big picture in decision making.

An Overview of Multi-Criteria Decision Analysis and the Applications of AHP and TOPSIS Methods

“…This can be done by either adding the weights of criteria and then performing normalization to obtain the weight vector and hence final rankings of alternatives or as done in AHP, normalization is performed on the decision matrix of scores, and then the weighted sum value of criteria is taken to obtain weight vector. This method used in AHP causes rank reversal as it ignores the fact that the unit of scale used for the normalization of weights between specified intervals may differ for different criteria (Zahir, 2016).…”

Penilaian Penentuan Karyawan Terbaik Menggunakan Metode Simple Additive Weighting

“…Konsep dasar metode ini dengan mencari penjumlahan terbobot dari rating kinerja pada setiap alternatif pada semua kriteria [4], [6]. Langkahlangkah yang perlu dilakukan dengan menggunakan metode SAW ditunjukkan pada Gambar 1 [7], [8]. Gambar 1 menjelaskan bahwa proses penentuan bobot kriteria (W) dan penentuan alternatif (A i ) merupakan proses yang tidak saling mempengaruhi dan dapat dilakukan secara bersamaan.…”