Notes on the existence of solutions in the pairwise comparisons method using the Heuristic Rating Estimation approach

Pairwise comparisons are a well-known method for modelling of the subjective preferences of a decision maker. A popular implementation of the method is based on solving an eigenvalue problem for M - the matrix of pairwise comparisons. This does not take into account the actual values of preference. The Heuristic Rating Estimation (HRE) approach is a modification of this method in which allows modelling of the reference values. To determine the relative order of preferences is to solve a certain linear equation system defined by the matrix A and the constant term vector b (both derived from M). The article explores the properties of these equation systems. In particular, it is proven that for some small data inconsistency the A matrix is an M-matrix, hence the equation proposed by the HRE approach has a unique strictly positive solution.Comment: 8 page

On Axiomatization of Inconsistency Indicators for Pairwise Comparisons

We examine the notion of inconsistency in pairwise comparisons and propose an axiomatization which is independent of any method of approximation or the inconsistency indicator definition (e.g., Analytic Hierarchy Process, AHP). It has been proven that the eigenvalue-based inconsistency (proposed as a part of AHP) is incorrect.Comment: Enhanced text, with 21 pages and 3 figures, proves that arbitrarily inaccurate pairwise matrices are considered acceptable by theories with a inconsistency based on the principal eigenvalue (e.g., AHP). CPC (corner pairwise comparisons) matrix is the crucial part of this study as it invalidates any eigenvalue-based inconsistency. All comments are highly appreciate

Application of the Analytic Hierarchy Process (AHP) for Prioritize of Concrete Pavement

The analytic hierarchy process AHP is a structured technique for dealing with complex decisions that was developed by Thomas L Saaty in the 1980 year It provides a comprehensive and rational framework for structuring a decision problem for representing and quantifying its elements for relating those elements to overall goals and for evaluating alternative solutions The base of this model is comparing variables by pair wise by Matrix relationship In this way pair wise of the effective variables on the concrete Pavement were considered and based on relative weights the output was exten

Using multiple criteria decision making models for ranking customers of bank network based on loyalty properties in weighted RFM model

One of the most basic requirements of financial institutes, governmental and private banks in the present age is to have a good understanding on customers' behaviors of bank network. It helps banks determine customer loyalty, which yields profit making for bank. On the other hand, it is important to know about credit risk of customers with the goal of decreasing loss and better allocation of bank resources to applicants of receiving loan. According to nature of customer loyalty discussion and credit risk, these two issues are separately studied. The present article deals with studying customer loyalty and prioritizing based one private bank in Kurdistan province. The proposed model of this paper studies customer loyalty by using Recency Frequency Monetary (RFM) factor for prioritizing customer based on loyalty properties and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). In addition, in order to calculate the relative importance coefficient or weight of loyalty properties in RFM method, the pair wise comparison matrix based on analytical hierarchy process (AHP) is used. Results show that in the present study, necessarily customers having higher average monetary value during a specified time period does not have much higher priority compared with other customers