Non-uniqueness of Interval Weight Vector to Consistent Interval Pairwise Comparison Matrix and Logarithmic Estimation Methods

2016 ◽  
pp. 39-50 ◽  
Author(s):  
Masahiro Inuiguchi
Keyword(s):  
Pairwise Comparison ◽  
Weight Vector ◽  
Estimation Methods ◽  
Pairwise Comparison Matrix ◽  
Comparison Matrix ◽  
Interval Weight

Improving Interval Weight Estimations in Interval AHP by Relaxations

2017 ◽  
Vol 21 (7) ◽  
pp. 1135-1143 ◽  
Author(s):  
Masahiro Inuiguchi ◽  
◽  
Shigeaki Innan
Keyword(s):  
Objective Function ◽  
Conventional Method ◽  
Numerical Experiments ◽  
Pairwise Comparison ◽  
Estimation Methods ◽  
Pairwise Comparison Matrix ◽  
Comparison Matrix ◽  
The Third ◽  
Interval Weight

From the viewpoint that the vagueness of a decision maker’s evaluation causes inconsistencies in a pairwise comparison matrix, interval weights have been estimated using the interval AHP. However, the estimated interval weights are often insufficient to express the vagueness of the decision maker’s evaluation. We propose three modified estimation methods for interval weights. The first is based on a relaxation of the optimality of estimated interval weights in the conventional method. The second employs a modified objective function and the third is based on a relaxation of the optimality with respect to the modified objective function. Two of the proposed methods include parameters with degrees of relaxation. Through numerical experiments with 100,000 pairwise comparison matrices generated from 100 true interval weight vectors, we demonstrate the advantages of the proposed methods over the conventional method, and determine the best method and the suitable degree of relaxation.

scholarly journals Two Approximation Models of Fuzzy Weight Vector from a Comparison Matrix

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Tomoe Entani
Keyword(s):  
Analytic Hierarchy Process ◽  
Weight Vector ◽  
Analytic Hierarchy ◽  
Lower Approximation ◽  
Comparison Matrix ◽  
Fuzzy Weight ◽  
Interval Weight ◽  
Hierarchy Process ◽  
Interval Comparison ◽  
Approximation Models

In this study, our uncertain judgment on multiple items is denoted as a fuzzy weight vector. Its membership function is estimated from more than one interval weight vector. The interval weight vector is obtained from a crisp/interval comparison matrix by Interval Analytic Hierarchy Process (AHP). We redefine it as a closure of the crisp weight vectors which approximate the comparison matrix. The intuitively given comparison matrix is often imperfect so that there could be various approaches to approximate it. We propose two of them: upper and lower approximation models. The former is based on weight possibility and the weight vector with it includes the comparison matrix. The latter is based on comparison possibility and the comparison matrix with it includes the weight vector.

A Linear Goal Programming Model for Weight Calculation in Fuzzy AHP and its Application in Product Development

2010 ◽  
Vol 118-120 ◽  
pp. 712-716 ◽  
Author(s):  
Li Jun Yan ◽  
Zong Bin Li ◽  
Xiao Chun Yang
Keyword(s):  
Product Development ◽  
Goal Programming ◽  
Programming Model ◽  
Pairwise Comparison ◽  
Analysis Method ◽  
Pairwise Comparison Matrix ◽  
Wrong Decision ◽  
Comparison Matrix ◽  
Linear Goal Programming ◽  
Goal Programming Model

The key issue of FAHP application is how to derive fuzzy weights from fuzzy pairwise comparison matrix. The most of applications, however, were founding avoiding the use of sophisticated approaches such as fuzzy least squares method and using a simple extent analysis method to derive fuzzy weight from pairwise comparison matrix for the sake of simplicity. But the extent analysis method proves to be incorrect and may lead to a wrong decision result. So, this paper proposes a sound yet simple linear goal programming model to derive weights from pairwise fuzzy comparison matrix, which takes minimizing inconsistence degree of comparison matrix as objective and obtain a normalized weight vector finally. The proposed model is validated by an application to new product development scheme screening decision making.

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