Estimating fuzzy weight vector from interval pairwise comparison matrix with various processed matrices

2017 ◽  
Author(s):  
Tomoe Entani
Keyword(s):  
Pairwise Comparison ◽  
Weight Vector ◽  
Pairwise Comparison Matrix ◽  
Comparison Matrix ◽  
Fuzzy Weight

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.

Improved Consistency Ratio for Pairwise Comparison Matrix in Analytic Hierarchy Processes

2016 ◽  
Vol 33 (03) ◽  
pp. 1650020
Author(s):  
L. N. Pradeep Kumar Rallabandi ◽  
Ravindranath Vandrangi ◽  
Subba Rao Rachakonda
Keyword(s):  
Error Function ◽  
Pairwise Comparison ◽  
Large Set ◽  
Simulation Experiments ◽  
Analytic Hierarchy ◽  
Chi Square ◽  
Pairwise Comparison Matrix ◽  
Comparison Matrix ◽  
Hierarchy Process ◽  
Original Information

The analytical hierarchy process (AHP) uses pairwise comparison matrix (PCM) to rank a known set of alternatives. Sometimes the comparisons made by the experts may be inconsistent which results in incorrect weights and rankings for the AHP. In this paper, a method is proposed which identifies inconsistent elements in a PCM and revises them iteratively until the inconsistency is reduced to an acceptable level. An error function similar to chi-square is used to identify the inconsistent elements which are revised with suitable values. The method is illustrated with some numerical examples mentioned in the literature and a comparative study of the results in terms of deviation from the PCM and preservation of original information is taken up. Monte Carlo simulation experiments over a large set of random matrices indicate that the proposed method converges for the moderately inconsistent matrices.

scholarly journals Utilization of AHP-MAUT Method to Determine the Country of Exhibition Abroad in Batik Hatta Boutique

2021 ◽  
Vol 5 (02) ◽  
pp. 52-56
Author(s):  
Saifur Rohman Cholil ◽  
Tria Ardianita
Keyword(s):  
Decision Making ◽  
Rank Correlation ◽  
Pairwise Comparison ◽  
Hierarchical Level ◽  
Spearman Rank Correlation ◽  
Ahp Method ◽  
Pairwise Comparison Matrix ◽  
Spearman Rank ◽  
Comparison Matrix ◽  
A Value

This research was conducted with the aim of helping decide the destination country for overseas exhibitions at the Batik Hatta Boutique. By knowing all the data and information of a country, boutique owners can decide which country to visit in the batik exhibition. Because if you attend the cast in all countries, there will be overruns in costs. The methods used are AHP and MAUT. The AHP method is used as a weighting using a linguistic value scale. Weights are obtained from the pairwise comparison matrix between two elements of all elements that occur at the same hierarchical level. The MAUT method is used to determine the importance of each alternative for the ranking process. The results of this study indicate that Cambodia was chosen as the location to be visited for the batik exhibition. The results of the validation using the Spearman Rank correlation comparison obtained a value of 0.951 meaning that this method can be used as a decision making.

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