Divergence Behaviour of the Successive Geometric Mean Method of Pairwise Comparison Matrix Generation for a Multiple Stage, Multiple Objective Optimization Problem

2013 ◽  
Vol 21 (3-4) ◽  
pp. 197-208
Author(s):  
Prashant K. Tarun ◽  
Victoria C. P. Chen ◽  
H. W. Corley
Keyword(s):  
Optimization Problem ◽  
Geometric Mean ◽  
Pairwise Comparison ◽  
Multiple Objective ◽  
Multiple Objective Optimization ◽  
Pairwise Comparison Matrix ◽  
Comparison Matrix

ENHANCED INTERACTIVE SATISFYING OPTIMIZATION APPROACH TO MULTIPLE OBJECTIVE OPTIMIZATION WITH PREEMPTIVE PRIORITIES

2006 ◽  
Vol 05 (01) ◽  
pp. 47-63 ◽  
Author(s):  
CHAOFANG HU ◽  
SHAOYUAN LI
Keyword(s):  
Optimization Problem ◽  
Optimization Method ◽  
Previous Method ◽  
Optimization Models ◽  
Multiple Objective ◽  
Multiple Objective Optimization ◽  
Optimization Approach ◽  
Fuzzy Relations ◽  
Objective Functions ◽  
Preemptive Priority

This paper proposes an enhanced interactive satisfying optimization method based on goal programming for the multiple objective optimization problem with preemptive priorities. Based on the previous method, the approach presented makes the higher priority achieve the higher satisfying degree. For three fuzzy relations of the objective functions, the corresponding optimization models are proposed. Not only can satisfying results for all the objectives be acquired, but the preemptive priority requirement can also be simultaneously actualized. The balance between optimization and priorities is realized. We demonstrate the power of this proposed method by illustrative examples.

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.

INTERACTIVE ROBUST CONE CONTRACTION METHOD FOR MULTIPLE OBJECTIVE OPTIMIZATION PROBLEMS

2012 ◽  
Vol 11 (02) ◽  
pp. 327-357 ◽  
Author(s):  
MIŁOSZ KADZIŃSKI ◽  
ROMAN SŁOWIŃSKI
Keyword(s):  
Optimization Problems ◽  
Pairwise Comparison ◽  
Multiple Objective ◽  
Multiple Objective Optimization ◽  
Nondominated Solutions ◽  
Nondominated Points ◽  
Current Sample ◽  
Evaluation Space ◽  
Problem Setting ◽  
A Current

We introduce a new interactive procedure for multiple objective optimization problems. The identification of the most preferred solution is achieved by means of a systematic dialogue with the decision maker (DM) during which (s)he specifies pairwise comparisons of nondominated solutions from a current sample. We represent this preference information by a compatible form of the achievement scalarizing function, i.e., we are searching for weights of objectives which ensure that the reference solutions are compared by the function in the same way as by the DM. Directions of the isoquants of all compatible achievement scalarizing functions create a cone in the evaluation space, with the origin in a reference point. In successive iterations, each new pairwise comparison of solutions contracts the cone which is zooming on a subregion of nondominated points of greatest interest for the DM. The procedure ends when at least one satisfactory solution is selected or when the DM comes to conclusion that there is no such solution for the current problem setting.

Sign in / Sign up

Export Citation Format

Share Document