A MIN–MAX GOAL PROGRAMMING APPROACH TO PRIORITY DERIVATION IN AHP WITH INTERVAL JUDGEMENTS

2008 ◽  
Vol 07 (01) ◽  
pp. 175-182 ◽  
Author(s):  
DIMITRIS K. DESPOTIS ◽  
DIMITRIS DERPANIS
Keyword(s):  
Goal Programming ◽  
Programming Model ◽  
Programming Approach ◽  
Programming Formulation ◽  
Analytic Hierarchy ◽  
Interval Numbers ◽  
Numerical Examples ◽  
Decision Elements ◽  
Hierarchy Process ◽  
Pair Wise Comparison

We deal with the problem of priority elicitation in the analytic hierarchy process (AHP) on the basis of imprecise pair-wise comparison judgements on decision elements. We propose a min–max goal programming formulation to derive the AHP priorities in the case that the decision maker provides preference judgements in the form of interval numbers. By applying variable transformations, we formulate a linear programming model that is capable of estimating the priorities from both consistent and inconsistent interval judgements. The proposed method is illustrated by numerical examples.

A multibelief analytic hierarchy process and nonlinear programming approach for diversifying product designs: Smart backpack design as an example

2020 ◽  
Vol 234 (6-7) ◽  
pp. 1044-1056 ◽  
Author(s):  
Yu-Cheng Lin ◽  
Toly Chen
Keyword(s):  
Nonlinear Programming ◽  
Analytic Hierarchy Process ◽  
Programming Model ◽  
Programming Approach ◽  
Analytic Hierarchy ◽  
Nonlinear Programming Model ◽  
Judgment Matrix ◽  
The Cost ◽  
Analytic Hierarchy Process Method ◽  
Hierarchy Process

Owing to the cost constraint, it is difficult to incorporate all critical features into a single product design. To deal with this issue, analytic hierarchy process is a well-known method that compares the relative priorities of critical features. This study aims to illustrate that the judgment of a designer can be used to generate multiple diversified product designs. To this end, this study proposed a multibelief analytic hierarchy process and nonlinear programming approach. In the proposed methodology, a decision maker’s judgment matrix is decomposed into several single-belief judgment matrices that are more consistent than the original judgment matrix and represent diversified points of view regarding the relative priorities of factors. To this end, a nonlinear programming model is established and optimized. The proposed methodology was applied to a smart backpack design problem. It was concluded that a designer’s judgment was often inconsistent, which was ignored in the conventional analytic hierarchy process method but could be employed to diversify product designs.

WEIGHTED PRIORITIZATION MODELS IN THE FUZZY ANALYTIC HIERARCHY PROCESS

2011 ◽  
Vol 10 (04) ◽  
pp. 681-694 ◽  
Author(s):  
LUDMIL MIKHAILOV ◽  
HOSEIN DIDEHKHANI ◽  
SOHEIL SADI-NEZHAD
Keyword(s):  
Analytic Hierarchy Process ◽  
Goal Programming ◽  
Programming Model ◽  
Fuzzy Analytic Hierarchy Process ◽  
Linear Programs ◽  
Analytic Hierarchy ◽  
Goal Programming Model ◽  
Ranking Of Alternatives ◽  
Fuzzy Goal ◽  
Hierarchy Process

The paper deals with the group prioritization problem in the fuzzy analytic hierarchy process. We extend the fuzzy preference programming method to fuzzy group prioritization by introducing important weights of decision-makers (DMs). The modified prioritization problem is represented as a weighted fuzzy goal programming model. Additionally, we represent the uncertain DMs' importance weights as fuzzy numbers and modify the goal programming model by a possibilistic approach. Both proposed models transform the initial prioritization problems with fuzzy or crisp important weights into equivalent crisp linear programs. Unlike the known fuzzy prioritization methods, the proposed approach does not require an additional defuzzification procedure for final ranking of alternatives and can deal with incomplete set of comparison judgments.

A GOAL PROGRAMMING APPROACH TO GROUP DECISION MAKING WITH INCOMPLETE FUZZY AND INTERVAL PREFERENCE RELATIONS

2012 ◽  
Vol 20 (03) ◽  
pp. 355-367
Author(s):  
JIANG JIANG ◽  
XUAN LI ◽  
YINGWU CHEN ◽  
DAWEI TANG
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Goal Programming ◽  
Group Decision ◽  
Programming Model ◽  
Decision Makers ◽  
Programming Approach ◽  
Interval Numbers ◽  
Preference Relations ◽  
Priority Vector

In order to solve group decision making (GDM) problems where the preference relations are provided by decision makers with incomplete fuzzy and interval numbers, this paper develops a GDM approach on the basis of multiple objective optimization and goal programming methods. The proposed approach first analyzes the two types of preference relations and then builds their respective optimization models. Subsequently, an integrated programming model combining the two preference relations is developed to minimize the inconsistency among the decision makers' opinions. By solving the programming model, the ranking of alternatives or selection of the most desirable alternative can be obtained using the intermediate priority vector. Two numerical examples including incomplete fuzzy and interval preference relations are examined to illustrate and show the applicability of the proposed approach.

The Application Effectiveness Evaluation of the Educational Equipment Based on AHP

2011 ◽  
Vol 341-342 ◽  
pp. 384-389 ◽  
Author(s):  
Sha Sha Dong ◽  
You Nong Hu
Keyword(s):  
Analytic Hierarchy Process ◽  
Effectiveness Evaluation ◽  
Analytic Hierarchy ◽  
Research Application ◽  
Weight Measurement ◽  
Relevant Field ◽  
Decision Elements ◽  
Hierarchy Process ◽  
Pair Wise Comparison

This paper uses the principle and theory of analytic hierarchy process (AHP) to research application effectiveness of educational equipment. Seven decision elements are got by experts of the relevant field and the weight measurement is calculated via pair-wise comparison of two decision elements based on Delphi. Then this paper uses AHP to evaluate the application effectiveness of educational equipment comprehensively, and gives out the best solution according to the three evaluation results.

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