The analytic hierarchy process, max algebra and multi-objective optimisation

Gursoy, Buket Benek; Mason, Oliver; Sergeev, Sergĕı

doi:10.1016/j.laa.2012.11.020

Cited by 21 publications

(28 citation statements)

References 29 publications

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“…The number of levels in the hierarchy depends on problem complexities which combine with the decision maker's model of the initial problem. AHP uses matrix algebra for classification the factors to arrive at a mathematically optimal solution [32]. The main difference between AHP and TOPSIS is in how the evaluation of criteria is done.…”

Section: Proposed Approachmentioning

confidence: 99%

A Fuzzy Decision Support Approach for Model-Based Tradeoff Analysis of Non-functional Requirements

Saadatmand

Tahvili

2015

2015 12th International Conference on Information Technology - New Generations

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One of the main challenges in addressing NonFunctional Requirements (NFRs) in designing systems is to take into account their interdependencies and mutual impacts. For this reason, they cannot be considered in isolation and a careful balance and tradeoff among them should be established. This makes it a difficult task to select design decisions and features that lead to the satisfaction of all different NFRs in the system, which becomes even more difficult when the complexity of a system grows. In this paper, we introduce an approach based on fuzzy logic and decision support systems that helps to identify different design alternatives that lead to higher overall satisfaction of NFRs in the system. This is achieved by constructing a model of the NFRs and then performing analysis on the model. To build the model, we use a modified version of the NFR UML profile which we have introduced in our previous works, and using model transformation techniques we automate the analysis of the model.

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Section: Proposed Approachmentioning

confidence: 99%

A Fuzzy Decision Support Approach for Model-Based Tradeoff Analysis of Non-functional Requirements

Saadatmand

Tahvili

2015

2015 12th International Conference on Information Technology - New Generations

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“…The 20 l/m 2 -h permeated flux is based on pilot plant best performance as indicated by the model (increasing the flux in the system may cause blocking and fouling problems) The comparative performance of configuration technologies by the various alternative methods is very complex and is highly depending on various site-specific operational and economic attributes. General attributes must be fulfilled by an objective function (Gursoy et al, 2013): (i) minimization of energy consumption; (ii) minimization of brine production; (iii) minimization of brine concentration; and (iv) minimization of membrane types and passes. In order to support adequate selection the decision-maker has to define a utility function (Z T ) (Equation 5) that takes in account all the previous attributes.…”

Section: Case Studiesmentioning

confidence: 99%

Brackish groundwater membrane system design for sustainable irrigation: optimal configuration selection using analytic hierarchy process and multi-dimension scaling

Lew

Trachtengertz

Ratsin

et al. 2014

Front. Environ. Sci.

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The recent high demands for reuse of salty water for irrigation affected membrane producers to assess new potential technologies for undesirable physical, chemical, and biological contaminants removal. This paper studies the assembly options by the analytic hierarchy process (AHP) model and the multi-dimension scaling (MDS) techniques. A specialized form of MDS (CoPlot software) enables presentation of the AHP outcomes in a two dimensional space and the optimal model can be visualized clearly. Four types of 8" membranes were selected: (i) Nanofiltration low rejection and high flux (ESNA1-LF-LD, 86% rejection, 10,500 gpd); (ii) Nanofiltration medium rejection and medium flux (ESNA1-LF2-LD, 91% rejection, 8200 gpd); (iii) Reverse Osmosis high rejection and high flux (CPA5-MAX, 99.7 rejection, 12,000 gpd); and (iv) Reverse Osmosis medium rejection and extreme high flux (ESPA4-MAX, 99.2 rejection, 13,200 gpd). The results indicate that: (i) Nanofiltration membrane (High flux and Low rejection) can produce water for irrigation with valuable levels of nutrient ions and a reduction in the sodium absorption ratio (SAR), minimizing soil salinity; this is an attractive option for agricultural irrigation and is the optimal solution; and (ii) implementing the MDS approach with reference to the variables is consequently useful to characterize membrane system design.

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“…Tropical optimization presents an important research domain in this area, focused on optimization problems that are formulated and solved in the tropical mathematics setting. Methods and techniques of tropical optimization are applied to solve many well-known and new optimization problems in various fields, including decision making [6,7,8,9,10].…”

Section: Introductionmentioning

confidence: 99%

Tropical implementation of the Analytical Hierarchy Process decision method

Krivulin

Sergeev

2019

Fuzzy Sets and Systems

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We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-criteria problems of rating alternatives from pairwise comparison data. In this framework, we first consider the minimax Chebyshev approximation of pairwise comparison matrices by consistent matrices in the logarithmic scale. Recasting this approximation problem as a problem of tropical pseudo-quadratic programming, we then write out a closed-form solution to it. This solution might be either a unique score vector (up to a positive factor) or a set of different score vectors. To handle the problem when the solution is not unique, we develop tropical optimization techniques of maximizing and minimizing the Hilbert seminorm to find those vectors from the solution set that are the most and least differentiating between the alternatives with the highest and lowest scores, and thus are well representative of the entire solution set.

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The analytic hierarchy process, max algebra and multi-objective optimisation

Cited by 21 publications

References 29 publications

A Fuzzy Decision Support Approach for Model-Based Tradeoff Analysis of Non-functional Requirements

A Fuzzy Decision Support Approach for Model-Based Tradeoff Analysis of Non-functional Requirements

Brackish groundwater membrane system design for sustainable irrigation: optimal configuration selection using analytic hierarchy process and multi-dimension scaling

Tropical implementation of the Analytical Hierarchy Process decision method

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