Algebraic solution to constrained bi-criteria decision problem of rating alternatives through pairwise comparisons

We consider a decision-making problem to evaluate absolute ratings of alternatives from the results of their pairwise comparisons according to two criteria, subject to constraints on the ratings. We formulate the problem as a bi-objective optimization problem of constrained matrix approximation in the Chebyshev sense in logarithmic scale. The problem is to approximate the pairwise comparison matrices for each criterion simultaneously by a common consistent matrix of unit rank, which determines the vector of ratings. We represent and solve the optimization problem in the framework of tropical (idempotent) algebra, which deals with the theory and applications of idempotent semirings and semifields. The solution involves the introduction of two parameters that represent the minimum values of approximation error for each matrix and thereby describe the Pareto frontier for the bi-objective problem. The optimization problem then reduces to a parametrized vector inequality. The necessary and sufficient conditions for solutions of the inequality serve to derive the Pareto frontier for the problem. All solutions of the inequality, which correspond to the Pareto frontier, are taken as a complete Pareto-optimal solution to the problem. We apply these results to the decision problem of interest and present illustrative examples.Comment: 30 pages, 2 figure

Tropical implementation of the Analytical Hierarchy Process decision method

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.Comment: 37 pages (added a new example and a discussion). arXiv admin note: text overlap with arXiv:1801.1052

Algebraic solution to box-constrained bi-criteria problem of rating alternatives through pairwise comparisons

We consider a decision-making problem to evaluate absolute ratings of alternatives that are compared in pairs according to two criteria, subject to box constraints on the ratings. The problem is formulated as the log-Chebyshev approximation of two pairwise comparison matrices by a common consistent matrix (a symmetrically reciprocal matrix of unit rank), to minimize the approximation errors for both matrices simultaneously. We rearrange the approximation problem as a constrained bi-objective optimization problem of finding a vector that determines the approximating consistent matrix, and then represent the problem in terms of tropical algebra. We apply methods and results of tropical optimization to derive an analytical solution of the constrained problem. The solution consists in introducing two new variables that describe the values of the objective functions and allow reducing the problem to the solution of a system of parameterized inequalities constructed for the unknown vector, where the new variables play the role of parameters. We exploit the existence condition for solutions of the system to derive those values of the parameters that belong to the Pareto front inherent to the problem. Then, we solve the system for the unknown vector and take all solutions that correspond to the Pareto front, as a complete solution of the bi-objective problem. We apply the result obtained to the bi-criteria decision problem under consideration and present illustrative examples.Comment: 29 page

Biodiesel from microalgae : the use of multi-criteria decision analysis for strain selection

Microalgae strain selection is a vital step in the production of biodiesel from microalgae. In this study, Multi-Criteria Decision Analysis (MCDA) methodologies are adopted to resolve this problem. The aim of this study is to identify the best microalgae strain for viable biodiesel production. The microalgae strains considered here are Heynigia sp., Scenedesmus sp., Niracticinium sp., Chlorella vulgaris, Chlorella sorokiniana and Auxenochlorella protothecoides. The five MCDA methods used to evaluate different strains of microalgae are Analytic Hierarchy Process (AHP), Weighted Sum Method (WSM), Weighted Product Method (WPM), Discrete Compromise Programming (DCP) and Technique for the Order of Preference to the Ideal Solution (TOPSIS). Pairwise comparison matrices are used to determine the weights of the evaluation criteria and it is observed that the most important evaluation criteria are lipid content and growth rate. From the results, Scenedesmus sp. is selected as the best microalgae strain among the six alternatives due to its high lipid content and relatively fast growth rate. The AHP is the most comprehensive of the five MCDA methods because it considers the importance of each criterion and inconsistencies in the rankings are verified. The implementation of the MCDA methods and the results from this study provide an idea of how MCDA can be applied in microalgae strain selection

ASSESSMENT OF FLOOD HAZARD SUSCEPTIBILITY IN SOUTH SUDAN’S UPPER NILE STATE USING GIS-BASED MULTICRITERIA ANALYSIS

openLe alluvioni sono tra i rischi naturali più rovinosi. I loro effetti avversi comprendono danni alle strutture fisiche, sociali ed economiche, ed un deterioramento dei mezzi di sussistenza. Allo stesso tempo, attribuito alle variazioni climatiche ed eventi estremi causati dal cambiamento climatico, è stato registrato un incremento nella frequenza di alluvioni a livello globale, aumentando la necessita di comprendere gli aspetti spazio-temporali di questi fenomeni. Questo studio esamina la dimensione spaziale del rischio di inondazione nell’Alto Nilo, Sudan del Sud, regione con una riconosciuta vulnerabilità verso le inondazioni, causata principalmente dal suo posizionamento geografico all’interno di una pianura alluvionale caratterizzata da una notevole variabilità della portata di piena. L’obiettivo di questa indagine è quello di mappare la potenziale estensione spaziale degli allagamenti all’interno dell’area di studio in uno scenario di inondazione. La mappa del rischio di inondazioni, fondata su diversi indici, è stata sviluppata utilizzando una decisione d’analisi multicriteriale (MCDA) basata su GIS, ed il analytical hierarchy process (AHP). Gli otto fattori d’influenza per le alluvioni utilizzati per lo studio sono: distanza da fiumi, indice di umidità topografica, densità di drenaggio, copertura del suolo (LULC), precipitazioni medie annue, pendenza, altitudine, e tipo di suolo. La mappa del rischio di inondazione sviluppata per l’area di studio è composta da cinque zone di suscettibilità: molto alta, alta, moderata, bassa, molto bassa. Queste zone coprono rispettivamente il 12%, 26%, 29%, 22%, e 9% dell’area di studio. La mappa è stata ulteriormente validata tramite un confronto con la mappa satellitare dello storico delle inondazioni, ed è risultata soddisfacente nello stimare la probabile estensione spaziale degli allagamenti. Il modello della mappa è potrà risultare strumentale per le misure di preparazione alle inondazioni, e come guida per future indagini specifiche nella dimensione spazio-temporale di eventi alluvionali nella regione dell’Alto Nilo.Floods are among the most ruinous of all natural hazards. Its adverse effects include damages to the physical, social, and economic structures, and disruption of livelihoods. contemporary, attributed to climate change-induced climate variations and extreme weather events, the frequency of flood occurrence has increased all around the globe. This has therefore, augmented the necessity to comprehend the spatial and temporal dimension of flood phenomena. The current study examines the spatial dimension of flood hazard in the Upper Nile state, South Sudan, a region acknowledged to be highly vulnerable to inundation, mainly due to is geographical position within a flood plain characterized by a notable variability in discharge. The objective of this investigation is to map the potential spatial extent of floodwater within the boundaries of study area under flood scenarios. The index-based flood hazard map was developed using GIS-based multicriteria decision analysis (MCDA), and the analytical hierarchy process (AHP). Eight flood influencing factors were used in this study, namely; distance to rivers, topographic wetness index, drainage density, land-coverage (LULC), annual average rainfall, slope, elevation, and soil types. The flood hazard map developed for study area consist of five flood hazard susceptibility zones: very high, high, moderate, low, and very low. These zones encompass proportions of 12%, 26%, 29%, 22%, and 9% of the study area, respectively. The flood hazard map was further validated using satellite historical inundation map and determined to be satisfactory in depicting the probabilistic spatial extent of inundation. The flood hazard model developed is anticipated to be instrumental in pre-flood preparedness measures as well as a guide for future detailed investigations on the spatial–temporal dimension of flood incidents in the Upper Nile state

FLOOD SUSCEPTIBILITY MODELLING USING GEOSPATIAL-BASED MULTI-CRITERIA DECISION MAKING IN LARGE SCALE AREAS

Flood is one of the most hazardous natural disasters that cause damages and poses a major threat to human lives and infrastructures worldwide, and its prevention is almost unfeasible. Thus, the detection of flood susceptible areas can be a key to lessen the amount of destruction and mortality. This study aims to implement a framework to identify flood potential zones in an ungauged large-scale area with frequent flood events in recent years. We used two Multi-Criteria Decision Making (MCDM) approaches combined with geospatial analysis, and remote sensing observations for this susceptibility analysis. Nine geomorphological and environmental factors that have an impact on flood behaviour were selected and used for susceptibility modelling. At first, the criteria’s weights were estimated using two MCDM approaches and based on experts’ knowledge. The resultant weights revealed that Flow Accumulation, Topographic wetness index, and Distance to River were the most influential flood susceptibility criteria. After calculating these weights, the criteria’s layers were aggregated through geospatial analysis, which resulted in generating flood susceptibility map. The area under the curve (AUC) and statistical measures such as the Kappa index were used to evaluate the proposed method's efficiency. The validation results illustrate that hybrid FAHP, with AUC= 96.68 and Kappa = 81.36 performed more efficiently than standard AHP, with AUC= 94.53 and Kappa=76.35. Overlaying these maps with the historical flood inventory dataset revealed that 86.43% of flooded areas were categorized as “high” and “very high”. Therefore, the flood susceptibility maps generated through the proposed approach can help the decision-makers and managers allocate the mitigation equipment and facility in data-scarce and ungauged large-scale areas

Decision support systems for large dam planning and operation in Africa

Decision support systems/ Dams/ Planning/ Operations/ Social impact/ Environmental effects

The sustainable management of land and fisheries resources using multicriteria techniques: A meta-analysis

In recent years modern societies have attached a multifunctional requirement to the use of renewable resources, making their optimal sustainable management more complex. In the last decades, in many cases, this complexity is addressed by formulating management models with the help of the concepts and methods belonging to the well-known multicriteria decision-making (MCDM) paradigm. The purpose of this paper was to undertake a hermeneutic meta-analysis of the literature provided in primary journals on issues related to the management of these resources with the help of the MCDM paradigm. In this way, the paper aimed to obtain new, basic insights with considerations that might improve the efficiency of future research in the field studied. The meta-analysis was implemented by formulating and testing a battery of hypotheses of how the MCDM methods have been used in the past for the formulation of management models for the type of resource analyzed.The work of Carlos Romero, Carlos Iglesias-Merchan, and Luis Diaz-Balteiro was funded by the Ministry of Economy and Competitiveness of Spain under project AGL2015-68657-R. Additionally, this research was partially financed by the European Union’s H2020 Research and Innovation Programme under the Marie Sklodowska-Curie Actions, grant agreement No. 691149–SuFoRun

Using pairwise comparisons to determine consumer preferences in hotel selection

We consider the problem of evaluating preferences for criteria used by university students when selecting a hotel for accommodation during a professional development program in a foreign country. Input data for analysis come from a survey of 202 respondents, who indicated their age, sex and whether they have previously visited the country. The criteria under evaluation are location, accommodation cost, typical guests, free breakfast, room amenities and courtesy of staff. The respondents assess the criteria both directly by providing estimates of absolute ratings and ranks, and indirectly by relative estimates using ratios of pairwise comparisons. To improve the accuracy of ratings derived from pairwise comparisons, we concurrently apply the principal eigenvector method, the geometric mean method and the method of log-Chebyshev approximation. Then, the results from the direct and indirect evaluation of ratings and ranks are examined together to analyze how the results from pairwise comparisons may differ from each other and from the results of direct assessment by respondents. We apply statistical techniques, such as estimation of means, standard deviations and correlations, to the vectors of ratings and ranks provided directly or indirectly by respondents, and then use the estimates to make accurate assessment of the criteria under study.Comment: 27 pages, 16 table