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Optimization for Decision Making II
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Optimization for Decision Making II

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Fuzzy Sets, Systems and Decision Making".

Deadline for manuscript submissions: closed (31 May 2020) | Viewed by 52916

Special Issue Editors

Prof. Dr. Víctor Yepes

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Guest Editor
Construction Engineering Department, Universitat Politècnica de València, 46022 Valencia, Spain
Interests: multi-objective optimization; structure optimization; lifecycle assessment; social sustainability of infrastructures; reliability-based maintenance optimization; optimization and decision making under uncertainty
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. José Moreno-Jiménez

E-Mail Website
Guest Editor
Grupo Decisión Multicriterio Zaragoza (GDMZ), Facultad de Economía y Empresa, Universidad de Zaragoza, Gran Vía 2, 50005 Zaragoza, Spain
Interests: multicriteria decision making; environmental selection; strategic planning; knowledge management; evaluation of systems; logistics and public decision making (e-government, e-participation, e-democracy, and e-cognocracy)
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In the current context of the electronic governance of society, both administrations and citizens are demanding greater participation of all the actors involved in the decision-making process relative to the governance of society. In addition, the design, planning, and operations management rely on mathematical models, the complexity of which depends on the detail of models and complexity/characteristics of the problem they represent. Unfortunately, decision-making by humans is often suboptimal in ways that can be reliably predicted. Furthermore, the process industry seeks not only to minimize cost, but also to minimize adverse environmental and social impacts. On the other hand, in order to give an appropriate response to the new challenges raised, the decision-making process can be done by applying different methods and tools, as well as using different objectives. In real-life problems, the formulation of decision-making problems and application of optimization techniques to support decisions is particularly complex, and a wide range of optimization techniques and methodologies are used to minimize risks or improve quality in making concomitant decisions. In addition, a sensitivity analysis should be done to validate/analyze the influence of uncertainty regarding decision-making.

Prof. Víctor Yepes
Prof. José Moreno-Jiménez
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Multicriteria decision making
  • Optimization techniques
  • Multiobjective optimization

Published Papers (16 papers)

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Research

11 pages, 262 KiB  
Article
The Double Traveling Salesman Problem with Multiple Stacks and a Choice of Container Types
by Lars Magnus Hvattum, Gregorio Tirado and Ángel Felipe
Mathematics 2020, 8(6), 979; https://doi.org/10.3390/math8060979 - 16 Jun 2020
Cited by 5 | Viewed by 2080
Abstract
The double traveling salesman problem with multiple stacks involves the transportation of goods between two regions. In one region, a vehicle carrying a container visits customers, where pallets of goods are loaded into the container. The container is then shipped to a different [...] Read more.
The double traveling salesman problem with multiple stacks involves the transportation of goods between two regions. In one region, a vehicle carrying a container visits customers, where pallets of goods are loaded into the container. The container is then shipped to a different region, where another vehicle visits another set of customers where the pallets are unloaded. Pallets are loaded in several rows inside the container, where each row follows the last-in-first-out principle. The standard test instances for the double traveling salesman problem with multiple stacks implies the use of a 45-foot pallet wide container to carry EUR-1 pallets. This paper investigates the effect on transportation costs if an open side container could be used when transporting the pallets. Computational experiments show savings in transportation costs of up to 20%. Moreover, by using a container loaded from the side, rather than from the rear, the defining attributes of the double traveling salesman problem seem to be lost. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
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17 pages, 336 KiB  
Article
The Triads Geometric Consistency Index in AHP-Pairwise Comparison Matrices
by Juan Aguarón, María Teresa Escobar, José María Moreno-Jiménez and Alberto Turón
Mathematics 2020, 8(6), 926; https://doi.org/10.3390/math8060926 - 06 Jun 2020
Cited by 19 | Viewed by 3210
Abstract
The paper presents the Triads Geometric Consistency Index ( T - G C I ), a measure for evaluating the inconsistency of the pairwise comparison matrices employed in the Analytic Hierarchy Process (AHP). Based on the Saaty’s definition of consistency for AHP, the [...] Read more.
The paper presents the Triads Geometric Consistency Index ( T - G C I ), a measure for evaluating the inconsistency of the pairwise comparison matrices employed in the Analytic Hierarchy Process (AHP). Based on the Saaty’s definition of consistency for AHP, the new measure works directly with triads of the initial judgements, without having to previously calculate the priority vector, and therefore is valid for any prioritisation procedure used in AHP. The T - G C I is an intuitive indicator defined as the average of the log quadratic deviations from the unit of the intensities of all the cycles of length three. Its value coincides with that of the Geometric Consistency Index ( G C I ) and this allows the utilisation of the inconsistency thresholds as well as the properties of the G C I when using the T - G C I . In addition, the decision tools developed for the G C I can be used when working with triads ( T - G C I ), especially the procedure for improving the inconsistency and the consistency stability intervals of the judgements used in group decision making. The paper further includes a study of the computational complexity of both measures ( T - G C I and G C I ) which allows selecting the most appropriate expression, depending on the size of the matrix. Finally, it is proved that the generalisation of the proposed measure to cycles of any length coincides with the T - G C I . It is not therefore necessary to consider cycles of length greater than three, as they are more complex to obtain and the calculation of their associated measure is more difficult. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
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22 pages, 911 KiB  
Article
The Buttressed Walls Problem: An Application of a Hybrid Clustering Particle Swarm Optimization Algorithm
by José García, José V. Martí and Víctor Yepes
Mathematics 2020, 8(6), 862; https://doi.org/10.3390/math8060862 - 26 May 2020
Cited by 26 | Viewed by 2976
Abstract
The design of reinforced earth retaining walls is a combinatorial optimization problem of interest due to practical applications regarding the cost savings involved in the design and the optimization in the amount of CO 2 emissions generated in its construction. On the other [...] Read more.
The design of reinforced earth retaining walls is a combinatorial optimization problem of interest due to practical applications regarding the cost savings involved in the design and the optimization in the amount of CO 2 emissions generated in its construction. On the other hand, this problem presents important challenges in computational complexity since it involves 32 design variables; therefore we have in the order of 10 20 possible combinations. In this article, we propose a hybrid algorithm in which the particle swarm optimization method is integrated that solves optimization problems in continuous spaces with the db-scan clustering technique, with the aim of addressing the combinatorial problem of the design of reinforced earth retaining walls. This algorithm optimizes two objective functions: the carbon emissions embedded and the economic cost of reinforced concrete walls. To assess the contribution of the db-scan operator in the optimization process, a random operator was designed. The best solutions, the averages, and the interquartile ranges of the obtained distributions are compared. The db-scan algorithm was then compared with a hybrid version that uses k-means as the discretization method and with a discrete implementation of the harmony search algorithm. The results indicate that the db-scan operator significantly improves the quality of the solutions and that the proposed metaheuristic shows competitive results with respect to the harmony search algorithm. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
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20 pages, 21942 KiB  
Article
Supported Evacuation for Disaster Relief through Lexicographic Goal Programming
by Inmaculada Flores, M. Teresa Ortuño, Gregorio Tirado and Begoña Vitoriano
Mathematics 2020, 8(4), 648; https://doi.org/10.3390/math8040648 - 22 Apr 2020
Cited by 10 | Viewed by 3201
Abstract
Disasters have been striking human-beings from the beginning of history and their management is a global concern of the international community. Minimizing the impact and consequences of these disasters, both natural and human-made, involves many decision and logistic processes that should be optimized. [...] Read more.
Disasters have been striking human-beings from the beginning of history and their management is a global concern of the international community. Minimizing the impact and consequences of these disasters, both natural and human-made, involves many decision and logistic processes that should be optimized. A crucial logistic problem is the evacuation of the affected population, and the focus of this paper is the planning of supported evacuation of vulnerable people to safe places when necessary. A lexicographic goal programming model for supported evacuation is proposed, whose main novelties are the classification of potential evacuees according to their health condition, so that they can be treated accordingly; the introduction of dynamism regarding the arrival of potential evacuees to the pickup points, according to their own susceptibility about the disaster and the joint consideration of objectives such us number of evacuated people, operation time and cost, among which no trade-off is possible. The performance of the proposed model is evaluated through a realistic case study regarding the earthquake and tsunami that hit Palu (Indonesia) in September 2018. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
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18 pages, 19377 KiB  
Article
Probability-Based Wildfire Risk Measure for Decision-Making
by Adán Rodríguez-Martínez and Begoña Vitoriano
Mathematics 2020, 8(4), 557; https://doi.org/10.3390/math8040557 - 10 Apr 2020
Cited by 8 | Viewed by 3057
Abstract
Wildfire is a natural element of many ecosystems as well as a natural disaster to be prevented. Climate and land usage changes have increased the number and size of wildfires in the last few decades. In this situation, governments must be able to [...] Read more.
Wildfire is a natural element of many ecosystems as well as a natural disaster to be prevented. Climate and land usage changes have increased the number and size of wildfires in the last few decades. In this situation, governments must be able to manage wildfire, and a risk measure can be crucial to evaluate any preventive action and to support decision-making. In this paper, a risk measure based on ignition and spread probabilities is developed modeling a forest landscape as an interconnected system of homogeneous sectors. The measure is defined as the expected value of losses due to fire, based on the probabilities of each sector burning. An efficient method based on Bayesian networks to compute the probability of fire in each sector is provided. The risk measure is suitable to support decision-making to compare preventive actions and to choose the best alternatives reducing the risk of a network. The paper is divided into three parts. First, we present the theoretical framework on which the risk measure is based, outlining some necessary properties of the fire probabilistic model as well as discussing the definition of the event ‘fire’. In the second part, we show how to avoid topological restrictions in the network and produce a computable and comprehensible wildfire risk measure. Finally, an illustrative case example is included. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
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22 pages, 1270 KiB  
Article
A Hybrid k-Means Cuckoo Search Algorithm Applied to the Counterfort Retaining Walls Problem
by José García, Victor Yepes and José V. Martí
Mathematics 2020, 8(4), 555; https://doi.org/10.3390/math8040555 - 10 Apr 2020
Cited by 32 | Viewed by 4406
Abstract
The counterfort retaining wall is one of the most frequent structures used in civil engineering. In this structure, optimization of cost and CO2 emissions are important. The first is relevant in the competitiveness and efficiency of the company, the second in environmental [...] Read more.
The counterfort retaining wall is one of the most frequent structures used in civil engineering. In this structure, optimization of cost and CO2 emissions are important. The first is relevant in the competitiveness and efficiency of the company, the second in environmental impact. From the point of view of computational complexity, the problem is challenging due to the large number of possible combinations in the solution space. In this article, a k-means cuckoo search hybrid algorithm is proposed where the cuckoo search metaheuristic is used as an optimization mechanism in continuous spaces and the unsupervised k-means learning technique to discretize the solutions. A random operator is designed to determine the contribution of the k-means operator in the optimization process. The best values, the averages, and the interquartile ranges of the obtained distributions are compared. The hybrid algorithm was later compared to a version of harmony search that also solved the problem. The results show that the k-mean operator contributes significantly to the quality of the solutions and that our algorithm is highly competitive, surpassing the results obtained by harmony search. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
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17 pages, 615 KiB  
Article
A Mathematical Pre-Disaster Model with Uncertainty and Multiple Criteria for Facility Location and Network Fortification
by Julia Monzón, Federico Liberatore and Begoña Vitoriano
Mathematics 2020, 8(4), 529; https://doi.org/10.3390/math8040529 - 03 Apr 2020
Cited by 9 | Viewed by 6400
Abstract
Disasters have catastrophic effects on the affected population, especially in developing and underdeveloped countries. Humanitarian Logistics models can help decision-makers to efficiently and effectively warehouse and distribute emergency goods to the affected population, to reduce casualties and suffering. However, poor planning and structural [...] Read more.
Disasters have catastrophic effects on the affected population, especially in developing and underdeveloped countries. Humanitarian Logistics models can help decision-makers to efficiently and effectively warehouse and distribute emergency goods to the affected population, to reduce casualties and suffering. However, poor planning and structural damage to the transportation infrastructure could hamper these efforts and, eventually, make it impossible to reach all the affected demand centers. In this paper, a pre-disaster Humanitarian Logistics model is presented that jointly optimizes the prepositioning of aid distribution centers and the strengthening of road sections to ensure that as much affected population as possible can efficiently get help. The model is stochastic in nature and considers that the demand in the centers affected by the disaster and the state of the transportation network are random. Uncertainty is represented through scenarios representing possible disasters. The methodology is applied to a real-world case study based on the 2018 storm system that hit the Nampula Province in Mozambique. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
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23 pages, 1512 KiB  
Article
A New Ant Colony-Based Methodology for Disaster Relief
by José M. Ferrer, M. Teresa Ortuño and Gregorio Tirado
Mathematics 2020, 8(4), 518; https://doi.org/10.3390/math8040518 - 03 Apr 2020
Cited by 10 | Viewed by 2379
Abstract
Humanitarian logistics in response to large scale disasters entails decisions that must be taken urgently and under high uncertainty. In addition, the scarcity of available resources sometimes causes the involved organizations to suffer assaults while transporting the humanitarian aid. This paper addresses the [...] Read more.
Humanitarian logistics in response to large scale disasters entails decisions that must be taken urgently and under high uncertainty. In addition, the scarcity of available resources sometimes causes the involved organizations to suffer assaults while transporting the humanitarian aid. This paper addresses the last mile distribution problem that arises in such an insecure environment, in which vehicles are often forced to travel together forming convoys for security reasons. We develop an elaborated methodology based on Ant Colony Optimization that is applied to two case studies built from real disasters, namely the 2010 Haiti earthquake and the 2005 Niger famine. There are very few works in the literature dealing with problems in this context, and that is the research gap this paper tries to fill. Furthermore, the consideration of multiple criteria such as cost, time, equity, reliability, security or priority, is also an important contribution to the literature, in addition to the use of specialized ants and effective pheromones that are novel elements of the algorithm which could be exported to other similar problems. Computational results illustrate the efficiency of the new methodology, confirming it could be a good basis for a decision support tool for real operations. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
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14 pages, 2085 KiB  
Article
Robust Design Optimization for Low-Cost Concrete Box-Girder Bridge
by Vicent Penadés-Plà, Tatiana García-Segura and Víctor Yepes
Mathematics 2020, 8(3), 398; https://doi.org/10.3390/math8030398 - 11 Mar 2020
Cited by 24 | Viewed by 5178
Abstract
The design of a structure is generally carried out according to a deterministic approach. However, all structural problems have associated initial uncertain parameters that can differ from the design value. This becomes important when the goal is to reach optimized structures, as a [...] Read more.
The design of a structure is generally carried out according to a deterministic approach. However, all structural problems have associated initial uncertain parameters that can differ from the design value. This becomes important when the goal is to reach optimized structures, as a small variation of these initial uncertain parameters can have a big influence on the structural behavior. The objective of robust design optimization is to obtain an optimum design with the lowest possible variation of the objective functions. For this purpose, a probabilistic optimization is necessary to obtain the statistical parameters that represent the mean value and variation of the objective function considered. However, one of the disadvantages of the optimal robust design is its high computational cost. In this paper, robust design optimization is applied to design a continuous prestressed concrete box-girder pedestrian bridge that is optimum in terms of its cost and robust in terms of structural stability. Furthermore, Latin hypercube sampling and the kriging metamodel are used to deal with the high computational cost. Results show that the main variables that control the structural behavior are the depth of the cross-section and compressive strength of the concrete and that a compromise solution between the optimal cost and the robustness of the design can be reached. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
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27 pages, 9330 KiB  
Article
A Variation of the ATC Work Shift Scheduling Problem to Deal with Incidents at Airport Control Centers
by Antonio Jiménez-Martín, Faustino Tello and Alfonso Mateos
Mathematics 2020, 8(3), 321; https://doi.org/10.3390/math8030321 - 02 Mar 2020
Cited by 3 | Viewed by 3002
Abstract
This paper deals with a variation of the air traffic controller (ATC) work shift scheduling problem focusing on the tactical phase, in which the plan for the day of operations can be modified according to real-time traffic demand or other possible incidents (one [...] Read more.
This paper deals with a variation of the air traffic controller (ATC) work shift scheduling problem focusing on the tactical phase, in which the plan for the day of operations can be modified according to real-time traffic demand or other possible incidents (one or more ATCs become sick and/or there is an increase in unplanned air traffic), which may lead to a new sectorization and a lower number of available ATCs. To deal with these issues, we must reassign the available ATCs to the new sectorization established at the time the incident happens, but also taking into account the work done by the ATCs up to that point. We propose a new methodology consisting of two phases. The goal of the first phase is to build an initial possibly infeasible solution, taking into account the sectors that have been closed or opened in the new sectorization, together with the ATCs available after the incident. In the second phase, we use simulated annealing (SA) and variable neighborhood search (VNS) metaheuristics to derive a feasible solution in which the available ATCs are used and all the ATC labor conditions are met. A weighted additive objective function is used in this phase to account for the feasibility of the solution but also for the number of changes in the control center at the time the incident happens and the similarity of the derived solution with templates usually used by the network manager operations center, a center managing the air traffic flows of an entire network of control centers. The methodology is illustrated by means of seven real instances provided by the Air Traffic Management Research, Development and Innovation Reference Center (CRIDA) experts representing possible incidents that may arise. The solutions derived by SA outperform those reached by VNS in terms of both the number of violated constraints in all seven instances, and solution compactability in six out the seven instances, and both are very similar with regard to the number of control center changes at the time of the incident. Although computation times for VNS are clearly better than for SA, CRIDA experts were satisfied with SA computation times. The solutions reached by SA were preferred. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
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13 pages, 301 KiB  
Article
A Spectral Conjugate Gradient Method with Descent Property
by Jinbao Jian, Lin Yang, Xianzhen Jiang, Pengjie Liu and Meixing Liu
Mathematics 2020, 8(2), 280; https://doi.org/10.3390/math8020280 - 19 Feb 2020
Cited by 18 | Viewed by 4031
Abstract
Spectral conjugate gradient method (SCGM) is an important generalization of the conjugate gradient method (CGM), and it is also one of the effective numerical methods for large-scale unconstrained optimization. The designing for the spectral parameter and the conjugate parameter in SCGM is a [...] Read more.
Spectral conjugate gradient method (SCGM) is an important generalization of the conjugate gradient method (CGM), and it is also one of the effective numerical methods for large-scale unconstrained optimization. The designing for the spectral parameter and the conjugate parameter in SCGM is a core work. And the aim of this paper is to propose a new and effective alternative method for these two parameters. First, motivated by the strong Wolfe line search requirement, we design a new spectral parameter. Second, we propose a hybrid conjugate parameter. Such a way for yielding the two parameters can ensure that the search directions always possess descent property without depending on any line search rule. As a result, a new SCGM with the standard Wolfe line search is proposed. Under usual assumptions, the global convergence of the proposed SCGM is proved. Finally, by testing 108 test instances from 2 to 1,000,000 dimensions in the CUTE library and other classic test collections, a large number of numerical experiments, comparing with both SCGMs and CGMs, for the presented SCGM are executed. The detail results and their corresponding performance profiles are reported, which show that the proposed SCGM is effective and promising. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
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19 pages, 1856 KiB  
Article
Relevant Aspects for an EF3-Evaluation of E-Cognocracy
by José María Moreno-Jiménez, Cristina Pérez-Espés and Pilar Rivera-Torres
Mathematics 2020, 8(2), 277; https://doi.org/10.3390/math8020277 - 19 Feb 2020
Cited by 1 | Viewed by 2328
Abstract
The search for an appropriate response to the new challenges and needs posed by the Knowledge Society in the area of public decisions has led to the development of a number of participation models whose value must be assessed and analysed in an [...] Read more.
The search for an appropriate response to the new challenges and needs posed by the Knowledge Society in the area of public decisions has led to the development of a number of participation models whose value must be assessed and analysed in an integral manner. Using a theoretical model based on structural equations, the present work identifies the relevant factors for an EF3-approach to the democracy model named e-Cognocracy: it comprises a conjoint evaluation of its effectiveness (doing what is right), efficacy (achieving goals) and efficiency (doing things correctly). The model was applied to a real-life e-Cognocracy experience undertaken in the municipality of Cadrete, Zaragoza. The evaluation resulted in the extraction and identification of a series of relationships that allow the advancement of an EF3-participation acceptance model, in line with the TAM model of Davis and the work of Delone and MacLean, which can be used for the integral evaluation of any e-participation model. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
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16 pages, 316 KiB  
Article
The Basic Algorithm for the Constrained Zero-One Quadratic Programming Problem with k-diagonal Matrix and Its Application in the Power System
by Shenshen Gu and Xinyi Chen
Mathematics 2020, 8(1), 138; https://doi.org/10.3390/math8010138 - 19 Jan 2020
Cited by 2 | Viewed by 2342
Abstract
Zero-one quadratic programming is a classical combinatorial optimization problem that has many real-world applications. However, it is well known that zero-one quadratic programming is non-deterministic polynomial-hard (NP-hard) in general. On one hand, the exact solution algorithms that can guarantee the global optimum are [...] Read more.
Zero-one quadratic programming is a classical combinatorial optimization problem that has many real-world applications. However, it is well known that zero-one quadratic programming is non-deterministic polynomial-hard (NP-hard) in general. On one hand, the exact solution algorithms that can guarantee the global optimum are very time consuming. And on the other hand, the heuristic algorithms that generate the solution quickly can only provide local optimum. Due to this reason, identifying polynomially solvable subclasses of zero-one quadratic programming problems and their corresponding algorithms is a promising way to not only compromise these two sides but also offer theoretical insight into the complicated nature of the problem. By combining the basic algorithm and dynamic programming method, we propose an effective algorithm in this paper to solve the general linearly constrained zero-one quadratic programming problem with a k-diagonal matrix. In our algorithm, the value of k is changeable that covers different subclasses of the problem. The theoretical analysis and experimental results reveal that our proposed algorithm is reasonably effective and efficient. In addition, the placement of the phasor measurement units problem in the power system is adopted as an example to illustrate the potential real-world applications of this algorithm. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
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14 pages, 273 KiB  
Article
Evaluating Personal Default Risk in P2P Lending Platform: Based on Dual Hesitant Pythagorean Fuzzy TODIM Approach
by Xiaonan Ji, Lixia Yu and Jiapei Fu
Mathematics 2020, 8(1), 8; https://doi.org/10.3390/math8010008 - 18 Dec 2019
Cited by 25 | Viewed by 2548
Abstract
An extended approach proposed in this paper is to make a more reasonable assessment of personal default risk in peer to peer (P2P) online lending platform, which reduces uncertainty while taking into account the psychological characteristics of lenders to avoid risk. The TODIM [...] Read more.
An extended approach proposed in this paper is to make a more reasonable assessment of personal default risk in peer to peer (P2P) online lending platform, which reduces uncertainty while taking into account the psychological characteristics of lenders to avoid risk. The TODIM (an acronym in Portuguese of interactive and multi-criteria decision making) approach, which can describe the psychological behaviors of decision maker, has been proved to be effective to solve multi-attribute decision making (MADM) problems. The definitions of dual hesitant Pythagorean fuzzy set (DHPFS) and the processes of traditional TODIM approach are firstly introduced in this paper. Then, the TODIM approach is extended to solve the MADM problems with a dual hesitant Pythagorean fuzzy number (DHPFN). Finally, a case study evaluating the personal default risk in P2P online lending is conducted to demonstrate that the proposed approach is applicable to solve MADM problems. In addition, some comparative analyses are performed to compare the dual hesitant Pythagorean fuzzy TODIM method with the other two integrated operators of DHPFS. Through the comparisons, we conclude that the advantage of the proposed method over other methods is that it reduces uncertainty while taking into account the psychological characteristics of lenders to avoid risk. Today’s credit environment is fraught with risks, and the psychological behaviors of decision makers are important factors that cannot be ignored. For these reasons, the dual Pythagorean hesitant fuzzy TODIM method is applicable for evaluating personal default risk. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
13 pages, 291 KiB  
Article
Pythagorean 2-Tuple Linguistic VIKOR Method for Evaluating Human Factors in Construction Project Management
by Tingting He, Guiwu Wei, Jianping Lu, Cun Wei and Rui Lin
Mathematics 2019, 7(12), 1149; https://doi.org/10.3390/math7121149 - 24 Nov 2019
Cited by 32 | Viewed by 2696
Abstract
Since the reform and opening up, Chinese economic and social development has undergone great changes, and the people’s living standards have improved markedly. For the national economy, the engineering construction is not only a carrier for specific economic tasks, but also a driving [...] Read more.
Since the reform and opening up, Chinese economic and social development has undergone great changes, and the people’s living standards have improved markedly. For the national economy, the engineering construction is not only a carrier for specific economic tasks, but also a driving force for rapid and sustained economic development. With the continuous expansion of the scale of construction projects, safety management problems of construction projects are constantly exposed. How to effectively avoid accidents has become an important issue to be solved urgently in the construction industry. This paper mainly evaluates human factors in the process of construction project management, such as workers’ proficiency, workers’ safety awareness, technical workers’ quality, and workers’ emergency capacity, with the purpose of helping China’s construction projects proceed smoothly. In this research, we provide a multiple attribute group decision-making (MAGDM) technique based on Pythagorean 2-tuple linguistic numbers (P2TLNs) and the VIseKriterijumska Optimizacija I KOmpromisno Resenje (VIKOR) method for evaluating the human factors of construction projects. P2TLNs are used to represent the performance assessments of decision makers. Relying on a P2TLWA operator, P2TLWG operator, and the essential VIKOR method, a general framework is established. An application is presented to test the validity of the new method, and a comparative analysis with two algorithms and the P2TL-TODIM method is illustrated with detail. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
16 pages, 353 KiB  
Article
A Compact Representation of Preferences in Multiple Criteria Optimization Problems
by Francisco Salas-Molina, David Pla-Santamaria, Ana Garcia-Bernabeu and Javier Reig-Mullor
Mathematics 2019, 7(11), 1092; https://doi.org/10.3390/math7111092 - 11 Nov 2019
Cited by 6 | Viewed by 1969
Abstract
A critical step in multiple criteria optimization is setting the preferences for all the criteria under consideration. Several methodologies have been proposed to compute the relative priority of criteria when preference relations can be expressed either by ordinal or by cardinal information. The [...] Read more.
A critical step in multiple criteria optimization is setting the preferences for all the criteria under consideration. Several methodologies have been proposed to compute the relative priority of criteria when preference relations can be expressed either by ordinal or by cardinal information. The analytic hierarchy process introduces relative priority levels and cardinal preferences. Lexicographical orders combine both ordinal and cardinal preferences and present the additional difficulty of establishing strict priority levels. To enhance the process of setting preferences, we propose a compact representation that subsumes the most common preference schemes in a single algebraic object. We use this representation to discuss the main properties of preferences within the context of multiple criteria optimization. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
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