# A Web-Based Approach for Visualizing Interactive Decision Maps

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Optimization and Visualization of Interactive Decision Maps

#### 2.2. Implementations

#### 2.2.1. Standalone Implementation

#### 2.2.2. Java Applets Implementation

#### 2.2.3. PHP Implementation

## 3. Results

^{−1}).

#### Forest Management Application

^{6}m

^{3}); standing volume at the end of the planning horizon or volume of ending inventory (90 years), (Vol_Per9esc measured in 10

^{6}m

^{3}); the average carbon sequestration during the planning horizon (CTOTALesc, measured in Mg year

^{−1}); net present value (NPV, resulting from the silvicultural operations and value of cut wood in the planning horizon, measured in 10

^{8}EUR). Definitions of discrepancy, facets, and tops are the same as in the previous example.

^{8}EUR. In this example, if the user wants to analyze only a specific value of CTOTALesc, this is also an option as shown in Figure 10.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Disclaimer

## References

- Kitano, H. Computational systems biology. Nature
**2002**, 420, 206. [Google Scholar] [CrossRef] - Reynolds, K.M.; Twery, M.; Lexer, M.J.; Vacik, H.; Ray, G.; Shao, D.; Borges, J.G. Decision support systems in natural resource management. In Handbook on Decision Support Systems; International Handbooks on Information Systems Series; Handbook on Decision Support System 2; Burstein, F., Holsapple, C., Eds.; Springer: Berlin/Heidelberg, Germany, 2008; pp. 499–534. [Google Scholar] [CrossRef]
- Borges, J.G.; Nordström, E.M.; Garcia-Gonzalo, J.; Hujala, T.; Trasobares, A. (Eds.) Computer-Based Tools for Supporting Forest Management. In The Experience and the Expertise World-Wide; Deptartment of Forest Resource Management; Swedish University of Agricultural Sciences: Umeå, Sweden, 2014; 503p. [Google Scholar]
- Tóth, S.F.; Ettl, G.J.; Rabotyagov, S.S. ECOSEL: An auction mechanism for forest ecosystem services. Math. Comput. Nat. Resour. Sci.
**2010**, 2, 99–116. [Google Scholar] - Marques, A.F.; Borges, J.G.; Sousa, P.; Pinho, A.M. An enterprise architecture approach to forest management support systems design: An application to pulpwood supply management in Portugal. Eur. J. For. Res.
**2011**, 130, 935–948. [Google Scholar] [CrossRef] - Marques, A.F.; Fricko, A.; Kangas, A.; Rosset, C.; Ferreti, F.; Rasinmaki, J.; Packalen, T.; Gordon, S. Empirical guidelines for forest management decision support systems based on the past experiences of the expert’s community. For. Syst.
**2013**, 22, 320–339. [Google Scholar] [CrossRef][Green Version] - Borges, J.G.; Garcia-Gonzalo, J.; Bushenkov, V.; McDill, M.E.; Marques, S.; Oliveira, M.M. Addressing multicriteria forest management with Pareto frontier methods: An application in Portugal. For. Sci.
**2014**, 60, 63–72. [Google Scholar] [CrossRef][Green Version] - Borges, J.G.; Marques, S.; Garcia-Gonzalo, J.; Rahman, A.U.; Bushenkov, V.; Sottomayor, M.; Carvalho, P.O.; Nordström, E.M. A multiple criteria approach for negotiating ecosystem services supply targets and forest owners’ programs. For. Sci.
**2017**, 63, 49–61. [Google Scholar] [CrossRef] - Sheppard, S.R.; Meitner, M. Using multi-criteria analysis and visualisation for sustainable forest management planning with stakeholder groups. For. Ecol. Manag.
**2005**, 207, 171–187. [Google Scholar] [CrossRef] - Chichernea, V.; Pop, D.P. Web operations management: A web-based decision support systems for concret transportation in industrial are of the smart city. J. Inf. Syst. Oper. Manag.
**2014**, 8, 48–60. [Google Scholar] - Reynolds, K.M.; Hessburg, P.F.; Bourgeron, P.S. Making Transparent Environmental Management Decisions; Springer: Berlin/Heidelberg, Germany, 2014. [Google Scholar] [CrossRef]
- Nute, D.; Potter, W.D.; Maier, F.; Wang, J.; Twery, M.; Rauscher, H.M.; Knopp, P.; Thomasma, S.; Dass, M.; Uchiyama, H.; et al. NED-2: An agent-based decision support system for forest ecosystem management. Environ. Model. Softw.
**2004**, 19, 831–843. [Google Scholar] [CrossRef] - Baskent, E.Z.; Başkaya, Ş.; Terzioğlu, S. Developing and implementing participatory and ecosystem based multiple use forest management planning approach (ETÇAP): Yalnızçam case study. For. Ecol. Manag.
**2008**, 256, 798–807. [Google Scholar] [CrossRef] - Küçüker, D.M.; Baskent, E.Z. Sustaining the Joint Production of Timber and Lactarius Mushroom: A Case Study of a Forest Management Planning Unit in Northwestern Turkey. Sustainability
**2017**, 9, 92. [Google Scholar] [CrossRef][Green Version] - Seely, B.; Nelson, J.; Wells, R.; Peter, B.; Meitner, M.; Anderson, A.; Harshaw, H.; Sheppard, S.; Bunnell, F.L.; Kimmins, H.; et al. The application of a hierarchical, decision-support system to evaluate multi-objective forest management strategies: A case study in northeastern British Columbia, Canada. For. Ecol. Manag.
**2004**, 199, 283–305. [Google Scholar] [CrossRef] - Damme, L.V.; Russell, J.S.; Doyon, F.; Duinker, P.N.; Gooding, T.; Hirsch, K.; Rothwell, R.; Rudy, A. The development and application of a decision support system for sustainable forest management on the Boreal Plain. J. Environ. Eng. Sci.
**2003**, 2, S23–S34. [Google Scholar] [CrossRef] - Ouhimmou, M.; Haddad, S.; Boukherroub, T. Decision support system for selection of harvest areas and wood allocation to mills. IFAC-PapersOnLine
**2015**, 48, 628–633. [Google Scholar] [CrossRef] - Efremov, R.; Insua, D.R.; Lotov, A. A framework for participatory decision support using Pareto frontier visualization, goal identification and arbitration. Eur. J. Oper. Res.
**2009**, 199, 459–467. [Google Scholar] [CrossRef] - Dietrich, J.; Schumann, A.H.; Lotov, A.V. Workflow oriented participatory decision support for integrated river basin planning. In Topics on System Analysis and Integrated Water Resources Management; Castelletti, A., Sessa, R.S., Eds.; Elsevier: Amsterdam, The Netherlands, 2006; pp. 207–221. [Google Scholar]
- Lotov, A.V.; Bushenkov, V.A.; Kamenev, G.K. Interactive Decision Maps: Approximation and Visualization of Pareto Frontier; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2013; Volume 89. [Google Scholar]
- Garcia-Gonzalo, J.; Bushenkov, V.; McDill, M.; Borges, J. A decision support system for assessing trade-offs between ecosystem management goals: An application in Portugal. Forests
**2015**, 6, 65–87. [Google Scholar] [CrossRef][Green Version] - Marques, S.; Marto, M.; Bushenkov, V.; McDill, M.; Borges, J. Addressing Wildfire Risk in Forest Management Planning with Multiple Criteria Decision Making Methods. Sustainability
**2017**, 9, 298. [Google Scholar] [CrossRef][Green Version] - Marto, M.; Reynolds, K.M.; Borges, J.G.; Bushenkov, V.A.; Marques, S. Combining decision support approaches for optimizing the selection of bundles of ecosystem services. Forests
**2018**, 9, 438. [Google Scholar] [CrossRef][Green Version] - Bittinger, R.R.; Fraenkel, M.L.; Housel, B.C., III; Lindquist, D.B. Client/Server Communication System. U.S. Patent 5,754,774, 19 May 1998. [Google Scholar]
- Climaco, J.N.; Antunes, C.H.; Alves, M.J.G. Programação Linear Multiobjectivo: Do Modelo de Programação Linear Clássico à Consideração Explícita de Várias Funções Objective; Imprensa da Universidade de Coimbra/Coimbra University Press: Coimbra, Portugal, 2003; p. 393. [Google Scholar]
- Goicoechea, A.; Hansen, D.R.; Duckstein, L. Multiobjective decision analysis with engineering and business applications. J. Oper. Res. Soc.
**1982**, 34, 449–450. [Google Scholar] - Steuer, R.E. Multiple Criteria Optimization: Theory, Computation, and Application; Wiley: New York, NY, USA, 1986. [Google Scholar]
- Climaco, J.C.N.; Antunes, C.H. Implementation of a user-friendly softwa-re package—A guided tour of TRIMAP. In Models and Methods in Multiple Criteria Decision Making; Elsevier: Amsterdam, The Netherlands, 1989; pp. 1299–1309. [Google Scholar] [CrossRef]
- Gass, S.; Saaty, T. The computational algorithm for the parametric objective function. Nav. Res. Logist. Q.
**1995**, 2, 39–45. [Google Scholar] [CrossRef] - Zeleny, M. Linear Multiobjective Programming; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2012; Volume 95. [Google Scholar] [CrossRef]
- Deterding, S.; Dixon, D.; Khaled, R.; Nacke, L. From game design elements to gamefulness: Defining gamification. In Proceedings of the 15th International Academic MindTrek Conference: Envisioning Future Media Environments, Tampere, Finland, 28–30 September 2011; pp. 9–15. [Google Scholar] [CrossRef]
- Preparata, F.P.; Hong, S.J. Convex hulls of finite sets of points in two and three dimensions. Commun. ACM
**1977**, 20, 87–93. [Google Scholar] [CrossRef] - Wierzbicki, A.P. A Mathematical Basis for Satisficing Decision Making. In Organizations: Multiple Agents with Multiple Criteria; Lecture Notes in Economics and Mathematical Systems; Morse, J.N., Ed.; Springer: Berlin/Heidelberg, Germany, 1981. [Google Scholar] [CrossRef][Green Version]
- Lewandowski, A.; Grauer, M. The Reference Point Optimization Approach—Methods of Efficient Implementation, WP-82-019; International Institute for Applied Systems Analysis: Laxenburg, Austria, 1982. [Google Scholar]
- Bouchard, V.; Skarke, H. Affine Kac-Moody algebras, CHL strings and the classification of tops. Adv. Theor. Math. Phys.
**2003**, 7, 205–232. Available online: https://arxiv.org/abs/hep-th/0303218 (accessed on 24 December 2020). [CrossRef][Green Version] - Marto, M.; Reynolds, K.M.; Borges, J.G.; Bushenkov, V.A.; Marques, S.; Marques, M.; Barreiro, S.; Botequim, B.; Tomé, M. Web-Based Forest Resources Management Decision Support System. Forests
**2019**, 10, 1079. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Generation of Pareto frontiers from the Pareto hull. (

**a**) Initial convex hull of feasible solutions (${x}_{i}$, ${x}_{j}$). (

**b**) Edgeworth–Pareto hull in the criteria decision space (${z}_{i}$, ${z}_{j}$). (

**c**) Set of efficient solutions in the criteria decision space (${z}_{i}$, ${z}_{j}$). (

**d**) Extension to the Pareto frontier for the efficient solutions set considering two criteria (${z}_{i}$, ${z}_{j}$) in order to simplify the representation. (

**e**) Pareto frontiers representation considering three criteria (${z}_{i}$, ${z}_{j},{z}_{k}$).

**Figure 5.**Web graphical user interface (wgui) to choose the criteria to maximize or minimize, define any constraints on the criteria space (in this case totcrop ≤ 80%) and generate the Edgeworth–Pareto hull. This wgui shows the discrepancy between the convergence process and the real hull, the number of facets of the hull and the number of tops of the hull.

**Figure 6.**Representation of Pareto frontiers for the criteria totcrop (horizontal axis; in %), leveldrp (vertical axis; in %), and lakepol (represented by slices; in mg L

^{−1}).

**Figure 7.**Representation of Pareto frontier with only one frontier (one color) with tradeoffs between totcrop (in %) and leveldrp (in mg L

^{−1}) and the lakepol (in %) defined by the movement of the slider.

**Figure 9.**Interactive decision map showing the tradeoff between four criteria: volume of ending inventory (10

^{6}m

^{3}; Vol_Per9esc) in the y-axis; total wood (10

^{6}m

^{3}; TOTTIMBesc) in the x-axis; the average carbon sequestered (Mg year

^{−1}; CTOTALesc) in the colored scale and the chosen level of net present value level (10

^{8}EUR; NPV) in the slider (0.64 × 10

^{8}EUR).

**Figure 10.**Interactive decision map showing the tradeoff between four criteria: volume of ending inventory (10

^{6}m

^{3}; Vol_Per9esc) in the y-axis; total wood (10

^{6}m

^{3}; TOTTIMBesc) in the x-axis; the chosen level of average carbon sequestered (Mg year

^{−1}; CTOTALesc) in the first slider (4.17 Mg year

^{−1}) and the chosen level of net present value level (10

^{8}EUR; NPV) in the second slider (0.64 × 10

^{8}EUR).

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**MDPI and ACS Style**

Marto, M.; Bushenkov, V.A.; Reynolds, K.M.; Borges, J.G.; Marques, S. A Web-Based Approach for Visualizing Interactive Decision Maps. *Information* **2021**, *12*, 9.
https://doi.org/10.3390/info12010009

**AMA Style**

Marto M, Bushenkov VA, Reynolds KM, Borges JG, Marques S. A Web-Based Approach for Visualizing Interactive Decision Maps. *Information*. 2021; 12(1):9.
https://doi.org/10.3390/info12010009

**Chicago/Turabian Style**

Marto, Marco, Vladimir A. Bushenkov, Keith M. Reynolds, José G. Borges, and Susete Marques. 2021. "A Web-Based Approach for Visualizing Interactive Decision Maps" *Information* 12, no. 1: 9.
https://doi.org/10.3390/info12010009