# A Takagi-Sugeno Fuzzy Inference System for Developing a Sustainability Index of Biomass

## Abstract

**:**

## 1. Introduction

## 2. Fuzzy Inference System: A Theoretical Review

_{1}is A

_{1}and ...and X

_{n}is A

_{n}then Y is B”, where A, A

_{n}, B are fuzzy sets [15]. The knowledge base, which comprehends general knowledge concerning a problem domain, joins antecedents with consequences or premises with conclusions [16] (see Figure 1). The most commonly used fuzzy inference technique was proposed by Mamdani. However, in Mamdani-type FIS the number of rules grows with the number of premise-part variables. As the number of rules grows the activity of assembling rules can become very burdensome and sometimes it becomes difficult to comprehend the relationships between the premises and consequences [17]. A Sugeno-type method (or Takagi-Sugeno-Kang) has fuzzy inputs and a crisp output (linear combination of the inputs). It is computationally efficient and suitable to work with optimization and adaptive techniques, so it is very adequate for control problems, mainly for dynamic nonlinear systems [18]. Sugeno method develops a systematic approach to generate fuzzy rules from a given input-output data set. It changes the consequent (then part) of Mamdani rule with a function (Equation) of the input variables. The T-S style fuzzy rule is: IF x is A AND y is B THEN z is f (x, y) where x, y and z are linguistic variables, A and B are fuzzy sets on universe of discourses X and Y and f (x, y) is a mathematical function [18]. Sugeno-type FIS uses weighted average to compute the crisp output while Mamdani-type FIS uses the technique of defuzzification of a fuzzy output. The first two parts of the fuzzy inference process, fuzzifying the inputs and applying the fuzzy operator, are the same [9]. The main difference is that the Sugeno output membership functions are either linear or constant [9]. In Figure 2 different types of fuzzy systems are shown. Type two is Mamdani FIS with output function based on overall fuzzy output, while type three is the Takagi-Sugeno fuzzy inference.

**Figure 2.**Different types of Fuzzy inference system [30].

## 3. Fuzzy Inference for Measuring the Sustainability of Biomass

^{j}rules, where p is the number of linguistic terms per input variable. As the dimension and complexity of a system increases, the size of the rule base increases exponentially [13]. In this system 81 if-then rules have been defined; in the following Figure 4 some of these are reported as examples.

^{–1}. Data from the literature [31] attributes an energy output value of between 260 GJ ha

^{–1}and 530 GJ ha

^{–1}for miscanthus, between 240 GJ ha

^{–1}and 600 GJ ha

^{–1}for the giant reed, between 155 GJ ha

^{–1}and 252 GJ ha

^{–1}for the cardoon and, finally, between 334 GJ ha

^{–1}and 507 GJ ha

^{–1}for sorghum. This input variable has three fuzzy sets: “Low”, “Medium”, and “High”. MFs of “Low” and “High” are trapezoidal, while MF of “Middle” is triangular. Their Equations (1)–(3) are shown below:

^{-1}) refers to the total quantity of various fertilizers (N + K

_{2}O + P

_{2}O

_{5}) used on the crops [32,33].

## 4. Discussion and Testing

Input Data | ||||
---|---|---|---|---|

Crops | Energy Output (GJ ha^{–1}) | Energy O/I (ratio) | Fertilizer (kg/ha^{–1}) | Pesticide (score) |

Sweet Sorghum | 334–507 | 10–32 | 245–3900 | 3–10 |

Hemp | 128–270 | 5–20 | 156–295 | 0 |

Miscanthus | 260–530 | 12–66 | 152–252 | 0–15 |

Giant Reed | 240–600 | 11–75 | 167–227 | 0 |

Cardoon | 155–252 | 7–31 | 149–459 | 0–4 |

Switchgrass | 174–435 | 8–54 | 96–146 | 42 |

Crops | FSBI |
---|---|

Sweet Sorghum | 0.482–0.701 |

Hemp | 0.337–0.561 |

Miscanthus | 0.481–0.659 |

Giant Reed | 0.487–0.9 |

Cardoon | 0.303–0.482 |

Switchgrass | 0.288–0.482 |

## 5. Conclusions

## Conflicts of Interest

## References

- Mendoza, G.A.; Prabhu, R. Fuzzy methods for assessing criteria and indicators of sustainable forest management. Ecol. Econ.
**2003**, 3, 227–236. [Google Scholar] [CrossRef] - Pelt van, M.J.F.; Kuyvenhoven, A.; Nijkamp, P. Environmental sustainability: Issues and definition and measurement. Int. J. Environ. Pollut.
**1995**, 5, 204–223. [Google Scholar] - Heinen, J.T. Emerging, diverging and converging paradigms on sustainable development. Int. J. Sustain. Dev. World Ecol.
**1994**, 1, 22–33. [Google Scholar] [CrossRef] - Shearman, W. The meaning and ethics of sustainability. Environ. Manag.
**1997**, 14, 1–8. [Google Scholar] [CrossRef] - Mebratu, D. Sustainability and sustainable development: Historical and conceptual review. Environ. Impact Assess. Rev.
**1998**, 18, 493–520. [Google Scholar] [CrossRef] - Cavallaro, F. Assessment and Simulation Tools for Sustainable Energy Systems: Methodology and Applications; Springer-Verlag: London, UK, 2013. [Google Scholar]
- Cherubini, F. GHG balances of bioenergy systems–Overview of key steps in the production chain and methodological concerns. Renew. Ener.
**2010**, 35, 1565–1573. [Google Scholar] - Cherubini, F.; Strømman, A.H. Life cycle assessment of bioenergy systems: State of the art and future challenges. Bio. Tech.
**2011**, 102, 437–451. [Google Scholar] [CrossRef] [PubMed] - Cavallaro, F.; Ciraolo, L. Design and implementation of a fuzzy inference model for mapping the sustainability of energy crops. In Soft Computing Applications for Renewable Energy and Energy Efficiency; García-Cascales, M., Sánchez-Lozano, J.M., Masegosa, A.D., Cruz-Corona, C., Eds.; IGI Global: Hershey, PA, USA, 2015. [Google Scholar]
- Camastra, F.; Ciaramella, A.; Giovannelli, V.; Lener, M.; Rastelli, V.; Staiano, A.; Staiano, G.; Starace, A. A fuzzy decision system for genetically modified plant environmental risk assessment using Mamdani inference. Exp. Sys. App.
**2015**, 42, 1710–1716. [Google Scholar] [CrossRef] - Pappis, C.P.; Siettos, C.I. Fuzzy reasoning. In Introductory Tutorials in Optimization and Decision Support Techniques; Burke, E.K., Kendall, G., Eds.; Kluwer: Boston, MA, USA, 2005. [Google Scholar]
- Cornelissen, A.M.G.; van den Berg, J.; Koops, W.J.; Grossman, M.; Udo, H.M.J. Assessment of the contribution of sustainability indicators to sustainable development: A novel approach using fuzzy set theory. Agr. Eco. Env.
**2001**, 86, 173–185. [Google Scholar] [CrossRef] - Öztaysi, B.; Behret, H.; Kabak, Ö.; Uçal Sarı, I.; Kahraman, C. Fuzzy inference systems for disaster response. In Decision Aid Models for Disaster Management and Emergencies; Vitoriano, B., Montero, J., Ruan, D., Eds.; Atlantis-Springer: Amsterdam, Holland, 2013. [Google Scholar]
- Bezdek, J.C. Fuzzy models—What are they, and why? IEEE Trans. Fuzzy Sys.
**1993**, 1, 1–6. [Google Scholar] [CrossRef] - Dubois, D.; Esteva, F.; Godo, L.; Prade, H. Fuzzy-set based logics—An history-oriented presentation of their main developments. In Handbook of the History of Logic; Gabbay, D.M., Woods, J., Eds.; Elsevier: Amsterdam, The Netherlands, 2007. [Google Scholar]
- Klir, G.J.; Yuan, B. Fuzzy Sets and Fuzzy Logic—Theory and Applications; Prentice Hall: Upper Saddle River, NJ, USA, 1995. [Google Scholar]
- Tanaka, K. An Introduction to Fuzzy Logic for Practical Applications; Springer-Verlag: New York, NY, USA, 1991. [Google Scholar]
- Takagi, T.; Sugeno, M. Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Sys. Man. Cybern.
**1985**, 15, 116–132. [Google Scholar] [CrossRef] - Phillis, Y.A.; Andriantiatsaholiniaina, L.A. Sustainability: An ill-defined concept and its assessment using fuzzy logic. Ecol. Econ.
**2001**, 37, 435–456. [Google Scholar] [CrossRef] - Phillis, Y.A.; Grigoroudis, E.; Kouikoglou, V.S. Sustainability ranking and improvement of countries. Ecol. Econ.
**2011**, 70, 542–553. [Google Scholar] [CrossRef] - Phillis, Y.A.; Kouikoglou, V.S.; Andriantiatsaholiniaina, L.A. Sustainable development: A definition and assessment. Env. Eng. Manag. J.
**2003**, 2, 345–355. [Google Scholar] - William Ocampo-Duque, W.; Ferré-Huguet, N.; Domingo, J.L.; Schuhmacher, M. Assessing water quality in rivers with fuzzy inference systems: A case study. Env. Int.
**2006**, 32, 733–742. [Google Scholar] [CrossRef] [PubMed] - Icaga, Y. Fuzzy evaluation of water classification. Ecol. Indic.
**2007**, 7, 710–718. [Google Scholar] [CrossRef] - Lermontov, A.; Yokoyama, L.; Lermontov, M.; Machado, M.A.S. River quality analysis using fuzzy water quality index: Ribeira do Iguape river watershed, Brazil. Ecol. Indic.
**2009**, 9, 1188–1197. [Google Scholar] [CrossRef] - Fischer, B.E.A. Fuzzy approaches to environmental decisions: Application to air quality. Env. Sci. Pol.
**2006**, 9, 22–31. [Google Scholar] [CrossRef] - Prato, T. Adaptively managing wildlife for climate change: A fuzzy logic approach. Env. Manag.
**2011**, 48, 142–149. [Google Scholar] [CrossRef] [PubMed] - Marchini, A.; Facchinetti, T.; Mistri, M. F-IND: A framework to design fuzzy indices of environmental conditions. Eco. Indic.
**2009**, 9, 485–496. [Google Scholar] [CrossRef] - Gonzalez, B.; Adenso-Daz, B.; Gonzalez-Torre, P.L. A fuzzy logic approach for the impact assessment in LCA. Res. Cons. Rec.
**2002**, 37, 61–79. [Google Scholar] [CrossRef] - Silvert, W. Ecological impact classification with fuzzy sets. Ecol. Model.
**1997**, 96, 1–10. [Google Scholar] [CrossRef] - Takagi-Sugeno Fuzzy Modeling for Process Control. Available online: https://www.staff.ncl.ac.uk/damian.giaouris/pdf/IA%20Automation/TS%20FL%20tutorial.pdf (accessed on 15 June 2015).
- Venturi, P.; Venturi, G. Analysis of energy comparison for crops in European agricultural systems. Biom. Bioen
**2003**, 2, 235–255. [Google Scholar] [CrossRef] - Cavallaro, F.; Ciraolo, L. Fuzzy promethee for the environmental quality assessment of energy dedicated crops. In Computational Intelligence Applications in Industrial Engineering; Kahraman, C., Ed.; Atlantis & Springer: Amsterdam, Holland, 2012. [Google Scholar]
- Environmental Impact Assessment (EIA) of Energy Crops Production in Europe. Available online: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CB8QFjABahUKEwiformEx9rHAhXCDCwKHSWVADU&url=http%3a%2f%2fmoodle.fct.unl.pt%2fmod%2fresource%2fview.php%3fid%3d161317%26redirect%3d1&usg=AFQjCNH6ee_XJ_6iT98Rv2LTiKO3iatCHQ&bvm=bv.101800829,d.bGg&cad=rja (accessed on 26 August 2015).
- Wilson, C.; Tisdell, C. Why farmers continue to use pesticides despite environmental, health and sustainability costs. Ecol. Econ.
**2001**, 39, 449–462. [Google Scholar] [CrossRef] - Pimentel, D.; Acquay, H.; Biltonen, M.; Rice, P.; Silva, M.; Nelson, J.; Lipner, V.; Giordano, S.; Horowitz, A.; D’Amore, M. Environmental and economic costs of pesticide use. Bioscience
**1992**, 42, 750–760. [Google Scholar] [CrossRef] - Zimmermann, H.J. Fuzzy Set Theory and Its Application; Kluwer Academic Publishers: London, UK, 1991. [Google Scholar]

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**MDPI and ACS Style**

Cavallaro, F. A Takagi-Sugeno Fuzzy Inference System for Developing a Sustainability Index of Biomass. *Sustainability* **2015**, *7*, 12359-12371.
https://doi.org/10.3390/su70912359

**AMA Style**

Cavallaro F. A Takagi-Sugeno Fuzzy Inference System for Developing a Sustainability Index of Biomass. *Sustainability*. 2015; 7(9):12359-12371.
https://doi.org/10.3390/su70912359

**Chicago/Turabian Style**

Cavallaro, Fausto. 2015. "A Takagi-Sugeno Fuzzy Inference System for Developing a Sustainability Index of Biomass" *Sustainability* 7, no. 9: 12359-12371.
https://doi.org/10.3390/su70912359