16th IFAC Conference on Technology, Culture and International Stability 16th IFAC Conference on Technology,Available Culture and International online at www.sciencedirect.com 16th IFAC Conference Technology, Culture and International September 24-27, 2015.on Sozopol, Bulgaria Stability Stability September 24-27, 2015. Sozopol, Bulgaria September 24-27, 2015. Sozopol, Bulgaria
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A New Mathematical Modelling Approach for Viticulture and Winemaking Using A Approach for Viticulture A New New Mathematical Mathematical Modelling Modelling Approach for Maps Viticulture and and Winemaking Winemaking Using Using Fuzzy Cognitive Fuzzy Cognitive Maps Fuzzy Cognitive Maps
Groumpos P. Peter*. Anninou P. Antigoni* Groumpos P. P. Groumpos Vasileios.** Groumpos P. Peter*. Peter*.P.Anninou Anninou P. Antigoni* Antigoni* Vasileios.** Groumpos P. Groumpos P. Vasileios.** * Laboratory of Automation and Robotics, Department of Electrical and Computer Engineering, University of Patras, 26500 Laboratory * of Automation and Robotics, Department of Electrical Engineering, Rio, Greece, (e-mail: groumpos@ece.upatras.gr, anninou@ece.upatras.gr) * Laboratory of Automation and Robotics, Department of Electrical and and Computer Computer Engineering, University University of of Patras, Patras, 26500 26500 Rio, Greece, (e-mail: groumpos@ece.upatras.gr, anninou@ece.upatras.gr) ** Master Student, Agricultural University of Athens, Athens, Greece Rio, Greece, (e-mail: groumpos@ece.upatras.gr, anninou@ece.upatras.gr) ** ** Master Master Student, Student, Agricultural Agricultural University University of of Athens, Athens, Athens, Athens, Greece Greece Abstract: The aim of this paper is to present a new approach in modelling wine quality and quantity Abstract: The aim paper is new modelling wine and using Fuzzy Maps trained by non aalinear Hebbian in algorithm. The methodology Abstract: TheCognitive aim of of this this paper is to to present present new approach approach inlearning modelling wine quality quality and quantity quantity using Fuzzy Cognitive Maps trained by non linear Hebbian learning algorithm. The methodology described extracts the knowledge from the experts and exploits their experience on wine production. Two using Fuzzy Cognitive Maps trained by non linear Hebbian learning algorithm. The methodology described extracts the knowledge from the experts and exploits their experience on wine production. Two case studies with data from real vineyards were examined. The results of this study show that software described extracts the knowledge from the experts and exploits their experience on wine production. Two case with from vineyards were examined. The results of study show that software tools studies using Fuzzy Cognitive Maps could be explored further problems arise during wine case studies with data data from real real vineyards were examined. Theand results of this thisthat study show that the software tools using Fuzzy Cognitive Maps could be explored further and problems that arise during the wine production could be prevented by an efficient decision support system. tools using Fuzzy Cognitive Maps could be explored further and problems that arise during the wine production could be by decision support system. production could be prevented prevented by an an efficient efficient decision support system. © 2015, IFAC (International Federation ofFuzzy Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: wine quality, wine quantity, Cognitive Maps, viticulture, winemaking. Keywords: wine quality, wine quantity, Fuzzy Cognitive Maps, viticulture, winemaking. Keywords: wine quality, wine quantity, Fuzzy Cognitive Maps, viticulture, winemaking.
1. INTRODUCTION 1. INTRODUCTION Over the past ten or1.soINTRODUCTION years terms like, green, biodynamic, Over the past ten or so terms like, and biologique have become popular to Over the past ten or so years years termsincreasingly like, green, green, biodynamic, biodynamic, and biologique have become increasingly characterize vineyards and wineries from California and biologique have become increasingly popular popular to to characterize vineyards and wineries from California to Bordeaux, from New Zealand to Tuscany from South characterize vineyards and wineries fromandCalifornia to Bordeaux, from New Zealand to Tuscany and from South Africa to Greece as growers and winemakers have begun Bordeaux, from New Zealand to Tuscany and from South Africa to as and winemakers have paying to the of their practices on Africa increasing to Greece Greece attention as growers growers andimpact winemakers have begun begun paying increasing attention to the impact of their practices the environment. In addition in California since the late of paying increasing attention to the impact of their practices on on the environment. In addition in California since the late 2005, the term, sustainable agriculture, has begun to emerge. the environment. In addition in California since the late of of 2005, term, agriculture, begun emerge. Today I dare to sustainable challenge the scientifichas community the 2005, the the term, sustainable agriculture, has begun to to with emerge. Today II dare challenge term Todaysustainable dare to to Viticulture. challenge the the scientific scientific community community with with the the term sustainable Viticulture. term sustainable Viticulture. Environmental practices have been particularly important all Environmental practices have particularly important over the world and particularly in California. Over the past all 50 Environmental practices have been been particularly important all over the world and particularly in California. Over years there has been growing tension between agriculture over the world and particularly in California. Over the the past past 50 50 years has tension industrial thatgrowing are reluctant change agriculture and urban years there therepractices has been been growing tensiontobetween between agriculture industrial practices that change urban sprawl, has taken overreluctant much ofto wasand formerly industrialwhich practices that are are reluctant to what change and urban sprawl, which has taken over much of what was formerly prime farm land. Agricultural practices such as burning, flood sprawl, which has taken over much of what was formerly prime farm land. Agricultural practices such as burning, irrigation, pesticide spraying, groundwater, air contamination, prime farm land. Agricultural practices such as burning, flood flood irrigation, pesticide spraying, groundwater, air and other social, economic, and environmental problems have irrigation, pesticide spraying, groundwater, air contamination, contamination, and social, economic, and problems resulted increased government regulation, which have has and other other in social, economic, and environmental environmental problems have resulted in increased government regulation, which become an increasing burden on an already languishing resulted in increased government regulation, which has has become increasing agriculture become an anindustry. increasing burden burden on on an an already already languishing languishing agriculture industry. agriculture industry.to increasing government regulation and Partly in reaction Partly increasing government regulation and partly duereaction to an to increased awareness of the agriculture Partly in in reaction to increasing government regulation and partly due to an increased awareness of the agriculture industry’s social and environmental responsibility, there has partly due to an increased awareness of the agriculture industry’s social and environmental responsibility, there been movement toward sustainable agriculture practices. industry’s social and environmental responsibility, there has has been toward agriculture Sustainable agriculture characterized by a practices. systems been movement movement toward issustainable sustainable agriculture practices. Sustainable by systems perspective stewardshipis natural and human Sustainable ofagriculture agriculture is ofcharacterized characterized by aa resources systems perspective of stewardship of natural and human resources and comprises three goals – environmental health, economic perspective of stewardship of natural and human resources and three goals –– environmental health, economic profitability, economic equity. and comprises comprisesand threesocial goals and environmental health, Achieving economic profitability, and social and economic equity. Achieving sustainable agricultural practices is viewed as a process profitability, and social and economic equity. Achieving sustainable agricultural practices is viewed as a requiring small, realistic, and measurable steps. Due to the sustainable agricultural practices is viewed as a process process requiring small, realistic, and measurable steps. Due the peculiarities of specific agriculture sectors, it is requiring small, realistic, and measurable steps. Due to tovery the peculiarities of specific agriculture sectors, it is very important and necessary to treat every different agriculture peculiarities of specific agriculture sectors, it is very important important and and necessary necessary to to treat treat every every different different agriculture agriculture
sector with special care and attention. Such is the case of sector special care viticulture wine making. sector with withand special care and and attention. attention. Such Such is is the the case case of of viticulture and wine making. viticulture and wine making. Nowadays wine is increasingly enjoyed by a wider range of Nowadays enjoyed wider range consumers. Wineis quality is attributed to aa many Nowadays wine wine is increasingly increasingly enjoyed by by wider different range of of consumers. Wine quality is attributed to many different factors of the wine working collectively to bear a sensory consumers. Wine quality is attributed to many different factors collectively to experience thatwine is working not apparent from considering these factors of of the the wine working collectively to bear bear aa sensory sensory experience that is not apparent from considering components in isolation. The various chemical components in experience that is not apparent from considering these these components in isolation. The various chemical components wine give the wine its distinct taste and aroma. Appreciation components in isolation. The various chemical components in in wine give wine distinct taste aroma. of quality involves our innate winewine give the the wine its its distinct moving taste and and beyond aroma. Appreciation Appreciation of involves moving beyond preferences, (Orth, 2011), (Schamel, 2000). of wine wine quality quality involves moving beyond our our innate innate preferences, (Orth, 2011), (Schamel, 2000). preferences, (Orth, 2011), (Schamel, 2000). Certification prevents the illegal adulteration of wines (to Certification prevents the illegal adulteration of (to safeguard human health) assures quality for the wine Certification prevents the and illegal adulteration of wines wines (to safeguard human health) and assures quality for the wine market. Wine certification is often assessed by safeguard human health) and assures quality for the wine market. Wine certification is often assessed physicochemical and sensory tests. Physicochemical market. Wine certification is often assessed by by physicochemical and tests. laboratory tests routinely used to characterise wine include physicochemical and sensory sensory tests. Physicochemical Physicochemical laboratory used wine include determination density, alcohol pH values, while laboratory tests testsof routinely routinely used to toorcharacterise characterise wine sensory include determination of density, alcohol or pH values, while sensory tests rely mainly on human experts. It should be stressed that determination of density, alcohol or pH values, while sensory tests rely mainly on human experts. It should be stressed taste is the least understood of the human senses, thus wine tests rely mainly on human experts. It should be stressed that that taste of human thus classification is aunderstood difficult task. Moreover, the relationships taste is is the the least least understood of the the human senses, senses, thus wine wine classification aa difficult the relationships between the is and sensory are classification isphysicochemical difficult task. task. Moreover, Moreover, the analysis relationships between the physicochemical and sensory analysis complex and still not fully understood, Orth (2011). between the physicochemical and sensory analysis are are complex and still not fully understood, Orth (2011). complex and still not fully understood, Orth (2011). These difficulties could be dealt with the flourishing of new These could be with the of theories and techniques synergy fields provide These difficulties difficulties could that be dealt dealt withdiscipline the flourishing flourishing of new new theories and techniques that synergy discipline fields provide such as: Fuzzy Logic, Neural Networks, Neutrosophic, theories and techniques that synergy discipline fields provide such Logic, Neural Neutrosophic, Genetic Algorithms, Reasoning, Soft such as: as: Fuzzy Fuzzy Logic, Probabilistic Neural Networks, Networks, Neutrosophic, Genetic Algorithms, Probabilistic Reasoning, Computing Techniques, Intelligent Control (IC) and Fuzzy Genetic Algorithms, Probabilistic Reasoning, Soft Soft Computing Techniques, Cognitive (FCM). Intelligent ComputingMaps Techniques, Intelligent Control Control (IC) (IC) and and Fuzzy Fuzzy Cognitive Maps Cognitive Mapsa (FCM). (FCM). In this paper new mathematical modelling approach of In this paper a modelling viticulture and winemaking will be implemented in order of to In this paper a new new mathematical mathematical modelling approach approach of viticulture and winemaking will be implemented in order check the quality and quantity of the produced wine. Two viticulture and winemaking will be implemented in order to to check the and quantity the Two case with data real of vineyards will bewine. examined checkstudies the quality quality and from quantity of the produced produced wine. Two case with data from will examined so to test andvineyards simulation results with caseasstudies studies withour data model from real real vineyards will be be examined so as to test our model and simulation results conclusions will be presented. so as to test our model and simulation results with with conclusions conclusions will will be be presented. presented.
2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2015, IFAC 2015 15 Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. Copyright © IFAC 2015 15 10.1016/j.ifacol.2015.12.049 Copyright © IFAC 2015 15
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2. BASIC OF VITICULTURE AND WINE MAKING
Brazil
3.5
-1%
92
0%
Wine has been around for a long time since the ancient times. Before water was safe to drink, beverages like wine helped to sustain mankind. In many cases in the ancient times wine was used for medical purposes, which is true even today. Dr. Patrick McGovern, an archeochemist at the University of Pennsylvania observed, with reference to the symposia of ancient Greece, that wine was a beverage that “greased the skids” of Western civilization. Beginning with the hawthorns berries that were used to make a fermented drink nine thousand years ago in China, and continuing with the cultivation of grapes by the Egyptians, Greeks and Romans, wine has formed an integral part of the culinary, religious, and social history of man. We have evidence that the ancient Babylonians and Egyptians practiced viticulture, while the Greeks were the first to conduct a brisk industry and trade in wine. Afterwards the Greeks passed wine to the Romans who in return pushed the grape into France and Germany, thereby planting the seeds of the tradition that is so venerated today. Despite this long history, the fundamentals of winemaking and the plant itself have not changed; wine is still fermented by yeast using grapes of the same botanical origin as those that existed millennia ago. Wine and other alcoholic products always accompanied territorial expansion. History wants William Penn to bring vines with him when he arrived in the New World in 1684. However historically one thing cannot be disputed: viticulture and winemaking was originated on East and mainly in the East Mediterranean regions. Table 1 shows the top 16 wine-producing countries and the total vineyard area in 2011 (Fraga and al. 2012).
Greece
2.6
-26%
111
-6%
Hungary
2.4
-24%
65
-13%
New Zealand
2.4
59%
37
21%
Bulgaria
1.3
-29%
73
-22%
We now live in a global age of viticulture and enology, extending from Italy, France, Greece and Germany in the Old World to new regions such as Australia, South America, United States and even in the Far East New Zealand. They all are employing and refining modern viticultural methods that have improved wine quality and contributed to an increasingly competitive marketplace. For example, vertical shoot positioned training has replaced many traditional systems and is now used in almost all of the great winemaking regions. Such shared practices and methods are just one reason why wine is so fascinating. We can now make direct comparisons between Cabernet Sauvignon grown on the left bank in Bordeaux with that grown in Virginia or Napa Valley of USA or Marlborough of New Zealand. Viticulture and enology speak a common language, and wine growers can travel to different countries to talk shop and learn something new. So while the wine industry in the East (its birthplace) is still in its infancy, relatively speaking, it has access to the same knowledge and technology that is being used in the great vineyards of the world. Most vineyards start with a love of wine, and an idea that turns into a passion, but after the light bulb has been switched on … where does one start? Most people who contact the cooperative extension service for advice about grape growing are at the mid-point or near the end of their professional careers, when a vineyard and life as a gentleman farmer as a retirement business or serious hobby looks extremely attractive. A top consultant describes his typical client as “educated, wealthy, ambitious and burned-out.” The timeless and irresistible allure of wine is understandable, but the truth to be faced is that if you have come to wine and agriculture later in your life, you will have to overcome immense producing countries in 2011.
Table 1. Top 16 wine-producing countries in 2011 (with respective growth rate from 2007). Total vineyard area in 2011 is also shown (with respective growth rate from 2007). Country
Wine production (Mhl)/ growth rate
Vine area (mha)/ growth rate
France
49.6
9%
807
-7%
Italy
41.6
10%
776
-6%
Spain
34.3
-1%
1032
-4%
USA
18.7
-6%
405
2%
Argentina
15.5
3%
218
-4%
China
13.2
6%
560
4%
Australia
11.0
14%
174
0%
Chile
10.6
29%
202
3%
South Africa
9.3
-1%
131
-12%
Portugal
5.9
-2%
240
-3%
Romania
4.7
-11%
204
0%
3. FUZZY COGNITIVE MAPS-NON LINEAR HEBBIAN LEARNING The method that will be used in order to model wine production is Fuzzy Cognitive Maps, trained with non linear Hebbian learning algorithm (Anninou and Groumpos, 2014). This algorithm is described by the following steps: Step 1: Read input state A0 and initial weight matrix W0 Step 2: Repeat for each iteration step k 2.1: Calculate Ai according to (1) Ai ( k 1)
N
f (k2 Ai ( k ) k1 Aj ( k ) w ji ) j i j 1
2.2: Update Wij(k) according to (2)
16
(1)
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wish to produce. It is based on the physiological and technological maturity of the grapes which is calculated with checks carried out on representative samples of grapes. The early harvest will give us fine wines with low alcohol content while late harvesting would give us wines with high alcohol content and low acidity. The different grape varieties and local and annual weather conditions unavoidably affect the date (Golan and Shalit, 1993).
(2) Step 3: Repeat until the termination conditions are met Step 4: Return the final weights Wfinal and concept values in convergence region Ai(k+1) is the value of the concept Ci at the iteration step k+1, Ai(k) is the value of the concept Cj at the iteration step k, Wij is the weight of interconnection from concept Ci to concept Cj and f is the sigmoid function. “k1” expresses the influence of the interconnected concepts in the configuration of the new value of the concept Ai and k2 represents the proportion of the contribution of the previous value of the concept in the computation of the new value (Groumpos, 2010),(Groumpos and Stylios, 2000).
There are many aspects of grape maturity that determine the best time to harvest wine grapes. Some of these are quantitative and can be determined to a high degree of numerical accuracy, and others are qualitative and are more subjective. There is also a wide variance of maturity time from one varietal to another. Qualitative indicators of grape maturity include appearance of the grapes including the color and firmness of the skins, the appearance of the stems, the color and taste of the seeds, the taste of the grapes and the condition of the vines and leaves. Current and expected weather conditions also play a role in deciding when to pick.
The sigmoid function f belongs to the family of squeezing functions, and the following function is usually used to describe it (Papageorgiou, 2013): f
1 1 e x
17
(3)
Quantitative indicators include measurements of the actual chemistry of the grape itself. They include the analysis of pH, and titratable acid (TA). These indicators are useful in determining if a wine is balanced.
This is the unipolar sigmoid function, in which λ>0 determines the steepness of the continuous function f(x). The parameter h is the learning rate and g is the weight decay parameter. These parameters ensure that the learning process converges quickly in a desired state.
Pruning is one of the most important procedures in vineyard. The reasons why to prune are the following:
FCMs lead to the proposed decision making approach following the experts’ knowledge strictly (Groumpos and Anninou, 2012), (Runkler, 1997). 4. A FCM FOR WINE MAKING Weather conditions at any moment act decisively, positive or negative, in the process of growth of the vine and the ripening of the grape and therefore predetermine the quality of wine to be produced. More specifically rainfall rate in conjunction of course with the absorbency of the soil, determines the available water quantities. If these quantities are very small circulation of nutrients within the plant is not possible. But if on the other hand they are extravagant we have quality degradation due to increased production. Rainfalls are necessary in the winter months for stockpiling that will help the plant in dry summer months. Around 27 inches of rainfall throughout the year in order to produce grapes are suitable for winemaking. In ideal circumstances the vine will receive most of the rainfall during the winter and spring months. But a rainfall before the harvest can be fatal, because, due to the wet and warm atmosphere the development of diseases, that also leads to the destruction of production, is favored (Rodo and Comin, 2000). So the concept of “rainfall before the harvest” is necessary for our model.
Maintain vine form
Regulate the number and positions of shoots on a vine, and cluster number and size.
Improve fruit quality and stabilize production over time.
Improve bud fruitfulness by bud selection and placement.
Pruning of grapevines is recommended anytime after leaf fall, which may occur late fall or throughout the winter. Once the leaves fall, the vascular system becomes inactive and plugs up. Before this time, minerals and carbohydrates are transferred from the leaves into the permanent, woody structures of the vine for winter storage. For this reason, pruning before leaf fall can affect storage leading to mineral deficiencies and poor bud maturation, which can affect the growth of the vine and the crop in the following season. Timing of pruning within the dormant season may also affect the time of bud break. Vines pruned very late in the season usually start spring growth slightly later than those pruned mid-dormancy. The rest of the concepts are (Clarke and Bakker, 2004): Soil and vineyard are basic parts of a single chain, which starts in the vineyard and ends in a wine bottle, (Gladstones, 1999). The concept of 'territory' (territoir) is the result of the following three natural parameters: subsoil and the bedrock
The harvesting of wine grapes is one of the most crucial steps in the process of winemaking. The time of harvest is determined primarily by the ripeness of the grape as measured by sugar, acid and tannin levels with winemakers basing their decision to pick based on the style of wine they 17
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C1: The special characteristics of the soil
from which it derives, the topography of the area and the climate that interferes with the evolution of the ‘territory’.
C2: The climatic conditions in the region's vineyard
The climate of each region is a component of several factors. The main factors are: latitude, average temperatures during the year, altitude, humidity, levels of sunshine and wind, water masses, etc. The climatic conditions prevailing in an area affect the growth of the vine and the quality of wine as well. The cold, the heat, the sun, the rain have a positive or a negative impact on the development of the vine and the maturation of the grapes and thus can predefine the quality of the wine that will be produced. The volume of rainfall in combination of course with the absorbency of the ground and the winds indirectly affect the quality of wine.
C3: The grape variety C4: The Human Factor (cultivation tasks and farming cares in the vineyard) C5: The Alcoholic Fermentation C6: Diseases, alterations and deterioration of the quality of the wine C7: Additional Oenological Substances to wine C8: The Storage of wine in barrels
The grape variety is one of the most important factors that influence or determine the type, the distinct aroma and the flavor of wine that will be produced. The size of the grape berry, the composition and the color of the crust, the texture, the ratio of sugars and acids etc. depend directly on the genetic traits of each vineyard.
C9: The Maturation - Aging of wine C10: Rainfall before the Harvest C11: Time of Harvest C12: Pruning
For centuries, vine and man are tied to an interactive relationship, as regards the production of wine. The wine grower can enhance the soil ingredients by applying many cultivation techniques and farming cares, either natural (eg. plowing, pruning) or chemical (eg. annual fertilization, protection from diseases and pests). He can choose the grape variety and also the planting density so it could be suitably adapted to the environment.
C13 (Output): Wine Quality C14 (Output): Wine Quantity Experts after assessing and evaluating the relationships between concepts conclude to the Table 2. A Fuzzy Cognitive Map model is illustrated in Fig. 1.
The alcoholic fermentation is the conversion process of fresh grape juice into wine and is the most critical point of winemaking. The alcoholic fermentation caused by yeasts (yeast), single-celled organisms that are found in the crust of the grape and have penetrated into the juice. Their main job is to convert the sugars of fresh juice of the grape into alcohol. The wine may possibly has diseases due to other microorganisms that are aerobic or anaerobic while other alterations of the wine are usually due to a bad winemaking practice. In an effort to limit the growth of undesirable microorganisms found in the wine and to keep the conduct of the alcoholic fermentation smooth, we use certain additional oenological substances that will help both to produce a qualitative wine and to keep it in good condition.
Fig. 1. Fuzzy Cognitive Map Model 5. CASE STUDIES
The storage conditions of wine in the barrel such as its exposure, the material of the barrel, the level of humidity, the temperature, the ventilation provided, the blocking of other odors, the appropriate lighting, etc. significantly affect the quality of the wine.
5.1 First Case Vineyard in Patras with ideal soil features has climate characteristics for 2014 shown in the following figures (Anon, 2015):
The maturation-aging of the wine is a great and interesting process, in which many changes in color, smell and taste occur. As long as the wine stays in the cellar, it loses its "harshness" and becomes "soft" in taste, it also loses the smell of "yeast" and acquires a fragrance, which, with the passage of time, becomes more complex. So we conclude to the following concepts:
Fig. 2. Rainy Days in Patras. 18
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Table 2. Linguistic Variables describing the relationships between concepts
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14
C1 S0 W W W -
C2 W -
C3 VS S M -
C4 M VS W W -
C5 M S S M S S W -
C6 M S M S W S M M M -
C7 M W M M M VS -
C8 M W W M -
C9 M M S W W M S S -
C10 -
C11 -
C12 -
C13 VS VS VS VS S S S VS VS VS VS VS -H
C14 S S S S S VS VS VS VS -H -
the produced wine would be the best possible. This result is validated by the statistics of Achaia Clauss, a Greek winery located in Patras, in Peloponnese. 5.2 Second Case In 2014 wine producers in Italy faced their worst grape harvest for more than half a century due to an unusually wet spring and summer. Thus we will examine Puglia, where the production was reduced up to 30% that year.
Fig. 3. Min and Max Temperatures in Patras.
That year’s harvest started later than usual because of the poor weather and continued until late October. So concepts C10 and C11 were most affected.
The grape variety is Roditis which is a rose colored grape. The time of harvest is by the end of September and pruning was implemented in March.
By examining the growth conditions of Bombino Bianco and implementing them in order to validate the production, indeed the wine quality and quantity were influenced.
By using these information to extract the initial values of input concepts, we conclude to the simulation results illustrated in the next figure:
Simulation results are illustrated in Fig. 5
Fig. 4. Simulation Results till Convergence.
Fig. 5. Simulation Results till Convergence
With these almost perfect conditions the quality and quantity of the wine (C13, C14) are the best. Both values of these two concepts are over 0.9. That means that there is no doubt that by following these conditions the results of
In that case quantity is affected most as its value is the lowest in the equilibrium point (C14= 0.3320). That ensures that quantity will be limited with the specific data. As far as quality is concerned it is not so affected 19
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(C13=0.68) so that means that the quality in that year’s production is satisfactory.
maps. Chaos, Solitons & Fractals, 11(1-3), pp.329336. Orth, U. (2001). Quality signals in wine marketing: the role of exhibition awards. The International Food and Agribusiness Management Review, 4(4), pp.385-397. Papageorgiou, E. (2013) Fuzzy cognitive maps for applied sciences and engineering. Rodo, X. and Comin, F. (2000). Links between large-scale anomalies, rainfall and wine quality in the Iberian Peninsula during the last three decades. Global Change Biol, 6(3), pp.267-273. Runkler, T. (1997). Selection of appropriate defuzzification methods using application specific properties. IEEE Trans. Fuzzy Syst., 5(1), pp.72-79. Schamel, G. (2000). Individual and collective reputation indicators of wine quality. Adelaide: Centre for International Economic Studies.
6. CONCLUSIONS In this paper, the mathematical theories and tools of FCM, developed previously, have been used to theoretically model the wine quality and quantity. The proposed model provides a total new approach which is clear, simple, userfriendly, real time, easily accessible, fast, reliable and of low-cost. In addition the aforementioned software tool can support the laboratories to have on their desk a first evaluation of the wine that they are going to inspect. The interesting results obtained here show new and promising future research areas. More simulations are necessary in order to ensure the good wine production. 7. ACKNOWLEDGMENTS The work of the second author, Ms Antigoni Anninou, a Ph.D student at the Department of Electrical and Computer Engineering, was financially supported by the “Andreas Mentzelopoulos Scholarships University of Patras”. REFERENCES Anninou, A. and Groumpos, P. (2014). Modeling of Parkinson's Disease Using Fuzzy Cognitive Maps and Non-Linear Hebbian Learning. International Journal on Artificial Intelligence Tools, 23(05), p.1450010. Anon, (2015). [online] Available at: Weather-andclimate.com, 'Weather and Climate: Patras, Greece, average monthly, Rainfall (millimeter), Sunshine, Temperatures (celsius), Sunshine, Humidity, Water Temperature, Wind Speed', 2015. [Online]. Available: http://www.weather-and-climate.com/averagemonthly-Rainfall-TemperatureSunshine,Patras,Greece. [Accessed 31 Jul. 2015]. Clarke, R. and Bakker, J. (2004). Wine flavour chemistry. Oxford, UK: Blackwell Pub. Fraga, H., Malheiro, A., Moutinho-Pereira, J. and Santos, J. (2012). An overview of climate change impacts on European viticulture. Food Energy Secur, 1(2), pp.94110. Gladstones, J. (1999). Viticulture and environment. Adelaide: Winetitles. Golan, A. and Shalit, H. (1993). Wine Quality Differentials in Hedonic Grape Pricing. Journal of Agricultural Economics, 44(2), pp.311-321. Groumpos, P. (2010). Fuzzy Cognitive Maps: Basic Theories and their Application to Complex Systems. In: M. Glykas, ed., Fuzzy Cognitive Maps: Advances in Theory, Methodologies, Tools and Applications., 4th ed. Heidelberg: Springer-Verlag Berlin, pp.1-22. Groumpos, P. and Anninou, A. (2012). A theoretical mathematical modeling of Parkinson’s disease using Fuzzy Cognitive Maps. In: International Conference on Bioinformatics and Bioengineering (BIBE 2012). pp.677-682. Groumpos, P. and Stylios, C. (2000). Modelling supervisory control systems using fuzzy cognitive
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