Gianni Bellocchi

Gianni Bellocchi (born July 22, 1969) is a researcher in agricultural and related sciences. He is credited with the development of approaches and tools in validation of estimates and measurements. Introduction of fuzzy logic in the context of validation is often considered to be the most significant contribution to the field of model and method validation (Agronomy Journal, volume 94, pages 1222–1233 ; Food Analytical Methods, volume 2, pages 126-135 ).

He also helped spark the validation issues in agro-ecological modelling and analytical methods through his reviews of specialistic literature. His approach to the aggregation of multiple validation metrics has influenced the way validation results are viewed. In this respect he is credited with the establishment of hierarchy of preferences in validation and classification of models and methods in terms of aggregated, weighted metrics.

Biography

Gianni Bellocchi was born in Acquapendente and spent formative years in San Lorenzo Nuovo, in province of Viterbo (Italy), near Lago di Bolsena. His parents, Giuseppe (born 1944) and Adriana (born 1946), are retired farmers. He attended at primary and middle schools in his village, and at agricultural high school in Bagnoregio. Starting in 1988, he studied agricultural sciences at the University of Pisa and at the Sant'Anna School of Advanced Studies of Pisa. He graduated in 1993 and got a PhD in 1997. He learned statistical data processing and modelling approaches from entomologist Fabio Quaglia, physicist Franco Martorana, and modellers Frits W.T. Penning de Vries (Wageningen University, Netherlands) and Claudio O. Stockle (Washington State University, Pullman, Washington, U.S.). Gianni joined the staff of agronomy and agro-meteorology modelers of the Research Institute for Industrial Crops of Bologna in 1999, and developed a large number of scientific contributions under the leaderhsip of Marcello Donatelli. In 2006–2009 he was appointed contractual agent at European Commission - Joint Research Centre of Ispra, Italy. In 2010, he became senior scientist at French National Institute for Agricultural Research (INRA), Grassland Ecosystem Research Unit (UREP) and, as of February 1, 2014, research director. In 2011, January 25, he got the Habilitation à Diriger des Recherches from Blaise Pascal University of Clermont-Ferrand (France). He joined as member of the Italian Society for Agronomy, the European Society for Agronomy, the American Society of Agronomy, and the International Environmental Modelling and Software Society. As affiliated to the Monte Pino Met European Research Observatory, he is co-editor of the book "Storminess and Environmental Change" (Diodato and Bellocchi, 2014, Springer). Since November 1, 2013, he is coordinator of the project MODEXTREME of the 7th Framework Programme funded by the European Union.

Model and method validation

Bellocchi's work in validation has had implications for model and analytical method assessment. Genuine insights in model results, as well as results from an analytical method, imply concomitant understandings of multiple aspects of quality assessment to be taken into account and formalized. The fuzzy set theory formalized by Professor Lofti Zadeh at the University of California in 1965 was pointed out as having a direct use to assess numerical outcomes for its ability to aggregate multiple, possibly contradictory, evaluation measures. Many of the more basic principles of this theory are now generally accepted in many areas. Its application in a context of validation opened up to a new way to investigate results from a modelling process or an analytical method. In 2001, Bellocchi and co-workers firstly introduced the possibility to use fuzzy logic to evaluate model estimates at the Second International Symposium on Modelling Cropping Systems (Florence, Italy), and in 2002 the same approach was internationally acknowledged (Agronomy Journal, volume 94, pages 1222–1233). Further extensions and applications followed (as reported in Authorship).

Fuzzy logic

Main article: Fuzzy logic

Multiple-metric aggregation

The procedure based on the multi-valued fuzzy set introduced by Professor Lofti Zadeh, follows the Sugeno method of fuzzy inference (Information Sciences, volume 36, pages 59–83 ). Three membership classes are basically defined for all metrics used in the validation work, according to an expert judgment, i.e. Favorable (F), Unfavorable (U), and partial (or fuzzy) membership, using S-shaped curves as transition possibilities in the range F to U:

where: x = the value of the basic input; a = the lower bound of the transition interval [min(F, U)]; b = the upper bound of the transition interval [max(F, U)]; c = (a + b) /2. According to the equation, if a = F, then x ≤ a means x = F, and S(x;a;b) gives the degree of membership of the index value x to the set U. Its complement, 1 - S(x;a;b), gives the degree of membership of the index value x to the set F.

A two-stage design of a fuzzy-based rules' inferring system is applied where firstly inputs with similar characteristics are aggregated into modules and then, using the same procedure, the modules can be aggregated into a second level integrated index called indicator. Both modules and indicator range from 0 to 1.

The control rules for estimating module values are based on logic relationships between inputs and outputs, expressed in linguistic terms by 'if-then' statements. For example, when two input variables (validation metrics) are aggregated four rules are required, formalized as:

____PREMISE____CONCLUSION

if x1 is F and x2 is F then yi is B1

if x1 is F and x2 is U then y2 is B2

if x1 is U and x2 is F then y3 is B3

if x1 is U and x2 is U then y4 is B4

where xi is an input variable, yi is an output variable and Bi is a conclusion (or expert weight). The value of each conjunction (… and …) is the minimum of the quantified fuzzy groups, which are obtained from complementary S-shaped distribution curves.

The output fuzzy sets for all the rules are then aggregated into a single fuzzy set. This group encompasses a range of output values, and is de-fuzzified in order to resolve a single crisp output value from the group (i.e. a value between 0 and 1). This approach uses the centroid method to obtain the representative non-fuzzy value for the output, as commonly adopted in the Sugeno-type systems. The expert reasoning runs as follows: if all input variables are F, the value of the module is 0 (good response according to all metrics used); if all indices are U, the value of the module is 1 (bad response according to all inputs used), while all the other combinations assume intermediate values. Limits F and U may come from experience, may be extracted from literature, or may be set by law. The weights can be chosen based on the analyst own experience in handling each input.

Authorship (selected)

See a full bibliography on Bellocchi's web site .

Fuzzy logic and validation

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