Magyar Internetes Agrárinformatikai Újság No 04	HU ISSN 1419-1652
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There should be found an adequate (best) problem solver method to the problem. There should be defined the types of problems and the types of methods.

The sets of the potential methods/problems contains infinite elements. The sets of well-know methods/problems contains relative few number of elements.

It is presumably not possible defining an absolute universal type of problem-description and problem solver. An UPT must be capable to describe all inputs of all problem-situations. A GPS must to capable of finding the best type of connection between inputs and outputs for all problems.

Creating a possibly universal problem type (PUPT). An input structure with object-attribute-time co-ordinates opens the way to describe a large bundle of problem situation.

To create a possibly general problem-solver method (PGPS). The context free methods (incl. AI-methods and statistical-mathematical methods for classification) makes possible to test one or more function types and parameter combinations.

The theory of neural (abductive) classification (Peirce, 1955) describes explicitly a PUPT. Here can be identified the combinatorial principle: To the object-attribute-structure of inputs must be define a set of attributes and a the set of options/values pro attribute. This applies to the set of output attributes yet.

PUPT

The input sets define a combinatorial space (ex. deductive decision table or input-output pattern of neural networks). This combinatorial space contains a set of analogies. On the base of this analog cases it is possible finding a generalisation. This generalisation (connection, function) is capable to define the conclusion of unknown cases (new input situation) yet. The base question in a PUPT is: What is the value or trend of change of attributes in all objects in the future, assumed that a lot of last values of the attributes are well-known. (Using of triangular input-structures is possible yet, if the functions and the criteria are appropriate.)

PGPS: Meta interpretation of methods for classification, simulation and construction

The potential connections between inputs and outputs (functions) have positions for variables, operators and parameters. The combinatorial space of solutions is infinite, because of the length of the operator-variable-chains are unrestricted. This chains can be interpreted as a computer program. All chains have to accept the input structure fully or partially. All chains have to give complete outputs for all input objects. All context free methods make possible to realise the automatical knowledge acquisition (ex.: from a simple regression analysis to the neural networks).

Since this combinatorial logic (for input structure and functions) it makes possible comparing all of the methods for classification problems (Neural Networks, Fuzzy Methods, GA, AL, Time Series Analysis, Discrim. Analysis, Cluster methods, Box Jenkins, etc. - Deutscher-Tiemann, 1995, Pitlik, 1993). All methods can be described according to operator-variable-chains. The differences between the methods due to on which way (heuristical selection) the start sets (of inputs, potential functions and criteria) are assembled for searching in the combinatorial space.

Criteria for validation and verification and selection of functions as solutions

To find the best method in a problem situation is necessary having a set of criteria (ex.: correlation coefficients). On the base of this criteria it is possible to make a rank of potential connections between inputs and outputs. The best connection must be capable to transfer the good learn-fitting to the test cases (Fig. 1.). A good fitting in the learning phase does not lead necessarily into a good approximation in the test phase. A step-wise search (ex.: evolution strategy) in the combinatorial space of functions must to lead defining a series of functions, which have parallel development of learn and test error in trend, but not necessarily for each training-test couples. The best system of criteria is unknown. The sets of the potential criteria contains infinite elements.

Fig. 1. Sequential development of learn an test fitting
 

The following picture (Fig. 2.) presents a simple flow-chart of the software “Function-Generator” (software). This algorithm generate operator-variable-chains according to the principles of the evolution strategy, if the sets of inputs, criteria and the rules for building of chains are determinated. A new chain can be realised as a modification of previous version (deleting and adding sequences, mutation, cross-over, etc.) without a population of functions (genetic algorithm vs. this “biotechnological” algorithm). With this method it is possible using simultaneously the numerical and logical operators and the any parentheses-structures.

Fig. 2. Flow-chart of building of functions according to the combinatorial principle
 

Alternative Methods of Function-Generator

Special-Model: Pattern-Generator (Prototype): Inputs = Object-attribute-time-matrix. Algorithm = Generating artificial time series of inputs, Combination of attributes according to Function-Generator, Evaluation of the generated time series according to trend analysis, Searching for best-fitting combinations of attributes

Complete-Model: Future-Generator (Prototype): Inputs = Object-attribute-time-matrix with modification. Modification = Transformation of base-values according to their co-ordinates and co-ordinates of question fields to obtain definition of a new object-attribute-matrix. New attributes = Fields in original matrix (time = 1,...,t). New objects = Question fields (time = t+1). Algorithm = Identical with Function-Generator

Hybrid-Model: Weight-Activity-Model (WAM). Inputs = Object-attribute-matrix. Steps of transformation: Definition of thresholds of attributes for building of activities (= numerical operators). Building of connections between attributes (AND: logical operator). Change of values in the input matrix to activities according to the thresholds of attributes. Searching of weights (random) according to activities and attributes. Integration of weights and activities as a functions. Classification of cases according to the values of this function. Find the best function.

The intuition of human is used to define the combinatorial space of inputs (description of the problem situation), criteria (for selection, validation, verification) and potential type of functions. The speed of the search is dependent on the fitting of this heuristical definitions.

Examples for Function-Generator

Question: What is the trend of change (+ or -) in a share in 5 days, when the data of the 30 last days (time series) are well-known. Number of input patterns: 7 (maximum-, minimum-, last-price, trend, difference between max.- and last-price and min.- and last-price). Number of cases for training: 18. Number of test-cases: 17. Fitting of solution: 65% in the learn phase, 72% in the testing phase (Pitlik, 1993).

Question: What is the trend of change (+ or -) of the price and mass of eggs in 3 days on the market, if data-series of the 40 last days (time series) for maximum-, minimum-, average-price and mass of eggs are well-known. Number of input patterns: 160. Number of cases for training: 98. Number of test-cases: 98. Fitting of solution for price and mass of eggs: 86% and 81% in the learn phase, 65% and 70% in the testing phase (Szabó, 1994).

Question: What is the trend of change (+ or -) of the sum of temperature in 1 month, if data of the 12 last months (time series) for precipitation and temperature are well-known. Number of input patterns: 23. Number of cases for training: 30. Number of test-cases: 16. Fitting of solution according to 2 outputs: 73% in the learning phase, 81% in the testing phase. Fitting of solution according to 3 output categories: 21/30 and 10/16 (Pitlik, 1993).

Fig. 3. A simple and short solution of temperature forecast for 1 month (Pitlik, 1993)

Question: Brings the tomato production with irrigation more yields as a threshold or not in 1 year, if data of the 1 last year (time series) for base 3-daily weather attributes are well-known. Number of input patterns: 183. Number of cases for training: 20. Number of test-cases: 12. Fitting of classification: 100% in the learning and in the testing phase (Popovics, 1995).

Question: What is the trend of change (+ or -) of the sum of temperature in 6 months, if data of the 9 last years (time series) for temperature are well-known. Number of input patterns: 14. Number of cases for training: 24. Number of test-cases: 10. Fitting of solutions: 80% in the learning phase, 80% in the testing phase. The identical fittings was detected with the Weight-Activity-Model (Pitlik, 1993).

Question: What is the potential value of the yield of maize in 10 months, if agricultural data of the 3 last years and data of technology in the production-year are well-known. Number of input patterns: 47. Number of cases for training: 48. Number of test-cases: 16. Fitting of solution: average value of absolute differences between estimations and observations < 1 t/ha parallel with the test and the learn phases (Pitlik, 1993).

Examples for Pattern- and Future-Generator

Question: What is the trend of change (+ or -) of production, export and import of agricultural product (3*4) in diverse countries (11) in 1 year, if data of the 2-11 last years (time series) are well-known. Dimension of input matrix: (12*11*11). Number of input patterns: 2-800. Number of cases for training: 2-6. Number of test cases: 2-6. Fitting of solution: » 80% in the learn phase, 80% in the test phase (Pásztor, 1994, 1995).

Types of potential applications

Classification of cases according to anticipatory fitting of estimation for this cases. The question of adaptive modification of function according to the new cases and attributes is open to debates.
 

Az utolsó módosítás: 2005.05.29.
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