• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1041-1043
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• 1993

Fuzzy logic based Control Theory has gained much interest in the industrial world, thanks to its ability to formalize and solve in a very natural way many problems that are very difficult to quantify at an analytical level. This paper shows a solution for treating membership function inside hardware circuits. The proposed hardware structure optimizes the memoried size by using particular form of the vectorial representation. The process of memorizing fuzzy sets, i.e. their membership function, has always been one of the more problematic issues for the hardware implementation, due to the quite large memory space that is needed. To simplify such an implementation, it is commonly [1,2,8,9,10,11] used to limit the membership functions either to those having triangular or trapezoidal shape, or pre-definite shape. These kinds of functions are able to cover a large spectrum of applications with a limited usage of memory, since they can be memorized by specifying very few parameters ( ight, base, critical points, etc.). This however results in a loss of computational power due to computation on the medium points. A solution to this problem is obtained by discretizing the universe of discourse U, i.e. by fixing a finite number of points and memorizing the value of the membership functions on such points [3,10,14,15]. Such a solution provides a satisfying computational speed, a very high precision of definitions and gives the users the opportunity to choose membership functions of any shape. However, a significant memory waste can as well be registered. It is indeed possible that for each of the given fuzzy sets many elements of the universe of discourse have a membership value equal to zero. It has also been noticed that almost in all cases common points among fuzzy sets, i.e. points with non null membership values are very few. More specifically, in many applications, for each element u of U, there exists at most three fuzzy sets for which the membership value is ot null [3,5,6,7,12,13]. Our proposal is based on such hypotheses. Moreover, we use a technique that even though it does not restrict the shapes of membership functions, it reduces strongly the computational time for the membership values and optimizes the function memorization. In figure 1 it is represented a term set whose characteristics are common for fuzzy controllers and to which we will refer in the following. The above term set has a universe of discourse with 128 elements (so to have a good resolution), 8 fuzzy sets that describe the term set, 32 levels of discretization for the membership values. Clearly, the number of bits necessary for the given specifications are 5 for 32 truth levels, 3 for 8 membership functions and 7 for 128 levels of resolution. The memory depth is given by the dimension of the universe of the discourse (128 in our case) and it will be represented by the memory rows. The length of a world of memory is defined by: Length = nem (dm(m)＋dm(fm) Where: fm is the maximum number of non null values in every element of the universe of the discourse, dm(m) is the dimension of the values of the membership function m, dm(fm) is the dimension of the word to represent the index of the highest membership function. In our case then Length=24. The memory dimension is therefore 128*24 bits. If we had chosen to memorize all values of the membership functions we would have needed to memorize on each memory row the membership value of each element. Fuzzy sets word dimension is 8*5 bits. Therefore, the dimension of the memory would have been 128*40 bits. Coherently with our hypothesis, in fig. 1 each element of universe of the discourse has a non null membership value on at most three fuzzy sets. Focusing on the elements 32,64,96 of the universe of discourse, they will be memorized as follows: The computation of the rule weights is done by comparing those bits that represent the index of the membership function, with the word of the program memor . The output bus of the Program Memory (μCOD), is given as input a comparator (Combinatory Net). If the index is equal to the bus value then one of the non null weight derives from the rule and it is produced as output, otherwise the output is zero (fig. 2). It is clear, that the memory dimension of the antecedent is in this way reduced since only non null values are memorized. Moreover, the time performance of the system is equivalent to the performance of a system using vectorial memorization of all weights. The dimensioning of the word is influenced by some parameters of the input variable. The most important parameter is the maximum number membership functions (nfm) having a non null value in each element of the universe of discourse. From our study in the field of fuzzy system, we see that typically nfm 3 and there are at most 16 membership function. At any rate, such a value can be increased up to the physical dimensional limit of the antecedent memory. A less important role n the optimization process of the word dimension is played by the number of membership functions defined for each linguistic term. The table below shows the request word dimension as a function of such parameters and compares our proposed method with the method of vectorial memorization[10]. Summing up, the characteristics of our method are: Users are not restricted to membership functions with specific shapes. The number of the fuzzy sets and the resolution of the vertical axis have a very small influence in increasing memory space. Weight computations are done by combinatorial network and therefore the time performance of the system is equivalent to the one of the vectorial method. The number of non null membership values on any element of the universe of discourse is limited. Such a constraint is usually non very restrictive since many controllers obtain a good precision with only three non null weights. The method here briefly described has been adopted by our group in the design of an optimized version of the coprocessor described in [10].

• KOREAN JOURNAL OF CROP SCIENCE
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• v.8 no.1
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• pp.129-177
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• 1970

For the purpose of establishing the systematized technical scheme of the cooperative rice cultivation which has most significant impact to improve rice productivity and the farm management, the author have studied the cultivation practices, and the variation of rice growth and yield between the cooperative rice cultivation and the individual rice cultivation at random selected 18 paddy fields. The author also have investigated through comparative method on the cultivation practices, management, organization and operation scheme of the two different rice cultivation methods at 460 paddy fields. The economic feasibility has been ana lysed and added in this report. The results obtained from this study are summarized as follows; 1. In the nursery, the average amount of fertilizer application, especially, phosphate and potassium, and the frequency of chemicals spray for the disease, insect and pest control at the cooperative rice cultivation are significantly higher than those of the individual rice cultivation. 2. The cultivation techniques of the cooperative rice farming after the transplanting can be characterized by a) the earlier transplanting of rice, b) the denser hills per unit area and the lesser number of seedlings per hill, c) the application of larger quantities of fertilizer including nitrogen, phosphate and potassium, d) more divided application of fertilizers, split doses of the nitrogen and potassium, e) the increased frequencies of the chemicals spray for the prevention of disease, insect and pest damages. 3. The rate of lodging in the cooperative rice cultivation was slightly higher than that of the individual rice cultivation, however, the losses of rice yield owing to the occurrence of rice stem borer and grass leaf roller in the cooperative rice cultivation were lower than that of the individual rice cultivation. 4. The culm length, panicle length, straw weight and grain-straw ratio are respectively higher at the cooperative rice cultivation, moreover, the higher variation of the above factors due to different localities of the paddy fields found at the individual rice cultivation. 5. The number of panicles, number of flowers per panicle and the weight of 1, 000 grains, those contributing components to the rice yield were significantly greater in the cooperative rice cultivation, however, not clear difference in the maturing rate was observed. The variation coefficient of the yield component in the cooperative cultivation showed lower than that or the individual rice cultivation. 6. The average yield of brown rice per 10 are in the cooperative rice cultivation obtained 459.0 kilograms while that of the individual rice cultivation brought 374.8 kilograms. The yield of brown rice in the cooperative rice cultivation increased 84.2 kilogram per 10 are over the individual rice cultivation. With lower variation coefficient of the brown rice yield in the cooperative rice cultivation, it can be said that uniformed higher yield could be obtained through the cooperative rice cultivation. 7. Highly significant positive correlations shown between the seeding date and the number of flowers per panicle, the chemical spray and the number of flowers per panicle, the transplanting date and the number of flowers per panicle, phosphate application and yield, potassium application and maturing rate, the split application of fertilizers and yield. Whilst the significant negative correlation was shown between the transplanting date and the maturing rate 8. The results of investigation from 480 paddy fields obtained through comparative method on the following items are identical in general with those obtained at 18 paddy fields: Application of fertilizers, chemical spray for the control of disease, insects and pests both in the nursery and the paddy field, transplanting date, transplanting density, split application of fertilizers and yield n the paddy fields. a) The number of rice varieties used in the cooperative rice cultivation were 13 varieties while the individual rice cultivation used 47 varieties. b) The cooperative rice cultivation has more successfully adopted improved cultivation techniques such as the practice of seed disinfection, adoption of recommended seeding amount, fall ploughing, application of red soil, introduction of power tillers, the rectangular-type transplanting, midsummer drainage and the periodical irrigation. 9. The following results were also obtained from the same investigation and they are: a) In the cooperative rice cultivation, the greater part of the important practices have been carried out through cooperative operation including seed disinfection, ploughing, application of red soil and compost, the control of disease, insects and pests, harvest, threshing and transportation of the products. b) The labor input to the nursery bed and water control in the cooperative rice cultivation was less than that of the individual rice cultivation while the higher rate of labor input was resulted in the red soil and compost application. 10. From the investigation on the organization and operation scheme of the cooperative rice cultivation, the following results were obtained: a) The size of cooperative rice cultivation farm was varied from. 3 ha to 7 ha and 5 ha farm. occupied 55.9 percent of the total farms. And a single cooperative farm was consisted of 10 to 20 plots of paddies. b) The educational back ground of the staff members involved in the cooperative rice cultivation was superior than that of the individual rice cultivation. c) All of the farmers who participated to the questionaires have responded that the cooperative rice cultivation could promise the increased rice yield mainly through the introduction of the improved method of fertilizer application and the effective control of diseases, insects and pests damages. And the majority of farmers were also in the opinion that preparation of the materials and labor input can be timely carried out and the labor requirement for the rice cultivation possibly be saved through the cooperative rice cultivation. d) The farmers who have expressed their wishes to continue and to make further development of the cooperative rice cultivation was 74.5 percent of total farmers participated to the questionaires. 11. From the analysis of economical feasibility on the two different methods of cultivation, the following results were obtained: a) The value of operation cost for the compost, chemical fertilizers, agricultural chemicals and labor input in the cooperative rice cultivation was respectively higher by 335 won, 199 won, 288 won and 303 won over the individual rice cultivation. However, the other production costs showed no distinct differences between the two cultivation methods. b) Although the total value of expenses for the fertilizers, agricultural chemicals, labor input and etc. in the cooperative rice cultivation were approximately doubled to the amount of the individual rice cultivation, the net income, substracted operation costs from the gross income, was obtained 24, 302 won in the cooperative rice cultivation and 20, 168 won was obtained from the individual rice cultivation. Thereby, it can be said that net income from the cooperative rice cultivation increased 4, 134 won over the individual rice cultivation. It was revealed in this study that the cooperative rice cultivation has not only contributed to increment of the farm income through higher yield but also showed as an effective means to introduce highly improved cultivation techniques to the farmers. It may also be concluded, therefore, the cooperative rice cultivation shall continuously renovate the rice production process of the farmers.