• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1993년도 Fifth International Fuzzy Systems Association World Congress 93
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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].

• 한국초지조사료학회지
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• 제25권1호
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• pp.71-82
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• 2005

Khori(高麗) refers to the Chaabog(reindeer) that live on lichens(蘚) on Mt. Soyon(鮮) in which pastures are the cold and dry plateau of North Eurasia. Thus, the origin region of the Khori or Koguryo that are the ancestors of the reindeer-herding pastoral nomads(馴鹿 遊牧民) can be said to be the Steppe-Taiga-Tundra pastoral areas of North Eurasia and North America. When the pastoral nomads moved on to the great mountain(大山) zone of the Jangbaek(長白) to the Baekdu(白頭) Mountains, they could have been in contact with pastoral farmers or agricultural farmers living there and they became the farmers remaining on agricultural farms. They were the Koryo people, the ancestors of Korea. Staying in one place, they gradually forgot the origin of their reindeer-herding pastoral nomadic history in the Northwest area of Mt. Soyon, the small mountain(小山) zone of the Steppe-Taiga-Tundra pastoral areas. In other words, they lost their identity as reindeer-herding pastoral nomads when they entered the agricultural area after leaving the pastoral area. However, since their basic genes had already formed when they lived on the cold and dry plateau of North Eurasia, it is possible to study their pastoral nomadic history focusing on 'the minority living in the broad area(廣域少數)', by utilizing highly advanced biotechnological science and focusing on genes and information technology innovation, and removing various past hindrances in research. Therefore, it is not so difficult to restore the reindeerherding pastoral nomadic history of the Koguryo(高句麗) people and secure their pastoral nomadic identity, of which the first steps have already been taken into their historical stages. The Eurasian continent and the Korean peninsula, especially the cold and dry plateau of North Eurasia and the Korean peninsula have been closely related to each other ecologically and historically. They can never be a separate space at all. The Eurasian continent lies horizontally east to west and thus, the continent forms an isothermal zone. Also, since the time of producing their own foods, it was relatively easy for people with their technology to move to other places owing to the pastoral nomadic characteristic of mobility. Unlike the Chungyen(中原) region, western Asia and the regions covering the Siberia-Manchu-Korean peninsula where food production revolution was first made were connected to the Mongolian lichens route(蘚苔之路: Ni, ukinii jam) and steppe roads. Although the ecological conditions of nature have changed a bit throughout a long history, it was natural for the many tribes in North Asia living on the largest Steppe-Taiga-Tundra area in the world to have believed 'the legends related to animals in relation to their founders and ancestors(獸祖傳說)'. Assuming that Siberian tigers and the tigers living on Mt. Baekdu were connected ecologically and genetically because of the ecological characteristics of the animals, and their migration from plateau to plateau, we would suspect that the Chosun(朝鮮) tribe living on Mt. Baekdu were ethnically and culturally more closely connected to the farther removed Ural-Altai tribes that lived on the cold and dry plateau region than to the Han(i14;) tribe who lived in Chungyen(中原) that was close to Mt. Baekdu. More evidence is the structure of the Korean language which has the form of 'Subject + Object + Verb', which is assumed to have originated from the speedy lifestyle of the reindeer-herding pastoral nomads. The structure is quite different from that of the Han(漢) language, which is based on agricultural life. Also, it is natural for reindeer riding reindeerherding pastoral nomads or horse-riding sheep-herding pastoral nomads(騎馬, 羊遊牧民) to have held military and political power over the region and eventually to have established an ancient pastoral nomadic empire in the process of their conquest of agricultural regions. The stages for founding global empires in the history of mankind maybe largely divided into two, in terms of ecological conditions and occupations. They are the steppes and the oceans. Of course, the steppe-based empires were established based on the skills to deal with horses and the ability to shoot arrows while riding horses, along with the use of iron ware in the 8th century BC. The steppe-based empires became the foundation for an oceanic empire, which could have been established by the use of warships and warship guns since the 15th Century. Based on those facts, we know that Chosun, Puyo(夫餘), and Koguryo are the products of a developmental process of pastoral nomadic empires on the steppes. Maybe we can easily find the pastoral nomadic identity of the Koguryo more than we expected when we trace the origins and history of the Korean tribe living in the pastures located in the northwest area of Mt. Jangbaek by focusing on pastoral nomadic mobility and organization just as we have investigated the historic origins of Anglo-Saxons in America by focusing on the times before the 15th Century. In the process, we should keep in mind that English culture originated from the Industrial Revolution and was directly delivered to the American continent, although America was far from England and was not an intermediate point on long sojourns either. Further, American culture came back to England in a more advanced form later. The most important thing currently to be resolved is to cause Koreans to look back on their own history in a freer way of thinking and with diverse, profound, and sharp insight, taking away the old and existing conventional recognition that is entangled with complicated interests with Korean people and other countries. The meanings of Chosun, Khori, and Solongos have been interpreted arbitrarily without any historic evidence by the scholars who followed conventional tradition of fixed-minded aristocrats in an agricultural society. If the Siberian cultural properties of the stone age, the earthenware age, the bronze age, and the iron age are analyzed in such a way, archaeological discovery will never be able to contribute to the restoration of the Koguryo's pastoral nomadic identity. One should transcend the errors that tend to interpret the cultural properties discovered in the pastoral nomadic regions as not being differentiated from those of agricultural regions and just interpret them altogether from the agricultural point of view. A more careful intention is required in the interpretation of cultural properties of ancient Korean empires that seem to have been formed due to mutual interactions of pastoral nomadic and agricultural cultures. Also, it is required that the conventional recognition chain of 'reverse-genes' be severed, which has placed more weight on agricultural properties than pastoral nomadic ones, since their settlement on agricultural farms was made after the establishment of their ancient pastoral nomadic empires. There is no reason at all to place priority on stoneware, earthenware, bronze ware, and iron ware than on wooden ware(木器) and other ware which were made of animal skins(皮器), bones and horns(骨角器), in analyzing the history in the regions of reindeer or sheep pastures. Reading ancient Korean history from the perspective of pastoral nomadic history, one feels strongly the instinctive emotions to return to the natural 'mother place'. The reindeer-herding pastoral nomadic identity of the Koguryo people that has been accumulated in volumes in their genes and hidden deep inside and have interacted organically could be reborn with Burqanism(Burqan refers to 不咸 in Chinese), which was their religion by birth and symbolized as the red willow(紅柳=不咸). The mother place of the Koguryo's people is the endless vast green pastures of North Eurasia and North America, where we anticipated the development of Korean livestock farming following the inherent properties in the genes of the reindeer-herding pastoral nomads with Korean ancestors. We anticipate that the place would be the core resource that could contribute to the development of life of living creatures following the inherent properties of their genes and biotechnological factors. In other words, biotechnology used for a search for clues on the well-being of humans could be the fruit brought by Burqanism of the Koguryo people and the fruit of the globalization of Korean livestock farming. It is the Chosun farmer in China come from the vast nomadic reindeer pastures of North Eurasia that resolved the food problem of a billion Chinese people with lowland paddy rice seeds (水稻) by transforming Heilongjiang Province(黑龍江省) into an oceanic lowland paddy rice field(水田). Even Mao Tse-tung(毛擇東) could not resolve the food problem by his revolution campaigns for tens of years. Today is the very time that requires the development of special livestock farming following the inherent properties of the ancient Korean reindeer-herding pastoral nomads that respected the dignity of life on the cold and dry plateau of North Eurasia and the America continent. I suggest that research should be started from the pastures of the Dariganga Steppe in East Mongolia that was the homeland of Hanwoo(韓牛) and the central horse-herding steppe place(牧馬場) of Chingis Khan's Mongolia. The Dariganga Steppe is awash with an affluent natural environment for pastoral nomadic living however, the quality of life of the pastoral nomads there is still low. I suggest we Koreans, the descendents of the Koguryo, should take our first steps for our livestock farming business project and develop the Northern nomadic pastures, here at the pastures of the Dariganga Steppe, which is the Mongolian core place of state-of-the-art technology for military weapons.