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боте предлагается концепция инструментального средства построения распределенных , , анализа проблемных областей общее функциональное ядро. Это ядро включает функции локального хранения и передачи данных между узлами хранения, механизм авто, , , сре детва определения обработчиков этих событий.
Вводится понятие документа - элементарной единицы пользовательских данных, наделенной набором атрибутов различных типов, значения которых в совокупности определяют статус и поведение документа в системе. Функциональные возможности системы в части управления документами определяются ее способностью задавать, изменять и интерпретировать значения их атрибутов. Ввиду необходимости определения логики поведения документов в зависимости от их текущего состояния вводится в рассмотрение механизм триггеров - процедур, выполнение которых привязывается к специфической совокупности значений атрибутов для документов определенного типа. В предлагаемой модели распределенного хранения данных локальные физические хранилища документов взаимодействуют друг с другом, образуя логически единое инфор-; -сти в этом пространстве в зависимости от того, на каких узлах системы он зарегистрирован и в какие рабочие группы на этих узлах он входит. Система принимает от пользователей на хранение данные в виде документов. Логически документ помещается в распределенное хранилище и каждому пользователю присваивается тот или иной диапазон прав на доступ к данному документу. Физическое хранение документа осуществляется локальным хранилищем одного из узлов системы, на всех остальных узлах, работающих с этим документом, хранится специальный объект, содержащий ссылку на реальное месторасположение документа. Действие триггеров распространяется только на , , реализовать на каждом узле системы специфические профили обработки документов.
Предложенное инструментальное средство, реализующее базовое ядро функциональности и предоставляющее возможности параметризации типов и жизненного цикла хранимых данных, логики управления информационным потоком, системы авторизации и разграничения доступа, использования различных физических сред хранения и передачи данных, может быть использовано при построении широкого класса распределенных ИС, таких как системы электронного документо-, ,
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УДК 658.512
O. Melikhova
FUZZY PROPOSITIONS AND OPERATIONS OVER THEM
A fuzzy proposition is called a proposal with respect to which we can reason about the truth degree or falsity degree at the current time. Truth and falsity degree of every fuzzy proposition obtains the fixed values from the infinite continuous closed interval [0,1]. The values 0 and 1 are the limiting values of falsity and truth degree and they are equal to the “falsity” and “truth” notions for the ordinary (clear) propositions. Fuzzy
proposition which truth degree is more or equal to 0.5 we shall call fuzzy truth proposition, but fuzzy one which truth degree is less or equal to 0.5 we shall call fuzzy false. Fuzzy proposition which truth degree is equal to 0.5 we shall call indifferent because this one is true in the same degree as false [1,2].
Let me show a few examples of fuzzy propositions. “Two is a little number", “The distance between Nanjing and Shanghai is very large" and “St.Petersburg is a beautiful city". Truth degree of fuzzy proposition is in general a subjective characteristic and depends on many factors in particular on use of fuzzy proposition. Fuzzy propositions, like truth degrees of fuzzy propositions, we shall denote by capital latin letters with the tilde. Let us assume that
truth degree of the first fuzzy proposition A =0.9, the second B =0.25 and the third C =0.85.
Fuzzy propositions may be simple and composite. Composition of propositions are formed from the simple ones with a help of logical operations such as negation, conjunction, disjunction, implication and equivalence.
Let A, B be some fuzzy propositions. A fuzzy proposition denoted by — A truth degree of which is defined by the expression — A = 1 - A is called negation of fuzzy proposition A , where sign “ — ” reads “not" for brevity. It follows from this that the falsity degree of —A proposition is equal to the truth degree of A proposition.
A fuzzy proposition denoted by A & B truth degree of which is defined as follows A & B = min(A, B) is called conjunction of fuzzy propositions A , B , where symbol “&” reads “and" for brevity, but symbol “min” means to choose the minimum of truth degrees
from A and B . Here and further we shall be of the min max interpretation of logical operations, introduced by Lotfy Zadeh in 1965.
A fuzzy proposition denoted by A v B truth degree of which is defined as follows
A v B = max^A, B) is called disjunction of fuzzy propositions A , B , where symbol
“ v ” reads “of’ for brevity. Therefore the truth degree of A v B fuzzy proposition is coincided with the truth degree of the more truth proposition.
A fuzzy proposition denoted by A ^ B truth degree of which is defined as follows
A ^ B = max(l - A, B) is called implication of fuzzy propositions A, B . It is easy to
notice that the truth degree of implication is not less than the falsity degree of its antecedent
(A) or truth degree of consequent (B ). Besides that the truth degree of implication is more the less is truth degree of antecedent or more is truth degree of consequent.
A fuzzy proposition denoted by A ^ B truth degree of which is defined as follows A ^ B = min((max(l - A, B)) (max(l - B, A))) is called equivalence of fuzzy propositions A, B . It is evident that the truth degree of fuzzy proposition A ^ B is equal to the truth degree of the less implications A ^ B or B ^ A. If truth degrees of fuzzy propositions A and B are equal then the value of truth degree of fuzzy proposition A ^ B is lying in the interval [0.5,1], obtaining the value 0.5 when A = B =0.5 and the value 1 when A = B =1 or A = B =0. When truth degrees of propositions A and B are different truth
degree of A ^ B fuzzy proposition can obtain the values from 0 (when A =0, B =1 or
A =1, B =0) to 1, except 1 itself.
It is not difficult to make sure of the definitions given above in the case when truth degree of propositions A and B obtains only two values 0 and 1 correspond to the definitions of logic operations over binary propositions.
Two propositions A and B we shall call fuzzy close (or fuzzy equivalent) if the truth degree of the proposition A ^ B is more or equal to 0.5. Otherwise, i.e. A ^ B < 0.5 the propositions A and B are not fuzzy close (or not fuzzy equivalent). In the case when A ^ B =0.5 we shall call two propositions A and B mutually indifferent. For example, concerning to the propositions A, B, C given above we can say that the propositions A
and C are fuzzy close, but the propositions A and B as B and C are not fuzzy close because it’s very easy to calculate that
A ^ C = 0.85, A ^ B = 0.25, B ^ C = 0.25.
In composition of fuzzy propositions the order of logical operations execution is defined by brackets and if they are absent the negation is executed firstly, then conjunction, further the disjunction and finally the implication and the equivalence.
Let us determine the truth degree of composition of fuzzy propositions
D = (a & —B v — A & B) ^ —(a & C) if A =0.7, B =0.4, C =0.9. Using the definitions of operations, their order execution, substituting the values of the truth degrees of propositions A, B, C and calculating we shall get
D = max((1 - (a & —B v —A & B)) —(a & C)) =
= max((1 - max(( & —B), (—A & B))), (1 - (a & B))) =
= max((1 - max(min(A,1 - B))), min(1 - A, B) - min(A, C)) =
= max((1 - max(min(0.7,0.6), min(0.3,0.4))),1 - min(0.7,0.9)) =
= max((1 - max(0.6,0.3)),0.3) = max(0.4,0.3) = 0.4 Thus D = 0.4 and this proposition is fuzzy false.
REFERENCES
1. Melikhov A.N., Bershtein L.S., Korovin S.Ya. Situational consulting systems on fuzzy logic. - Nauka, Phyzmathlit, Moscow, 1990.
2. Melikhov A.N., Baronetz V.D. Microprocessor tools design of fuzzy information processing. - Rostov University Publishing House, Rostov-on-Don, 1990.
