Lecture
Basic definitions
The acquisition of knowledge is the identification of knowledge from sources and their transformation into the desired form, as well as the transfer to the knowledge base of IP. Sources of knowledge can be books, archival documents, the contents of other knowledge bases, etc., that is, some objectified knowledge, translated into a form that makes them available to the consumer. Another type of knowledge is the expert knowledge that is available to specialists, but not recorded in the repositories external to it. Expert knowledge is subjective. Another type of subjective knowledge is empirical knowledge. Such knowledge can be acquired by IP by observing the environment (if IP has the means of observation).
Entering into the knowledge base objectivized knowledge does not represent a particular problem, the identification and input of subjective and especially expert knowledge is rather difficult. To develop a methodology for acquiring subjective knowledge gained from an expert, it is necessary to clearly distinguish between two forms of knowledge representation. One form is related to how and in which models this knowledge is stored by a human expert. At the same time, the expert does not always fully realize how his knowledge is represented. Another form is related to how the knowledge engineer who designs the information system is going to describe and present them. The degree of consistency of these two forms of representation among themselves depends on the effectiveness of the knowledge engineer.
In cognitive psychology, the forms of knowledge representation (cognitive structures of knowledge) characteristic of a person are studied. Examples are [Khafman, 19 86] : the presentation of a class of concepts through its elements (for example, the concept of "bird" is represented by a seagull, sparrow, starling, ...)
representation of class concepts using a basic prototype, reflecting the most typical properties of class objects (for example, the concept of "bird" is represented by the prototype of something with wings, beak, flies ...) representation using signs (for the concept of "bird", for example, the presence of wings, beak, two legs, feathers).
In addition to concepts, the relations between them are also represented. As a rule, relations between concepts are determined in a procedural way, and relations between components of concepts (determining the structure of a concept) in a declarative way. The presence of two types of descriptions forces the knowledge representation models to simultaneously have both components, for example, a semantic network and a production system, as represented in the cognitive model [Anderson, 1983].
When acquiring knowledge, an important role is played by the so-called field of knowledge which contains the basic concepts used in the description of the subject area, and the properties of all relationships used to establish relationships
between concepts. The field of knowledge is associated with the conceptual model of the problem area, which has not yet taken into account the limitations that inevitably arise in the formal presentation of knowledge in the knowledge base. The transition from the description of a certain area in the field of knowledge to the description in the knowledge base is similar to the transition from the conceptual model of the database to its logical scheme, when the database management system is already fixed. It is important to note that the transition is direct to the formal representations in the knowledge base without a stage of conceptual description in the field of knowledge leads to numerous errors, which slows down the process of forming the knowledge base of IP.
There are three possible modes of interaction of a knowledge engineer with a specialist expert: protocol analysis, interviews, and game imitation of professional activity. The protocol analysis consists in fixing (for example, recording the “thoughts out loud” of an expert during a problem solving and subsequent analysis of the information received. In the interview mode, the knowledge engineer conducts an active dialogue with the expert, directing it in the right direction. When playing a game The expert is placed in situations similar to those in which his professional activity is taking place. Observing his actions in various situations, the knowledge engineer will form his thoughts on expert knowledge, which Corollary can be specified with an expert in the interview mode. The principles of the game simulation have been used in a variety of business games, special simulators.
Each of these methods of extracting knowledge has its own advantages and disadvantages. Thus, when analyzing protocols, it is not easy for a knowledge engineer to separate concepts that are important for inclusion in the vocabulary of a subject area from those that appear out of “thinking out loud” by chance. In addition, there are gaps in the protocols, when the expert’s reasoning seems to be interrupted and continues on the basis of the missing output steps. Filling these lacunae is possible only in an interview mode. Thus, in all three approaches to extracting knowledge from experts, an interview stage is necessary, which makes it one of the most important methods for acquiring knowledge.
There are at least two dozen interviewing strategies. Three are best known: the division into steps, the repertory grid and the confirmation of similarity,
When dividing into steps, the expert is invited to name the most important, in his opinion, concepts of the subject area and indicate between them structuring relations, i.e., relationships such as "species-species", "element-class", "whole-part", etc. n. These concepts are used in the next step of the survey as basic. The strategy is aimed at creating a hierarchy of concepts of the subject area, highlighting in terms of closely related groups of haxons (clusters).
The strategy of the repertory grid is aimed at identifying the characteristic properties of concepts, allowing to separate some concepts from others. The technique consists in presenting an expert set of concepts with an offer to name the signs for every two concepts, which would separate them from the third. Since each concept is included in several triples, on the basis of such a procedure, the volumes of concepts are clarified and concept “symptom complexes” are formed, with the help of which these concepts can be identified in the knowledge base .
The strategy of confirming the similarity is that the expert is invited to establish the belonging of each pair of concepts from the subject area to a certain relation of similarity (tolerance). For this, the expert is asked a sequence of fairly simple questions, the purpose of which is to clarify the understanding of the similarity that the expert puts into the statement about the similarity of the two concepts of the subject matter.
The process of interaction of a knowledge engineer (analyst) with a specialist expert includes three main steps.
1. Preparatory stage. For the success of communication, both participants must carefully prepare for the dialogue or game. It is desirable that the expert was not only a competent specialist, but also an interested (morally or financially) person in achieving the ultimate goal-building of IP. He should be benevolent to the analyst and be able to explain his knowledge (the best case when an expert has teaching experience).
The analyst needs: deeply acquainted with the special literature on the subject area "not to ask very" stupid "questions (just" stupid "questions are extremely useful), as well as to increase the number of" packets of expectations "[Schenk et al., 1987]; be able to listen and competently ask questions; tune in to the role of "students, not the" examiner "; to understand models of cognitive psychology, as well as models of knowledge representation, to distinguish clear structures from expert knowledge.
In any joint activity, psychological qualities of researchers, such as personality, demeanor, style of scientific thinking, are of great importance. There are various classifications of researchers. As an example, we will cite the following: the initiator responds quickly to promising problems, that is, one of the first feels the need to solve a problem with elements of uncertainty; diagnostician is able to quickly assess the strengths and weaknesses of the solution of the problem, the erudite is endowed with an extraordinary memory, is distinguished by increased attention to detail and the desire for orderliness; craftsman - able to implement the poorly decorated ideas of others; an esthete - seeks to explore problems leading to elegant solutions, not prone to hard work; methodolosis is interested in methodological aspects of research; independent-seeking for individual problem solving; fanatic-selflessly passionate about his scientific problem, the same requires from others.
The affiliation of a scientist to a particular type is determined using indirect methods (personality tests, intelligence, cognitive styles, design techniques). Automation of the survey and obtaining a psychological portrait of the subject is realized, for example, in the AVTANTEST system [Gavrilov. 1984].
For the role of expert, the erudite initiator, diagnostician and artisan (together with the erudite analyst) are most preferable, and for the role of analyst-diagnostician, methodologist, erudite, initiator. At the same time, the best combination is given by combinations of different types. Due to the differences in approaches to solving the problem, in points of view, thinking style of perception, memory, etc., participants in this pair come from different angles to the goal, as a result, the total number of hypotheses, ideas, alternatives increases, and therefore enriches field of knowledge. However, not all combinations of even acceptable types improve interaction, and some types (for example, fanatic, esthete, independent artisan) are often poorly adapted for creative interaction, which leads to hidden and obvious conflicts that complicate the process of productive communication.
Leadership in the pair is also important. In the course of any dialogue, one party usually takes the leading position, most often this role is taken by the interviewer, i.e. the analyst. The role of the leader in the dialogue allows the analyst to direct and systematize the process of creating a field of knowledge without letting the expert " blur" or unnecessarily detail the process. On the other hand, dogmatism and perseverance can lead to an inadequate field. There is also the effect of a “facade”, i.e., the expert’s desire not to lose face with the analyst, and hence the generation of unconfirmed hypotheses.
2. Establish a "common code". To create a linguistic alliance of interaction, interaction participants must try to reduce "the distance between the object (that is, the subject area under study) and the analyst. It is necessary to define the main concepts, that is, to develop the vocabulary basis of the knowledge base; level of detail; interrelationships between the concepts.
3. Epistemological stage. At this stage, the elucidation of the laws inherent in the subject area, the conditions of authenticity and truth of statements, structuring due to the introduction of relationships, etc., takes place. This stage is decisive in the interaction of the analyst and expert. In the process of analyzing a game or dialogue, the expert is often formalized and for him, new knowledge is generated. The representation of the external world in his memory receives a material embodiment in the form of a field of knowledge.
In the process of extracting knowledge, it is first desirable to obtain surface knowledge from an expert, such as, for example, the representation of features), gradually moving to deep structures and more abstract concepts (such as prototypes, for example).
When forming the field of knowledge, the features of empirical knowledge are taken into account: modality, inconsistency, incompleteness, etc.
The analyst should always see the general behind the private, that is, to build chains 1 fact - a generalized fact - an empirical law - a theoretical law. "The central link of the chain is the formalization of empiricism. At the same time, the main thing at the formalization stage is not to extract blind connections understanding of the internal structural connection of the domain concepts The art of the analyst consists in striving to create a clear and understandable model of the problem domain.
It should also be borne in mind that experts in the problem area do not always rely on logical reasoning. Associative reasoning and likelihood reasoning are widely used in their ideas about the problem domain and methods for solving problems characteristic of it. We describe an approximate method of working with an expert on the formation of the field of knowledge.
Preparatory stage
1. A clear definition of the tasks of the designed system (narrowing the field of knowledge): the definition of what is in the input and output; determination of work schedule, consultations, training, etc.
2. Selection of experts: determining the number of experts; selection of the level of competence (it is not always good to choose the highest level right away); identification of ways and opportunities to interest experts in the work; testing experts.
3. Acquaintance of the analyst with the special literature in the subject area
4. Acquaintance analyst and experts (in the future, for simplicity, we assume that there is only one expert).
5. An expert's introduction to the popular literature on artificial intelligence (preferably, but not necessarily).
6. Attempt by the analyst to create a field of knowledge of the first approximation of a priori knowledge from the literature (prototype field of knowledge).
Main stage
1. "Pumping" the field of knowledge: a) depending on the subject area, the choice of interviewing method; b) recording thoughts out loud or recording the expert’s reasoning (the analyst should not, as far as possible, interfere with the reasoning).
2. "Homework". The analyst’s attempt to isolate some causal relationships in the reasoning of the expert; building a vocabulary of the subject area (possibly on cards) and preparing questions for the expert.
3. "Swap" field of view. Discussion with an expert of the prototype field of knowledge and homework, as well as answers to questions from the analyst.
4. Formalization of the conceptual model.
5. Building a knowledge field of the second approximation.
Knowledge acquisition systems from experts
One of the first reviews of an interview as a method of knowledge engineering was conducted in [Newel 1972]. Some psychologists associate the problems that arise when extracting expert knowledge with the so-called cognitive defense. The theory of human knowledge was developed in [Kelly, 1985], based on the concept of "personal constructs" that a person creates and tries to adapt to the realities of the world. In [Bose, 1984], the theory of personal constructs was used to create a system for extracting expert knowledge and showed its ability to successfully overcome cognitive protection, i.e., experts' reluctance to achieve a clear and conscious interpretation of basic concepts, relationships between concepts and methods for solving problems in the engineer of interest on knowledge of the problem area.
The methods of interviewing an expert with a knowledge domain using several different strategies were applied to create the TEIRESIAS system [Davis, 1982]. Eight different interview strategies were outlined in [Kahn et aL, 1984]; in [Kahn et aL, 1985], the possibility of automatic interviewing is explored based on these strategies. Automation of the method of protocol analysis is devoted to the work [Waterman, 1971, 1973; Krippendorf, 1980].
In [Kahn et al. 1985] on the example of the diagnostic system MORE; describes the interviewing technique, aimed at clarifying the following entities, hypotheses, symptoms, conditions, relationships and ways. Hypothesis - an event whose identification results in a diagnosis. A symptom-event resulting from the existence of a hypothesis, the observation of which approximates the subsequent acceptance of the hypothesis. A condition is an event or some set of events that is not directly symptomatic for any hypothesis, but which may have diagnostic value for some other events. Relationships - connections of entities (including other relationships). The path is a highlighted type of connection that connects hypotheses with symptoms. In accordance with this, the following interview strategies are used: differentiation of hypotheses, symptom discrimination, symptomatic causation, division of the path, etc.
Differentiation of hypotheses is aimed at finding symptoms that provide a more accurate distinction of hypotheses. The most powerful in this sense are those symptoms that originate from one diagnosed event. The distinction between symptoms reveals the specific characteristics of the symptom, which, on the one hand, identify it as a consequence of a certain hypothesis, and on the other, contrast it with another. Symptomatic conditionality is aimed at identifying negative symptoms, i.e., symptoms, the absence of which has a greater diagnostic weight than their presence. The division of the path provides the finding of symptomatic events that lie on the path to the already found symptom. If such a symptom exists, then it has a great diagnostic value than the one already found.
Similar expert interviewing strategies have been used to create the IDIS tool diagnostic system [Golubev et al., 1987].
В системе KRITON [Diederich et aL, 1987] для приобретения знаний используются два источника: эксперт с его знаниями, полученными на практике (эти знания, как правило, неполны, отрывочны, плохо структурированы); книжные знания, документы, описания инструкции (эти знания хорошо структурированы и фиксированы традиционными средствами). Для извлечения знаний из первого источника в KRITON применена техника интервью, использующая стратегии репертуарной решетки и разбиения на ступени. При этом применяется прием переключения стратегий: если при предъявлении тройки семантически связанных понятий эксперт не в состоянии назвать признак, отличающий два из них от третьего, система запускает стратегию разбиения на ступени и предпринимает попытку выяснения таксономической структуры этих понятий с целью выявления признаков, их различающих.
Для выявления процедурных знаний эксперта в KRITON применен метод протокольного анализа. Он осуществляется в пять шагов. На первом шаге протокол делится на сегменты на основании пауз, которые делает эксперт в процессе записи. Второй шаг-семантический анализ сегментов, формирование высказываний для каждого сегмента. На третьем шаге из текста выделяются операторы и аргументы. Далее делается попытка поиска по образцу в базе знаний для обнаружения переменных в высказываниях (переменная вставляется в высказывание, если соответствующая ссылка в тексте не обнаружена). На последнем шаге утверждения упорядочиваются в соответствии с их появлением в протоколе.
Анализ текста используется в KRITON для выявления хорошо структурированных знаний из книг, документов, описаний, инструкций.
В [Morik, 1987] описан метод выявления модели предметной области. Первая фаза-формирование инженером знаний грубой модели предметной области путем определения предикатов и сортов их возможных аргументов и сообщения системе фактов об области, выразимых этими предикатами. Система выявляет свойства предикатов и устанавливает отношения между ними, структурируя таким образом предметную область. На второй фазе с помощью метазнаний (общих структур), отражающих особенности человеческого мышления, осуществляется проверка соответствия фактов предикатам, индуктивный вывод правил из фактов, вывод правил из других правил.
В системах SIMER и ДИАПС [Осипов. 1987; Osipov et aL, 1987] основным методом приобретения знаний является автоматизированное интервьюирование эксперта, которое управляется знаниями, приобретенными системой. В системах SIMER и ДИАПС не выявляется предварительная модель области. Все объекты (события) и их атрибуты определяются в режиме прямого интервьюирования эксперта . Предполагается только, что на множестве объектов могут быть заданы ряд отношений из известного (конечного) множества: "элемент-множество", "часть - целое", "пример - прототип", отношения структурного сходства объектов, структурной иерархии и некоторые другие. Все отношения попарно различаются формальными свойствами. Так, отношений структурного сходства не обладает транзитивностью, но симметрично. Отношение структурной иерархии. напротив, не обладает симметричностью, однако транзитивно. На выяснение этих и ряда других свойств отношений и объектов направлено интервью.
В частности, для установления структурного сходства на первой фазе интервью для каждого вновь вводимого понятия эксперту предлагается указать (с помощью меню) те понятия предметной области, с которыми может быть связано данное (без спецификации отношения). Затем в процессе интервью для каждой пары понятий (из выделенных на первой фазе) связь специфицируется, устанавливаются свойства и тип отношения, в число элементов которого включается исследуемая пара. Так, для включения некоторой пары понятий Х и У. о которых эксперт сообщил, что Х влияет на У (например Х увеличивает возможность У), в число элементов некоторого отношения Я, обладающего среди прочих свойств симметричностью, необходимо задать эксперту вопрос: "Увеличивает ли У возможность ?". При положительном ответе на этот вопрос (и если прочие свойства уже установлены и удовлетворяют определению отношения Я) пара (X, У) включается в R, Для установления структурного сходства и структурной иерархии понятий используются стратегии подтверждения сходства и разбиения на ступени.
В модели имеются метапроцедуры и метаправила, которые проверяют корректность модели, используют формальные свойства отношений для пополнения модели и генерируют правила.
Сформулируем основные этапы реализации системы приобретения знаний.
1. Интервью для определения актуальной области, в которой происходит процесс решения интересующей проблемы, и расчленение ее на автономные области.
2. Автоматизированное интервью для выявления и формирования декларативной модели предметной области.
3. Протокольный анализ к выявленным на предыдущем этапе понятиям и отношениям предметной области для пополнения модели процедурными знаниями.
(этапы 2 и 3 можно использовать попеременно до тех пор, пока модель не достигнет нужной полноты).
4. Протокольный анализ для попонения декларативных знаний модели. b. Проверка полноты модели. Обычно протокольный анализ выявляет пустоты в модели. Имеется в виду случай, когда понятия, использованные в "мыслях вслух", недостаточно описаны. В этом случае интервью и протокольный анализ повторяются.
Формализация качественных знаний
При формализации качественных знаний может быть использована теория нечетких множеств [Заде, 1974], особенно те ее аспекты, которые связаны с лингенетической неопределенностью, наиболее часто возникающей при работе с экспертами на естественном языке. Под лингвистической неопределенностью подразумевается не полиморфизм слов естественного языка, который может быть преодолен на уровне понимания смысла высказываний в рамках байесовской модели [Налимов, 1974], а качественные оценки естественного языка для длины, времени, интенсивности, для целей логического вывода, принятия решений, планирования.
Лингвистическая неопределенность в системах представления знаний задается с помощью лингвистических моделей основанных на теории лингвистических переменных и теории приближенных .рассуждении [ Kikerf 1978]. Эти теории опираются на понятие нечеткого множества, систему операций над нечеткими множествами и методы построения функций принадлежности.
Одним из основных понятий, используемых в лингвистических моделях, является понятие лингвистической переменной. Значениями лингвистических переменных являются не числа, а слова или предложения некоторого искусственного либо естественного языка. Например, числовая переменная "возраст" принимает дискретные значения между нулем и сотней, а целое число является значением переменной. Лингвистическая переменная "возраст" может принимать значения: молодой, старый, довольно старый, очень молодой и т. д. Эти термы-лингвистические значения переменной. На это множество (как и на числа) также налагаются ограничения. Множество допустимых значений лингвистической переменной называется терм-множеством.
При вводе в ЭВМ информации о лингвистических переменных и терм-множестве ее необходимо представить в форме, пригодной для работы на ЭВМ. Лингвистическая переменная задается набором из пяти компонентов: <Л, Т(А), U, <7, Af>, где Л-имя лингвистической переменной; Г (Л)-ее терм-множество;
U- область, на которой определены значения лингвистической переменной; 6 описывает операции по порождению производных значений лингвистической переменной на основе тех значений, которые входят в терм-множество. С помощью правил из О можно расширить число значений лингвистической переменной, т. е. расширить ее терм-множество. Каждому значению а лингвистической переменной Л соответствует нечеткое множество Ха, являющееся подмножеством V. По аналогии с формальными системами правила из G часто называют синтаксическими Наконец, компонент М образует набор семантических правил. С их помощью происходит отображение значений лингвистической переменной а в нечеткие множества Ха и выполняются обратные преобразования. Именно эти правила обеспечивают формализацию качественных утверждений экспертов при формировании проблемной области в памяти ИС.
In fig. 2Л показаны все компоненты, определяющие лингвистическую переменную <возраста>. В качестве терм-множества использовано множество, состоящее из трех значений: очень молодой (Ом), пожилой (п) и старый (с), задаваемых функциями принадлежности на области V, которую называют носителем лингвистических значений. В примере область V -года жизни от 0 до 150 лет, В качестве семантических правил выступают отображения, задаваемые функциями принадлежности 0<Цд(")<1 к нечетким множествам Лои" Хи, Хе. Как видно из рис. 2Л. человек, возраст которого равен 60 годам, принадлежит
к Хоы со значением 0 (т. в, человек в 60 лет не является очень молодым), к Ха со значением 0.8 и к Хс со значением 0.4.
Для перехода от качественных описаний к формализованным необходимо построить отображения, входящие в М, т. е. построить функции принадлежности, В таком виде подобная задача была исследована в [Блишун, 198 7]
При получении от экспертов информации о виде функций принадлежности необходимо учитывать характер измерений (первичные и производные измерения) и тип шкалы, на которую проецируются измерения и на которой будут определяться функции принадлежности [Глотов и др.. 1976]. На этой шкале задается вид допустимых операторов и операций, т. е. некоторая алгебра для функций принадлежности. Кроме того, следует различать характеристики, которые можно измерять непосредственно и характеристики, которые являются качественными и требуют попарного сравнения объектов, обладающих этими характеристиками" чтобы определить их отношение к исследуемому понятию.
Можно выделить две группы методов построения функций принадлежности: прямые и косвенные. В прямых методах эксперт непосредственно задает правила определения значений функции принадлежности lia(u). Эти значения согласуются с его предпочтениями на множестве объектов следующим образом: для любых Ki, и 2 s U имеет место Ио(УО<Ио(и2) тогда и только тогда, когда йд предпочтительнее и\, т. е, в большей степени определяется понятием а; для любых уь u^eU имеет место Ца(1)=Ца(2) тогда и только тогда, когда Нч и иdo not differ in relation to the concept of a. By the method of a table, formula, or example [Zadeh, 1975; Ragade et aL, 1977; Thoie et a. 1979 ].
In indirect methods, the values of the membership function are chosen in such a way that pre-formulated conditions are satisfied. Expert information is only the source for further processing. Additional conditions may be imposed both on the type of information received and on the processing procedure. The following can serve as examples of additional conditions: the membership function should reflect the proximity to a pre-selected standard, the objects of the set are points in the parametric space [Scala, 1978]; the result of the processing procedure should be a membership function that satisfies the conditions of the interval scale [Zhukovin et al. 1983]; in pairwise comparison of objects, if one object is estimated to be k times stronger than another, then the second object is estimated to be \ / k times stronger than the first object [Saaty, 1974]. etc.
As a rule, direct methods are used to describe concepts that are characterized by measurable traits (height, height, weight, volume).
In this case, it is convenient to directly assign the membership function. Direct methods include methods based on the probabilistic interpretation of the membership functions: a (i) == P (a / i), i, e. The probability that the ueU object will belong to the set that characterizes the concept Since people often distort assessments, for example, shift them towards the ends of the rating scale [Thole et al., 1979]. Direct measurements based on direct determination of the membership function values can only be used if such distortions are minor or unlikely. Indirect methods are more laborious than direct ones, but are resistant to distortion in response. The result of the application of indirect methods is the interval scale. In [Thole et al. 1979], the “unconditional extremum condition” is put forward for indirect methods: in determining the degree of ownership, the set of objects to be studied must contain at least two objects whose numerical representations are in the interval [0. 1] - O and 1, respectively.
Membership functions may reflect the opinion of a group of experts, as well as one unique expert. By combining possible methods of constructing membership functions with two types of experts (collective and unique), one can get four types of expertise [Blishun, 1988]
An example of the formalization of quality knowledge
When analyzing a situation, the expert argues in a semantic space (space of scales) in which the estimated image corresponds to the situation. Semantic space is analogous to the subjective space of sensations in which an internal image of external signals is formed and subjective connections between properties (attributes, parameters) arise. Depending on individual perception, the same value of a characteristic can be evaluated differently. However, for a particular individual, the assessed situation is an invariant with respect to a certain class of situations. Therefore, when identifying the real values of features with a semantic image, the form of a fuzzy mapping of a feature space into a semantic space is essential.
The display of any situation on a unit interval occurs in such a way that the interval point characterizes the degree of manifestation of a certain property (0 corresponds to the absence of a property, the maximum manifestation of a property that interests us). When constructing the membership function, a measurement model is used, which is determined by two parameters: the type of membership scale, which the expert information is displayed on, and the measurement type (direct or indirect). The scale is called fundamental if it allows direct interaction of the set U and that fuzzy property that we are interested in This scale gives a direct measurement of the subjective perception of fuzzy sets on U with the properties of the concept and [Yager, 1982; Norwich et aL, 1984].. Table 2.1 shows the most often. trechayuschiesya types of scales and related assumptions.
The process of formalization of knowledge obtained from an expert consists of the following steps: choosing a method for measuring fuzziness, obtaining initial data by interviewing an expert, implementing an algorithm for constructing a membership function. Known methods for the formalization of fuzziness are systematized in Table. 2.2. In the process of implementing the method, the following characteristics are used: type of measurement method (P - direct, K - indirect); interpretation of belonging (HF-frequency probability, Sun-probability subjective, B - possibility, D - deterministic); procedure for obtaining the initial data (OF - definition of the membership function in the form of formulas, 03-assigning the values of the belonging to "ONE-assessment of" yes-no "type; OPO-assessment of pairs of objects; P-ranking, RP-ranking of pairs of objects, PS-pairwise comparison ); measurements (F-fundamental, P-derivative) '. type of scale (H-nominal "P-ordinal, I-interval, O-ratios, A - absolute),
We give an example of measuring fuzziness. A number of similarity estimates are given in Table. 2.3. In [Goryachev et al., 1984], it is assumed that the numerical values from Table 2 are used in assessing similarity. 2.3. The procedure for forming the values of the membership function is as follows: I) fixing the concept of "similarity";
2) ranking of pairs of similarity estimates from table. 2.3 by similarity in pairs (the greater the similarity, the lower the rank); a comparison matrix of pairs of similarity estimates is given in Table. 2.4, 2 5 respectively in lower case and matrix form.
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Presentation and use of knowledge
Terms: Presentation and use of knowledge