Papers by Teimuraz Manjafarashvili
Advances in Artificial Intelligence and Machine Learning
Expert knowledge representations often fail to determine compatibility levels on all objects, and... more Expert knowledge representations often fail to determine compatibility levels on all objects, and these levels are represented for a certain sampling of universe. The samplings for the fuzzy terms of the linguistic variable, whose compatibility functions are aggregated according to a certain problem, may also be different. In such a case, neither L.A. Zadeh’s analysis of fuzzy sets and even the dual forms of developing today R.R. Yager’s q-rung orthopair fuzzy sets cannot provide the necessary aggregations. This fact, as a given, can be considered as a source of new types of information, in order to obtain different levels of compatibility according to Zadeh, presented throughout the universe. This source of information can be represented as a pair ⟨A, fA⟩, where there is some crisp subset of the universe A that determines the sampling of objects from the universe, and a function fA determines the compatibility levels of the elements of that sampling. It is a notion of split fuzzy s...
Axioms
The use of discrete probabilistic distributions is relevant to many practical tasks, especially i... more The use of discrete probabilistic distributions is relevant to many practical tasks, especially in present-day situations where the data on distribution are insufficient and expert knowledge and evaluations are the only instruments for the restoration of probability distributions. However, in such cases, uncertainty arises, and it becomes necessary to build suitable approaches to overcome it. In this direction, this paper discusses a new approach of fuzzy binomial distributions (BDs) and their extensions. Four cases are considered: (1) When the elementary events are fuzzy. Based on this information, the probabilistic distribution of the corresponding fuzzy-random binomial variable is calculated. The conditions of restrictions on this distribution are obtained, and it is shown that these conditions depend on the ratio of success and failure of membership levels. The formulas for the generating function (GF) of the constructed distribution and the first and second order moments are al...
Mathematics, 2022
Nonadditivity of a fuzzy measure, as an indicator of defectiveness, makes a fuzzy mea-sure less u... more Nonadditivity of a fuzzy measure, as an indicator of defectiveness, makes a fuzzy mea-sure less useful in applications compared to additive, probabilistic measures. In order to neutralize this indicator of defectiveness to some degree, it is important to study the representations of fuzzy measures, including, in particular, additive, probabilistic representations. In this paper, we discuss a couple of probability representations of a fuzzy measure: the Campos-Bolanos representation (CBR) and the Murofushi–Sugeno representation (MSR). The CBR is mainly represented by the Associated Probability Class (APC). The APC is well studied and the aspects of its use can be found in many interesting studies. This is especially true for the environment of interactive attributes in their identification and multi-attribute group decision-making (MAGDM) models, related to the attributes’ Shapley values and interaction indexes. The MSR is a less-used tool in practice today. The main motivation of th...
Abstract—Fuzzy logic is a new and innovative technolo-gy that was used in order to develop a real... more Abstract—Fuzzy logic is a new and innovative technolo-gy that was used in order to develop a realization of engi-neering control. In recent years, fuzzy logic proved its great potential especially applied to automatization of industrial process control, where it enables the control design to be formed based on experience of experts and results of experiments. The projects that have been real-ized reveal that the application of fuzzy logic in the tech-nological process control has already provided us with better decisions compared to that of standard control technique. Fuzzy logic provides an opportunity to design an advisory system for decision-making based on opera-tor experience and results of experiments not taking a mathematical model as a basis. The present work deals with a specific technological process ─ designing a sup-port decision making information system for the opera-tional control of the lime kiln with the use of fuzzy logic based on creation of the relevant expert-ob...
International Journal of Information Technology and Computer Science, 2015
Fuzzy logic is a new and innovative technology that was used in order to develop a realization of... more Fuzzy logic is a new and innovative technology that was used in order to develop a realization of engineering control. In recent years, fuzzy logic proved its great potential especially applied to automatization of industrial process control, where it enables the control design to be formed based on experience of experts and results of experiments. The projects that have been realized reveal that the application of fuzzy logic in the technological process control has already provided us with better decisions compared to that of standard control technique. Fuzzy logic provides an opportunity to design an advisory system for decision-making based on operator experience and results of experiments not taking a mathematical model as a basis. The present work deals with a specific technological process ─ designing a support decision making information system for the operational control of the lime kiln with the use of fuzzy logic based on creation of the relevant expert-objective knowledge base.
Evaluation of bankruptcy risks by the method of fuzzy statistics
When controlling the financial assets in various spheres of the economy, the future is uncertain ... more When controlling the financial assets in various spheres of the economy, the future is uncertain because the control is carried out in the conditions of uncertainty as regards a future state of the financial assets themselves and of their financial environment [1,2,8,10,12,16]. Therefore the problem of evaluating a bankruptcy risk extent is topical for all persons concerned about the state of the enterprise – owners, managers, investors, creditors, auditors and so on. Since any considered enterprise has a unique character, the statistical probability theory cannot be applied. It is necessary to put the accent not on predicting a bankruptcy but on recognizing the situation formed and evaluating a distance that separates the enterprise from the bankruptcy state. Naturally, a plausibility extent of this evaluation must also be indicated. Therefore a suitable mathematical tool for such studies is not statistics and the probability theory, but the fuzzy set theory and fuzzy logic [1,4,5,...
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Papers by Teimuraz Manjafarashvili