Abstract: In this paper it is shown that for bipartite graphs the structure of the family of maximum independent sets can be described constructively, in the following sense. For a bipartite graph there are some “basic” maximum independent sets, in terms of which any maximum independent set can be described, in the sense that there is one-to-one correspondence between a maximum independent set and an irreducible combination of these “basic” maximum independent sets. König’s theorem states that there is duality between the cardinalities of maximum matching and minimum vertex cover. Viewing the mentioned structure, in this paper it is shown that another duality holds, which is between the sets rather than their cardinalities. We believe that this duality is not just of theoretical interest, but it also can yield to a usable algorithm for finding a maximum matching of bipartite graph. In this paper we do not present such algorithm; instead we mention what approaches we plan to use in further works to obtain such algorithm.

Keywords: bipartite graph, maximum independent set, distributive lattice, duality.

ACM Classification Keywords:G.2.1 Discrete mathematics: Combinatorics

Link:

ON THE STRUCTURE OF MAXIMUM INDEPENDENT SETS IN BIPARTITE GRAPHS

Vahagn Minasyan

http://www.foibg.com/ijita/vol17/ijita17-2-p06.pdf

Abstract: Current research concerns the following issues: n-dimensional discrete torus generated by cycles of even length is considered; the concept of standard arrangement in the torus is defined and some basic properties of this arrangement are investigated. The issues considered are similar to discrete isoperimetry constructions, being related to concept of neighbourhood in terms of linear arrangements of vertices. Considered are the basic properties of solving the discrete isoperimetry problem on torus.

Keywords: discrete torus, standard arrangement.

ACM Classification Keywords: G.2.1 Discrete mathematics: Combinatorics

Link:

SOME PROPERTIES IN MULTIDIMENSIONAL MULTIVALUED DISCRETE TORUS

Vilik Karakhanyan

http://www.foibg.com/ijita/vol17/ijita17-2-p05.pdf

Abstract: It is known that the minimal number of the steps in a proof of a tautology in a Frege system can be exponentially larger than in a substitution Frege system, but it is an open problem whether Frege systems can polynomially simulate substitution Frege systems by sizes. Many people conjecture that the answer is no. We prove that the answer is yes. As a bridge between substitution Frege systems and Frege systems we consider the Frege systems, augmented with restricted substitution (single renaming) rule. We prove that Frege systems with single renaming rule polynomially simulate by size Frege systems with substitution rule without any restrictions, and Frege systems without substitution rule polynomially simulate Frege systems with single renaming rule both by steps and by size.

Keywords: Frege system, proof complexity, depth-restricted substitution rule, k-bounded substitution rule, polynomial simulation, exponential speed-up.

ACM Classification Keywords: F.4.1 Mathematical Logic and Formal Languages, Mathematical Logic, Proof theory

Link:

COMPARISON OF PROOF SIZES IN FREGE SYSTEMS AND SUBSTITUTION FREGE SYSTEMS

Anahit Chubaryan, Hakob Nalbandyan

http://www.foibg.com/ijita/vol17/ijita17-2-p04.pdf

Abstract: In this paper we present some research results and propose solutions for natural language string lookup techniques. In particular a fast method is suggested for searching dictionary entries for possible matches of sentence words without using relational databases or full dictionary load into machine random access memory. Such approach is essential for minimizing the speed dependency from dictionary size and available machine resources as well as for the scalability of the analyzer software. The mentioned is based on an implementation of Aho-Corasick? Aho, Corasick, 1977 automata with a number of optimizations in the indexing and lookup algorithm.

Keywords: UNL, natural language processing, dictionary lookup, indexing, search, XML, pattern matching machine, string matching algorithm, information search

ACM Classification Keywords: F.2.2 Non-numerical Algorithms and Problems – Pattern matching, Sorting and searching, I.2.7 Natural Language Processing - Text analysis, Language parsing and understanding, I.7.2 Document Preparation – Index generation, Markup languages, H.3.1 Content Analysis and Indexing – Dictionaries, Indexing Methods, H.3.3 Information Search and Retrieval - Retrieval models, Search process.

Link:

IMPLEMENTATION OF DICTIONARY LOOKUP AUTOMATA FOR UNL ANALYSIS AND GENERATION

Igor Zaslawskiy, Aram Avetisyan, Vardan Gevorgyan

http://www.foibg.com/ijita/vol17/ijita17-2-p03.pdf

Abstract: Existence and reconstruction issues are considered for a class of (0,1)-matrices with different rows. Intending to define quantitative characteristics, maximization of which lead to matrices with different rows in case when the later exist, we consider the number of pairs of different rows.A greedy algorithm is introduced for this purpose and then its optimality is proven for local steps.

Keywords: (0,1)-matrices, greedy algorithms

ACM Classification Keywords: F.2.2 Nonnumerical Algorithms and Problems:Computations on discrete structures

Link:

APPROXIMATION GREEDY ALGORITHM FOR RECONSTRUCTING OF (0,1)-MATRICES WITH DIFFERENT ROWS

Hasmik Sahakyan

http://www.foibg.com/ijita/vol17/ijita17-2-p02.pdf

Abstract: This paper considers the association rule mining problem and provides an alternative to APRIORI algorithm, for solving this problem by splitting up the n-dimensional unit cube vertices into the chains using the well know technique introduced by G. Hansel. We use the further development of this technique given by G. Tonyan, which adds computability on levels of chains and chain splits. A brief description of the software implementation of the introduced alternative approach is given.

Keywords: association rule, data mining, unit cube.

ACM Classification Keywords: 1.5. Pattern recognition, H.2.8 Database applications, Data mining.

Link:

ASSOCIATION RULE MINING WITH N-DIMENSIONAL UNIT CUBE CHAIN SPLIT TECHNIQUE

Levon Aslanyan, Robert Khachatryan

http://www.foibg.com/ijita/vol17/ijita17-2-p01.pdf

Abstract: This paper considers construction of some composition permutation polynomials. For some permutation polynomials the explicit view of their self-compositions and inverse mappings are given. Also for some particular case the cycle structure is considered.

Keywords: finite field, polynomial factorization, polynomial composition

ACM Classification Keywords: F.2.1 Numerical Algorithms and Problems

Link:

Construction of Some Composition Permutations via Linear Translators

Sergey Abrahamyan, Knarik Kyuregyan

http://www.foibg.com/ijita/vol22/ijita22-03-p08.pdf

Abstract: The article describes the architecture and principles of work of the developed system of automated processing of large volumes of textual information. The system is based on the modification of the free software library LibSVM and on the implemented in it method of support vector machines. The system performs functions of search, classification, categorization, and clustering of text documents requested by the user.

Keywords: classification, categorization, clustering, text documents processing.

ACM Classification Keywords: H.3.3 Information Search and Retrieval, H.3.1 Content Analysis and Indexing.

Link:

THE SYSTEM OF MULTILINGUAL TEXT DATA PROCESSING ON THE BASE OF THE MODIFIED ALGORITHM SVM

Oleg Moyseenko

http://www.foibg.com/ijita/vol22/ijita22-03-p07.pdf

Abstract: This work deals in the usage of fractal analysis to determine the trend of dynamic characteristics of chaotic series based on R/S-analysis. We propose an algorithm using the method of dynamic roles with large dimensions, which can be specified Hurst at every step of aggregation without storing values of data stream based on neural network technology.

Keywords: Complex System of Structured Type (CSST), chaotic dynamic series, fractal analysis, Hausdorff rate, Hurst rate, algorithm R/S -analysis, persistence, antipersistence, prognosis, neural network.

ACM Classification Keywords: G.1.2 Approximation, F.1.1 Models of Computation (F.4.1)

Link:

ALGORITHMIZATION PROCESS FOR FRACTAL ANALYSIS IN THE CHAOTIC DYNAMICS OF COMPLEX SYSTEMS STRUCTURED TYPE

Igor Skiter, Еlena Trunova

http://www.foibg.com/ijita/vol22/ijita22-03-p06.pdf

Abstract: The general structure of Collect/Report Paradigm (CRP) is outlined in this paper. CRP is a new approach for storing and accessing large amounts of data. Main advantages of CRP are: (1) collecting information is done by all nodes independently in parallel. It is possible one node to send information to another; (2) reporting information is provided only by the nodes which really contain information related to the request; the rest nodes do not react, they remain silent; (3) input data as well as results are in RDF-triple or RDF-quadruple format.

Keywords: Collect/Report Paradigm, Big Data, Cloud computing.

ACM Classification Keywords: D.4.3 File Systems Management, Access methods.

Link:

GENERAL STRUCTURE OF COLLECT/REPORT PARADIGM FOR STORING AND ACCESSING BIG DATA

Krassimir Markov, Krassimira Ivanova

http://www.foibg.com/ijita/vol22/ijita22-03-p05.pdf

Abstract: Series of problems concerning systems of linear Diophantine equations and dis-equations with explicitly given parameters are offered below. For every problem from a series the conditions upon the parameters under which the problem is NP-complete are proved.

Keywords: NP-completeness, system of linear Diophantine equations, system of linear Diophantine dis-equations

ACM Classification Keywords: F.2.m Analysis of Algorithms and Problem Complexity Miscellaneous

Link:

SYSTEMS OF LINEAR DIOPHANTINE EQUATIONS AND DIS-EQUATIONS COMPLEXITY

Nikolay K. Kosovskii, Nikolay N. Kosovskii

http://www.foibg.com/ijita/vol22/ijita22-03-p04.pdf

Abstract: A model of self-modificated predicate network with cells implementing predicate formulas in the form of elementary conjunction is suggested. Unlike a classical neuron network the proposed model has two blocks: a training block and a recognition block. If a recognition block has a mistake then the control is transferred to a training block. Always after a training block run the configuration of a recognition block is changed. The base of the proposed predicate network is logic-objective approach to AI problems solving and level description of classes.

Keywords: artificial intelligence, pattern recognition, predicate calculus, level description of a class.

ACM Classification Keywords: I.2.4 Artificial Intelligence - Knowledge Representation Formalisms and Methods-- Predicate logic; I.5.1 Pattern Recognition Models – Deterministic; F.2.2 Nonnumerical Algorithms and Problems – Complexity of proof procedures.

Link:

SELF-MODIFICATED PREDICATE NETWORKS

Tatiana Kosovskaya

http://www.foibg.com/ijita/vol22/ijita22-03-p03.pdf

Abstract: Assistive technologies provide means for disabled or impaired people to extend their capabilities, communicate and control their environment using alternative and augmentative forms of interaction. Neural-computer interface (NCI) is a communication system that translates neural activity of human muscular system (electromyography (EMG) signals) into commands for a computer or other digital device. The paper discusses the development of the visual concept language for EMG speller (text entry application) based on the application of sound visual communication methodological principles. We present a description of language based on the Speller Visual Communication Language Ontology (SVCLO) developed on the analysis of basic requirements of impaired users living in a closed Ambient Assisted Living environment. Evaluation of the language is given.

Keywords: NCI, neural-computer interfaces, speller, visual concept language, ontology, language modeling

ACM Classification Keywords: H5.m. Information interfaces and presentation (e.g., HCI): Miscellaneous

Link:

A VISUAL CONCEPT LANGUAGE FOR EMG SPELLER

Mindaugas Vasiljevas, Tomas Šumskas, Ignas Plauska, Robertas Damaševičius

http://www.foibg.com/ijita/vol22/ijita22-03-p02.pdf

Abstract: The notion of consistency is used to evaluate the contradiction level of expert pairwise comparison judgments and their suitability for the purpose of calculation of weights of decision alternatives. Several consistency coefficients and criteria are used to measure inconsistency of a pairwise comparison matrix (PCM). Traditional approach to increase consistency of expert information is to organize a feedback with an expert. However, it is not always possible due to financial and time limitations. The paper deals with methods of improvement (increase) PCM consistency without participation of an expert. Computer simulation is used to provide a comparative study of these methods. It is shown that taking an inadmissibly inconsistent PCM, for example, with the consistency ratio equal to CR=0.2 or CR=0.3, methods of improvement PCM consistency help to decrease inconsistency up to admissible level CR≤0.1 for n≥5. Results reveal that these methods, unfortunately, are not always effective, that is, drawing near to admissible inconsistency does not ensure closeness to the vector of real weights of decision alternatives. Also an analysis of coefficients and criteria of consistency of expert pairwise comparison judgments depending on PCM properties and level of its consistency is carried out.

Keywords: pairwise comparison matrix, coefficients of consistency, admissible level of inconsistency, consistency criteria, weak consistency, methods of consistency improvement without participation of an expert, methods of identification of the most inconsistent judgment, an effective improvement of consistency

ACM Classification Keywords: H.4.2. Information System Application: type of system strategy

Link:

METHODS OF EVALUATION AND IMPROVEMENT OF CONSISTENCY OF EXPERT PAIRWISE COMPARISON JUDGMENTS

Nataliya Pankratova, Nadezhda Nedashkovskaya

http://www.foibg.com/ijita/vol22/ijita22-03-p01.pdf

Abstract: The analysis of adequacy of competitiveness assessments based only on the values of multiplicity function of multiset is made. Such assessments are not adequate according to representational theory of measurement. An example of adequate assessments based on fuzzy multisets is given.

Keywords: adequate assessment, competitiveness, representational theory of measurement, multiset.

ACM Classification Keywords: F.4.1 Mathematical Logic, G.2.1 Combinatorics, I.2.4 Knowledge Representation Formalisms and Methods

ON PROBLEM OF ADEQUACY OF MULTISET MATHEMATICAL MODELS

Iryna Riasna

http://www.foibg.com/ijita/vol22/ijita22-02-p08.pdf

Abstract: A problem of choosing an appropriate set of parameters for estimates calculating algorithms height optimization is considered. The task arises for example in AVO-polynomial recognition method that depends on height optimization of individual ECA items. Initially some subset of general ECA family was used for such an optimization according to the simplicity of the resulting algorithms. In the present article it is shown that on some general conditions the defined ECA subfamily is optimal meaning that the optimal solution in more general one will belong to the said subfamily.

Keywords: estimates calculating algorithm, optimization, algebraic approach, pattern recognition.

ACM Classification Keywords: I.5 Pattern Recognition — I.5.0 General

Link:

ON CHOOSING PARAMETERS SET FOR ECA HEIGHT OPTIMIZATION

Alexander Dokukin

http://www.foibg.com/ijita/vol22/ijita22-02-p07.pdf

Abstract: In this paper we continue the investigation related to the development of tools for the design and implementation of computer business games, aimed at creating a certain level of competence in the process of realization of the scenarios defined by models of the applied domain.

Keywords: competences, business process, business game, business game script, automata model, operational model

ACM Classification Keywords: K.3 Computers And Education: K.3.2 Computer and Information Science Education – Information Systems Education; K.4 Computers and Society: K.4.3 Organizational Impacts – Employment; I.2 Artificial Intelligence: I.2.1 Applications and Expert Systems – Games

Link:

АЛГОРИТМЫ ФОРМИРОВАНИЯ ОПЕРАЦИОННОЙ МОДЕЛИ СТУДИИ КОМПЕТЕНТНОСТНЫХ ДЕЛОВЫХ ИГР

(Algorithms for Generating Operational Model of Competence Business Games)

Ольга Викентьева, Александр Дерябин, Лидия Шестакова

http://www.foibg.com/ijita/vol22/ijita22-02-p06.pdf

Abstract: In this paper we address the following questions. Can we assume that choosing the best interval alternative by their pair-wise comparison, we thus choose the alternative that is preferable simultaneously all others in their given set (prefer ability “as a whole”)? Does the answer depend to this question from an amount of compared alternatives? It is shown that comparing interval alternatives "as a whole" reduces the values of chances of prefer ability for each alternative with respect to these values under pair-wise comparison. This in turn leads to a quantitative increasing risk of choice as preferred alternative the alternative, which will not be really such later, in future, when the uncertainty will be removed. The nature of this effect is that in the presence of intersection even for two comparable interval alternatives there is a non-zero risk of making the wrong decision. This risk increases with the amount of comparable alternatives, particularly if the chances of preferability for some of them are not very different from each other. Does generate the comparison "as a whole" other changes in the results of the pair-wise comparison of alternatives? Particularly important is the question of possible depending order of the alternatives in their set defined by preferebilities on using concrete approaches to comparing. The answer to this question is negative: the order established under the pair-wise comparison is the same as the order for comparing “as a whole”. However, an estimation of true value of the risk associated with decision-making is useful for decision-maker or expert. Mentioned risk is in fact greater than risk that was estimated by pair-wise comparison because is determined not only by the 168 International Journal “Information Theories and Applications”, Vol. 22, Number 2, 2015 configurations of the compared pairs of alternatives, but also the concrete set of compared alternatives i.e. the risk depends on the context. The presence of a large number of alternatives aimed at achieving the same goal is a characteristic of the upper hierarchical levels of decision-making. Perhaps this is why the risk of making not quit right decision is more likely to upper management levels. If because of some reasons it is necessary to select a number of alternatives to supporting, the delegation of authority to lower management levels with the assignment of appropriate rights of decision-making concerning corresponding subset of alternatives is presented in the framework of the considered here approach to comparing as the well-founded, because it reduces the risks of decision-making at each level of management.

Keywords: collective effect for comparing the interval alternatives, dependence of the risk of making the wrong decision about prefer ability on context, taking into account results comparing “as a whole” during deciding on preferebility

ACM Classification Keywords: H.1.2 Human information processing; G3 Distribution functions; I.2.3 Uncertainty, “fuzzy”, and probabilistic reasoning.

Link:

СРАВНЕНИЕ ИНТЕРВАЛЬНЫХ АЛЬТЕРНАТИВ “В ЦЕЛОМ”

(Comparing Interval Alternatives “As a Whole”)

Михаил Стернин, Геннадий Шепелев

http://www.foibg.com/ijita/vol22/ijita22-02-p05.pdf

Abstract: This paper proposes a logical-linguistic model extracting semi-structured facts in English texts. To identify the fact some entities expressed by lexical units as well as semantic relations between them are defined in the text. The semantic relations are expressed by semantic functions of sentence participants. A fact is written in form of a triplet: Subject - Predicate - Object, in which the Predicate represents the relations and Subject and Object define the subjects, objects or concepts. Two types of the facts are defined. The first type is fact that describes relation between two entities; the second one is fact that fixes the value of a predetermined attribute. The functions are described by predicates of algebra of finite predicates. The mathematical model allows associating meaning relations of concepts of a sentence with elements of the syntactic and morphological structure of the English sentence. The model is applied to the semantic stage of linguistic processor of information subsystem for facts identification, which are essential for business analysis, in the framework a semi-structured texts. Software implementation of the model is designed. The input subsystem receives text streams disparate sources of information of the integrated corporate system, basic facts of space of the system are output. The accuracy and completeness extracted facts from texts in English by the subsystem are compatible with extracted facts by an expert.

Keywords: the system of facts generation, the automatic facts extraction, semantic relations, the algebra of finite predicates, natural language processing.

ACM Classification Keywords: H.3.3 .Information Search and Retrieval, I.2.4. Knowledge Representation Formalisms and Methods

Link:

ЛОГИКО-ЛИНГВИСТИЧЕСКАЯ МОДЕЛЬ ГЕНЕРАЦИИ ФАКТОВ ИЗ ТЕКСТОВЫХ ПОТОКОВ ИНФОРМАЦИОННОЙ КОРПОРАТИВНОЙ СИСТЕМЫ

(Logic-linguistic model of fact generation from text streams of corporate information system)

Нина Хайрова, Наталья Шаронова, Аджит Пратап Сингх Гаутам

http://www.foibg.com/ijita/vol22/ijita22-02-p04.pdf

Abstract: In this paper the calculating estimates model, based on a system of logical regularities to solve the supervised classification problem is considered. A method of determining the weighting parameters of the decision rule, as well as two methods to eliminate bounce on the classification by introducing a logical disjunction of the negations of regularities and the approximation of regularities by sigmoid logic functions are proposed. The results of numerical experiments are presented.

Keywords: classification, pattern recognition, estimates calculation, multi-algorithmic approach, logical regularities

ACM Classification Keywords: I.2.4 Artificial Intelligence Knowledge Representation Formalisms and Methods – Predicate logic; I.5.1 Pattern Recognition Models – Deterministic, H.2.8 Database Applications, Data mining; I.5.3 Clustering.

Link:

ОБ ОДНОМ МЕТОДЕ МУЛЬТИАЛГОРИТМИЧЕСКОЙ КЛАССИФИКАЦИИ

(On a method of multi-algorithmic classification)

Сергей Львов, Владимир Рязанов

http://www.foibg.com/ijita/vol22/ijita22-02-p03.pdf

Abstract: It is shown, that under vector approach a decision-making problem by means of decomposition of alternative’s emergent properties can be presented by a hierarchical system of criteria. At the bottom level estimation of the alternative on separate properties is carried out through a vector of criteria, and at the top level by means of mechanism of composition the estimation of the alternative as a whole turns out. The problem is solved by method of nested scalar convolutions of vector-valued criteria. The methodology of the problem solving is based on complementarity principle by N. Bohr and theorem of imperfection by K. Gödel.

Keywords: hierarchy, emergence, embedded scalar convolutions, multicriteriality

ACM Classification Keywords: H.1 Models and Principles, H.1.1 Systems and Information Theory; H.4.2 Types of Systems

Link:

ИЕРАРХИЯ ЭМЕРДЖЕНТНЫХ СВОЙСТВ АЛЬТЕРНАТИВ В СИСТЕМНОМ АНАЛИЗЕ

(Hierarchy of Emergent Properties of Alternatives in Systems Analysis)

Альберт Воронин

http://www.foibg.com/ijita/vol22/ijita22-02-p02.pdf

Abstract: A set of functions and operations on ontologies for effective representation, analysis, transformation and construction of ontologies is defined.

Keywords: ontology, functions, operations, transformations, construction.

ACM Classification Keywords: I.2 Artificial Intelligence – I.2.4 Knowledge Representation Formalisms and Methods.

Link:

РАЗРАБОТКА, ИСЛЕДОВАНИЕ И ПРЕДСТАВЛЕНИЕ ФУНКЦИЙ И ОПЕРАЦИЙ НА ОНТОЛОГИЯХ

(Development, Study and Presentation of Functions and Operations on Ontologies)

Александр Палагин, Сергей Крывый, Николай Петренко

http://www.foibg.com/ijita/vol22/ijita22-02-p01.pdf

Abstract: The paper is devoted to analysis of effectiveness the usage of modern statistical model of digital image for revealing the stego images with data, embedded in transformation domain of cover images. It is considered the case of applying of standard Subtractive Pixel Adjacency Matrix model for detection the presence of stegodata, hidden with usage of various type the cover image transformation – Discrete Cosine Transform, Discrete Wavelets Transform, Singular Value Decomposition. It is established that accuracy of stego image detection by usage of the model rises by increasing the amount of stage the cover image processing and significantly depends on type of embedded stegodata.

Keywords: passive steganalysis, multistage embedding methods, digital images.

ACM Classification Keywords: D.4 Operating Systems – Security and protection – Information flow controls.

Link:

PASSIVE STEGANALYSIS OF MULTIDOMAIN EMBEDDING METHODS

Dmytro Progonov, Serhii Kushch

http://www.foibg.com/ijita/vol22/ijita22-01-p06.pdf

Abstract: Description of software solutions for logistic tasks and their comparative analysis are considered in the article. The selection of the functionality of Logistics Information System, which is designed to automate the planning of the transport delivery of freights, is presented. The logistical tasks considering features of transportation of agricultural freights, which should solve the Logistics Information System, are analyzed.

Keywords: logistics information system, automation of delivery routes, temporary infrastructure, GIS – technology, ERP-systems.

ACM Classification Keywords: D.2.0 Genera - Software Engineering.

Link:

REVIEW OF THE SOFTWARE SOLUTIONS OF LOGISTIC TASKS

Vitalii Lytvynov, Alina Posadska

http://www.foibg.com/ijita/vol22/ijita22-01-p05.pdf

Abstract: The problem of constructing an optimal portfolio of securities under uncertainty was considered. The global market crisis of recent years has shown that the existing theory of optimization of investment portfolios and forecasting stock indices exhausted and the revision of the basic theory of portfolio management is strongly needed. Therefore the fuzzy sets theory was used for getting an optimal portfolio. In this paper direct, dual and multicriteria problems with the use of triangular membership functions work were considered. The problem of portfolio optimization during the time period also was described in this article. In direct task we define structure of a portfolio, which will provide the maximum profitableness at the set risk level. In dual task we define structure of a portfolio, which will provide the minimum risk level at the set level of critical profitableness. In multicriteria problem we simultaneously maximize profitability and minimize risk level. The input data for the optimization system were predicted by using the Fuzzy Group Method of Data Handling (FGMDH). The optimal portfolios for assets were determined. The comparative analysis of optimal portfolios obtained by different methods and approaches was fulfilled.

Keywords: membership function, fuzzy sets theory, optimal portfolio, investments, stock securities, fuzzy number, FGMDH

ACM Classification Keywords: G.1.0 Mathematics of Computing– General – Error analysis; G.1.6 Mathematics of Computing – Numerical Analysis – Optimization - Gradient methods, Least squares methods; I.2.3 Computing Methodologies - Artificial Intelligence - Uncertainty, “fuzzy”, and probabilistic reasoning.

Link:

CONSTRUCTING AN OPTIMAL INVESTMENT PORTFOLIO BY USING FUZZY SETS THEORY

Yuri Zaychenko, Inna Sydoruk

http://www.foibg.com/ijita/vol22/ijita22-01-p04.pdf