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ITHEA Classification Structure > G. Mathematics of Computing  > G.1 NUMERICAL ANALYSIS  > G.1.6 Optimization 
ITHEA Classification Structure > G. Mathematics of Computing  > G.2 DISCRETE MATHEMATICS  > G.2.1 Combinatorics 
ITHEA Classification Structure > G. Mathematics of Computing  > G.2 DISCRETE MATHEMATICS  > G.2.m Miscellaneous 
ITHEA Classification Structure > G. Mathematics of Computing  > G.3 PROBABILITY AND STATISTICS 
ITHEA Classification Structure > H. Information Systems  > H.1 MODELS AND PRINCIPLES  > H.1.m Miscellaneous 
ITHEA Classification Structure > I. Computing Methodologies  > I.5 PATTERN RECOGNITION  > I.5.1 Models 
FUZZY SETS: MATH, APPLIED MATH, HEURISTICS? PROBLEMS AND INTERPRETATIONS
By: Volodymyr Donchenko (3715 reads)
Rating: (1.00/10)

Abstract: Number of Disciplines and Theories changed their status from status of Natural Science discipline to Mathematics. The Theory of Probability is the classical example of that kind. The main privilege of the new Math status is the conception of Math truth, which distinguishes Math from other theories. Some disciplines used in Applications pretended to be Math not really being it. It is entirely true of Fuzzy Subsets Theory with its pretension to be Math and to be exclusive tools in uncertainty handling. Fundamental pretensions of classical Fuzzy subset theory including pretension to be math as well as some gaps in the theory are discussed in the article. Statistical interpretation of membership functions is proposed. It is proved that such interpretation takes place for practically all supporters with minimal constraints on it. Namely, a supporter must be a space with a measure. Proposed interpretation explains modification of classical fuzzy objects to fill the gaps. It is then possible to talk about observations of fuzzy subset within the conception of modification and to extend likelihood method to the new area. Fuzzy likelihood equation is adduced as an example of new possibilities within the proposed approach. One more interpretation for the Fuzzy subset theory is proposed for a discussion: multiset theory.

Keywords: f Uncertainty, Plural model of uncertainty, Fuzzy subsets Theory, statistical interpretation of the membership function, modification of Fuzzy subsets, Fuzzy likelihood equation, Multiset theory.

ACM Classification Keywords: G.2.m. Discrete mathematics: miscellaneous,G.2.1 Combinatorics. G.3 Probability and statistics, G.1.6. Numerical analysis I.5.1.Pattern Recognition: Models Fuzzy sets; H.1.m. Models and Principles: miscellaneous:

Link:

FUZZY SETS: MATH, APPLIED MATH, HEURISTICS? PROBLEMS AND INTERPRETATIONS

Volodymyr Donchenko

http://foibg.com/ibs_isc/ibs-23/ibs-23-p07.pdf

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G.1.6 Optimization
article: CONSTRUCTING AN OPTIMAL INVESTMENT PORTFOLIO BY USING FUZZY SETS THEORY · FEATURES OF PLANNING TECHNOLOGIES IN COMPUTER-AIDED MANAGEMENT SYSTEMS ... · METHOD FOR CONTROLLING STATE CHANNEL WIRELESS NETWORKS UNDER A PRIORI ... · DIRECT AND DUAL PROBLEM OF INVESTMENT PORTFOLIO OPTIMIZATION UNDER UNCERTAINTY · MATRIXES LEAST SQUARES METHOD AND EXAMPLES OF ITS APPLICATION · КОМПЛЕКСНЫЙ АНАЛИЗ РИСКА БАНКРОТСТВА КОРПОРАЦИЙ В УСЛОВИЯХ НЕОПРЕДЕЛЕННОСТИ · CONSTRUCTING AN OPTIMAL INVESTMENT PORTFOLIO BY USING FUZZY SETS THEORY · A COMPARISON OF SOME APPROACHES TO THE RECOGNITION PROBLEMS IN CASE OF TWO ... · Automated Building Extraction System Applied On High Resolution Satellite ... · SPREADING THE MOORE - PENROSE PSEUDO INVERSE ON MATRICES EUCLIDEAN SPACES: ... · Solution Algorithm of Multicriteria Problems of Lexicographic Optimization ... · ABOUT CRITERIA FOR AN ESTIMATION OF NONLINEAR PARAMETERS IN MODELS OF ... · MATRIX “FEATURE VECTORS” IN GROUPING INFORMATION PROBLEM: LINEAR ... · VECTORS AND MATRIXES LEAST SQUARES METHOD: FOUNDATION AND APPLICATION ... · NUMERICAL INTEGRATION BY GENETIC ALGORITHMS · VECTORS AND MATRIXES IN GROUPING INFORMATION PROBLEM · NON SMOOTH OPTIMIZATION METHODS IN THE PROBLEMS OF CONSTRUCTING A LINEAR ... · RECURRENT PROCEDURE IN SOLVING THE GROUPING INFORMATION PROBLEM IN APPLIED... · АЛГОРИТМ ПОСТРОЕНИЯ ВЫПУКЛОГО ПРОДОЛЖЕНИЯ · ‘FEATURE VECTORS’ IN GROUPING INFORMATION PROBLEM IN APPLIED MATHEMATICS: .. · EFFECTIVE ENERGY RECOMPUTATION FOR LOW AUTOCORRELATION BINARY SEQUENCE PROBLEM · FUZZY SETS AS A MEAN FOR UNCERTAINTY HANDLING: MATH, APPLIED MATH, HEURISTICS · FUZZY SETS: MATH, APPLIED MATH, HEURISTICS? PROBLEMS AND INTERPRETATIONS · ИССЛЕДОВАНИЕ МНОГОКРИТЕРИАЛЬНОЙ ЗАДАЧИ ОП� · РАСПОЗНАВАНИЕ ЗДАНИЙ НА СПУТНИКОВЫХ СНИМКА · ПОСТРОЕНИЕ НЕЛИНЕЙНЫХ КЛАССИФИКАТОРОВ В СЛ · ЕВКЛИДОВЫ ПРОСТРАНСТВА ЧИСЛОВЫХ ВЕКТОРОВ И · TWO APPROACHES TO ONE OPTIMIZATION PROBLEM IN RECOGNITION THEORY · DIFFERENTIAL EVOLUTION – PARTICLE SWARM OPTIMIZATION · EXACT DISCRIMINANT FUNCTION DESIGN USING SOME OPTIMIZATION TECHNIQUES · IMPLEMENTATION OF GENETIC ALGORITHMS FOR TRANSIT POINTS ARRANGEMENT · APPLICATION OF DISCRETE OPTIMIZATION IN SOLVING A PROBLEM OF MULTI-ITEM ... · OPTIMAL DESIGN OF INTELLIGENT CONTROL SYSTEMS OF STEAM TURBINE USING GENETIC ... · OPTIMAL SYNTHESIS OF INTELLIGENT CONTROL SYSTEMS OF ATOMIC POWER STATION USING G · APPLICATION OF GENETIC ALGORITHMS TO VECTOR OPTIMIZATION OF THE AUTOMATIC CONTRO · REFERENCE-NEIGHBOURHOOD SCALARIZATION FOR MULTIOBJECTIVE INTEGER LINEAR ... · MINIMIZATION OF EMPIRICAL RISK IN LINEAR CLASSIFIER PROBLEM · BENCHMARK OF PSO-DE USING BBOB 2010 · PROTEIN STRUCTURE PREDICTION ON A THREE-DIMENSIONAL TRIANGULAR LATTICE · CLASSIFICATION OF HEURISTIC METHODS IN COMBINATORIAL OPTIMIZATION · APPLIED ASPECTS OF MATHEMATICAL MODELING AND OPTIMIZATION ... · DISTRIBUTED GENETIC ALGORITHM IMPLEMENTATION BY MEANS OF REMOTE METHODS ... · APPLICATION OF GENETIC ALGORITHMS TO VECTOR OPTIMIZATION ... · OPTIMAL SYNTHESIS OF INTELLIGENT CONTROL SYSTEMS OF ATOMIC POWER ... · OPTIMAL DESIGN OF INTELLIGENT CONTROL SYSTEMS OF STEAM TURBINE ... · FINDING THE RELATIONSHIP BETWEEN A SEARCH ALGORITHM AND ... · DATA FLOW ANALYSIS AND THE LINEAR PROGRAMMING MODEL1 · REPRESENTATION OF NEURAL NETWORKS BY DYNAMICAL SYSTEMS ·
G.2.1 Combinatorics
article: RANDOMIZED SET SYSTEMS CONSTRAINED BY THE DISCRETE TOMOGRAPHY · A NEW ALGORITM FOR THE LONGEST COMMON SUBSEQUENCE PROBLEM · ON THE STRUCTURE OF MAXIMUM INDEPENDENT SETS IN BIPARTITE GRAPHS · SOME PROPERTIES IN MULTIDIMENSIONAL MULTIVALUED DISCRETE TORUS · ON PROBLEM OF ADEQUACY OF MULTISET MATHEMATICAL MODELS · SPREADING THE MOORE - PENROSE PSEUDO INVERSE ON MATRICES EUCLIDEAN SPACES: ... · VECTORS AND MATRIXES IN GROUPING INFORMATION PROBLEM · CHOICE OF DIAGNOSTIC DECISION MAKING IN MEDICINE AND INTERVENTION MISTAKE ... · RECURRENT PROCEDURE IN SOLVING THE GROUPING INFORMATION PROBLEM IN APPLIED... · ‘FEATURE VECTORS’ IN GROUPING INFORMATION PROBLEM IN APPLIED MATHEMATICS: .. · DECOMPOSITION METHODS FOR LARGE-SCALE TSP · ON THE DISCRETIZATION OF DISTANCE GEOMETRY PROBLEMS · REGULAR INVERSIVE POLYTOPES · LOGARITHMIC DISTANCES IN GRAPHS · FUZZY SETS AS A MEAN FOR UNCERTAINTY HANDLING: MATH, APPLIED MATH, HEURISTICS · FUZZY SETS: MATH, APPLIED MATH, HEURISTICS? PROBLEMS AND INTERPRETATIONS · CROSS INTERSECTION SEQUEL OF DISCRETE ISOPERIMETRY1 · GENERATING MORE BOUNDARY ELEMENTS OF SUBSET PROJECTIONS · MULTICRITERION PROBLEMS ON THE COMBINATORIAL SET OF POLYARRANGEMENTS · CHAIN SPLIT OF PARTIALLY ORDERED SET OF K-SUBSETS · SOLVING LARGE SYSTEMS OF BOOLEAN EQUATIONS · LAGRANGEAN APPROXIMATION FOR COMBINATORIAL INVERSE PROBLEMS · MULTICRITERION PROBLEMS ON THE COMBINATORIAL SET OF POLYARRANGEMENTS · DESCRIPTION REDUCTION FOR RESTRICTED SETS OF (0,1) MATRICES 1 · DECOMPOSITION OF BOOLEAN FUNCTIONS – RECOGNIZING A GOOD SOLUTION BY TRACES · THE BOUNDARY DESCRIPTORS OF THE n-DIMENSIONAL UNIT CUBE SUBSET PARTITIONING1 · RANDOMIZED PARALLELIZATION – A NEW METHOD FOR SOLVING ... · OPTIMIZATION OF ATM TELECOMMUNICATION NETWORKS · VECTOR COMBINATORIAL PROBLEMS IN A SPACE OF COMBINATIONS ... ·
G.2.m Miscellaneous
article: SPREADING THE MOORE - PENROSE PSEUDO INVERSE ON MATRICES EUCLIDEAN SPACES: ... · MATRIX “FEATURE VECTORS” IN GROUPING INFORMATION PROBLEM: LINEAR ... · VECTORS AND MATRIXES IN GROUPING INFORMATION PROBLEM · RECURRENT PROCEDURE IN SOLVING THE GROUPING INFORMATION PROBLEM IN APPLIED... · ‘FEATURE VECTORS’ IN GROUPING INFORMATION PROBLEM IN APPLIED MATHEMATICS: .. · FUZZY SETS AS A MEAN FOR UNCERTAINTY HANDLING: MATH, APPLIED MATH, HEURISTICS · FUZZY SETS: MATH, APPLIED MATH, HEURISTICS? PROBLEMS AND INTERPRETATIONS · ЕВКЛИДОВЫ ПРОСТРАНСТВА ЧИСЛОВЫХ ВЕКТОРОВ И ·
G.3 PROBABILITY AND STATISTICS
article: DECISION-MAKING IN GROUPS OF INTERVAL ALTERNATIVES · RISK BEHAVIOUR IN A SET OF INTERVAL ALTERNATIVES · Peculiarities Analysis of Statistical Information in ICT · About convergence of fuzzy perceptive elements sequences, defined on ... · INFORMATION SYSTEM OF FORECASTING BASED ON COMBINED MODELS WITH TIME SERIES ... · Integrated Approach to the Study of Fractal Time Series · METHOD OF DATA ANALYSIS BASED ON CLUSTERING IN “SYNDROMES” INDICATORS SPACE · MATRIXES LEAST SQUARES METHOD AND EXAMPLES OF ITS APPLICATION · PHYSICAL PHENOMENON OF STATISTICAL STABILITY · ANALYSIS OF FEATURES AND POSSIBILITIES OF BANK FUNCTIONING EFFICIENCY BASED ... · SUB-OPTIMAL NONPARAMETRIC HYPOTHESES DISCRIMINATING WITH GUARANTEED DECISION · Solution of the Problem of Formal Evaluation of Effectiveness of ... · ANALYSIS OF THE PROPERTIES OF ORDINARY LEVY MOTION BASED ON THE ESTIMATION ... · SPREADING THE MOORE - PENROSE PSEUDO INVERSE ON MATRICES EUCLIDEAN SPACES: ... · Evaluating Expected Effectiveness of Interval Alternatives · · EVALUATING EXPECTED EFFECTIVENESS OF INTERVAL ALTERNATIVES · COMPARISON OF DIFFERENT WAVELET BASES IN THE CASE OF WAVELETS EXPANSIONS... · О ПРИМЕНИМОСТИ ОЦЕНКО МАТЕМАТИЧЕСКОГО ОЖИД · VECTORS AND MATRIXES LEAST SQUARES METHOD: FOUNDATION AND APPLICATION ... · VECTORS AND MATRIXES IN GROUPING INFORMATION PROBLEM · ОЦЕНКА ИНТЕРВАЛЬНЫХ АЛЬТЕРНАТИВ:... · ON SOME PROPERTIES OF REGRESSION MODELS BASED ON CORRELATION MAXIMIZATION ... · RECURRENT PROCEDURE IN SOLVING THE GROUPING INFORMATION PROBLEM IN APPLIED... · DIVERGENT AND MULTIPLE-VALUED SEQUENCES AND FUNCTIONS · ‘FEATURE VECTORS’ IN GROUPING INFORMATION PROBLEM IN APPLIED MATHEMATICS: .. · MODELING TELECOMMUNICATIONS TRAFFIC USING THE STOCHASTIC MULTIFRACTAL CASCADE... · INTERVALS AS ULTRAMETRIC APPROXIMATIONS ACCORDING TO THE SUPREMUM NORM · DIFFERENTIAL GEOMETRY DERIVED FROM DIVERGENCE FUNCTIONS... · COMPARATIVE ANALYSIS FOR ESTIMATING OF THE HURST EXPONET FOR STATIONARY AND ... · DISTURBANCE OF STATISTICAL STABILITY (PART II) · FUZZY SETS AS A MEAN FOR UNCERTAINTY HANDLING: MATH, APPLIED MATH, HEURISTICS · FUZZY SETS: MATH, APPLIED MATH, HEURISTICS? PROBLEMS AND INTERPRETATIONS · СИММЕТРИЯ В ЗАПИСИ ГЕНЕТИЧЕСКОЙ ИНФОРМАЦИИ · ЕВКЛИДОВЫ ПРОСТРАНСТВА ЧИСЛОВЫХ ВЕКТОРОВ И · METHOD FOR EVALUATING OF DISCREPANCY BETWEEN REGULARITIES SYSTEMS IN ... · CORRELATION MAXIMIZATION IN REGRESSION MODELS BASED ON CONVEX COMBINATIONS · NEURAL NETWORK SEGMENTATION OF VIDEO VIA TIME SERIES ANALYSIS · GOD-ICS. ON FUNDAMENTAL INFORMATION FIELD QUEST · ОЦЕНИВАНИЕ РИСКА РЕГРЕССИОННОЙ МОДЕЛИ В СЛ� · ПОСТРОЕНИЕ ЛОГИКО-ВЕРОЯТНОСТНЫХ МОДЕЛЕЙ В� · ОПТИМИЗАЦИЯ ОЦЕНКИ ВЕРОЯТНОСТИ ОШИБОЧНОЙ К · ON A PROBLEM OF QOS CHARACTERISTICS INTERPRETATION IN TRANSIT NETWORKS · OPTIMAL FORECASTING BASED ON CONVEXCORRECTING PROCEDURES · COMPARATIVE ANALYSIS OF STATISTICAL PROPERTIES OF THE HURST EXPONENT ... · DISTURBANCE OF STATISTICAL STABILITY · A SURVEY OF NONPARAMETRIC TESTS FOR THE STATISTICAL ANALYSIS OF EVOLUTIONARY ... · COGNITION HORIZON AND THE THEORY OF HYPER-RANDOM PHENOMENA · IMPROVED CRYPTOANALYSIS OF THE SELF-SHRINKING ... · EVALUATION OF PARETO/D/1/K QUEUE BY SIMULATION · N A PROBLEM OF QOS CHARACTERISTICS INTERPRETATION IN TRANSIT NETWORKS · APPLICATION OF THE HETEROGENEOUS SYSTEM PREDICTION METHOD · STUDY OF QUEUEING BEHAVIOUR IN IP BUFFERS · EXTREME SITUATIONS PREDICTION BY MULTIDIMENSIONAL HETEROGENEOUS ... · APPLICATION OF THE MULTIVARIATE PREDICTION METHOD TO TIME SERIES 1 · DETECTION OF LOGICAL-AND-PROBABILISTIC CORRELATION IN TIME SERIES1 ·
H.1.m Miscellaneous
article: MATRIXES LEAST SQUARES METHOD AND EXAMPLES OF ITS APPLICATION · SPREADING THE MOORE - PENROSE PSEUDO INVERSE ON MATRICES EUCLIDEAN SPACES: ... · VECTORS AND MATRIXES LEAST SQUARES METHOD: FOUNDATION AND APPLICATION ... · VECTORS AND MATRIXES IN GROUPING INFORMATION PROBLEM · RECURRENT PROCEDURE IN SOLVING THE GROUPING INFORMATION PROBLEM IN APPLIED... · ‘FEATURE VECTORS’ IN GROUPING INFORMATION PROBLEM IN APPLIED MATHEMATICS: .. · FUZZY SETS AS A MEAN FOR UNCERTAINTY HANDLING: MATH, APPLIED MATH, HEURISTICS · FUZZY SETS: MATH, APPLIED MATH, HEURISTICS? PROBLEMS AND INTERPRETATIONS ·
I.5.1 Models
article: POLLEN GRAINS RECOGNITION USING STRUCTURAL APPROACH AND NEURAL NETWORKS · Bankruptcy risk forecasting under uncertainty with application of fuzzy · CONVOLUTION NETWORKS AS A METHOD OF REALISATION OF CUSTOMS RISK-MANAGEMENT · АППРОКСИМАЦИЯ ФУНКЦИИ ЯРКОСТИ ОБЪЕКТА ПОЛУТОНОВОГО ИЗОБРАЖЕНИЯ · SELF-MODIFICATED PREDICATE NETWORKS · ON A METHOD OF MULTI-ALGORITHMIC CLASSIFICATION · PROCESSING SETS OF CLASSES’ LOGICAL REGULARITIES · ADAPTIVE FUZZY PROBABILISTIC CLUSTERING OF INCOMPLETE DATA · THE INVERSE MASLOV METHOD AND ANT TACTICS FOR EXHAUSTIVE SEARCH DECREASING · JOINT STUDY OF VISUAL PERCEPTION MECHANISM AND COMPUTER VISION SYSTEMS THAT ... · Online Handwritten Mathematical Expressions Recognition System Using Fussy ... · Automated Building Extraction System Applied On High Resolution Satellite ... · SPREADING THE MOORE - PENROSE PSEUDO INVERSE ON MATRICES EUCLIDEAN SPACES: ... · CONSTRUCTION OF CLASS LEVEL DESCRIPTION FOR EFFICIENT RECOGNITION OF ... · INFORMATION TECHNOLOGY OF PROCESSING INFORMATION OF THE CUSTOMS CONTROL · MODEL FOR ASTRONOMICAL DATING OF THE CHRONICLE OF HYDATIUS: ... · MATRIX “FEATURE VECTORS” IN GROUPING INFORMATION PROBLEM: LINEAR ... · EFFICIENT SIMULATION FOR PROLOG IMPLEMENTATION OF IMAGE RECOGNITION PROBLEM · VECTORS AND MATRIXES IN GROUPING INFORMATION PROBLEM · CROP STATE AND AREA ESTIMATION IN UKRAINE BASED ON REMOTE AND INSITU ... · THE INVERSE METHOD FOR SOLVING ARTIFICIAL INTELLIGENCE PROBLEMS IN ... · RECURRENT PROCEDURE IN SOLVING THE GROUPING INFORMATION PROBLEM IN APPLIED... · ‘FEATURE VECTORS’ IN GROUPING INFORMATION PROBLEM IN APPLIED MATHEMATICS: .. · ADAPTIVE CLUSTERING OF INCOMPLETE DATA USING NEURO-FUZZY KOHONEN NETWORK · INTELLIGENT ANALYSIS OF MARKETING DATA · FUZZY SETS AS A MEAN FOR UNCERTAINTY HANDLING: MATH, APPLIED MATH, HEURISTICS · PERFORMANCE OF COMPUTER-AIDED DIAGNOSIS TECHNIQUES IN INTERPRETATION OF ... · FUZZY SETS: MATH, APPLIED MATH, HEURISTICS? PROBLEMS AND INTERPRETATIONS · ОНЛАЙН РАСПОЗНАВАНИЕ РУКОПИСНЫХ МАТЕМАТИЧ� · РАСПОЗНАВАНИЕ ЗДАНИЙ НА СПУТНИКОВЫХ СНИМКА · СЛОЖНЫЕ ЗАДАЧИ РАСПОЗНАВАНИЯ ОБРАЗОВ И ВОЗМОЖНОСТИ ИХ РЕШЕНИЯ · THE USAGE OF NEURAL NETWORKS FOR THE MEDICAL DIAGNOSIS · SYNTHESIS OF CORRECTOR FAMILY WITH HIGH RECOGNITION ABILITY* · FLOOD RISK ASSESSMENT BASED ON GEOSPATIAL DATA · FUZZY ARTMAP NEURAL NETWORKS FOR COMPUTER AIDED DIAGNOSIS · STRUCTURAL MODEL OF HALFTONE IMAGE AND IMAGE SEGMENTATION EXPERIMENTS · HIGH-PERFORMANCE INTELLIGENT COMPUTATIONS ... · INTELLIGENCE ALGORITHMS FOR INCREASING NAVIGATION SYSTEMS ACCURACY · ADAPTIVE GUSTAFSON-KESSEL FUZZY CLUSTERING ALGORITHM BASED ON ... · UNCERTAINTY AND FUZZY SETS: CLASSIFYING THE SITUATION · LOGIC BASED PATTERN RECOGNITION - ONTOLOGY CONTENT (1) 1 · EVALUATING MISCLASSIFICATION PROBABILITY USING EMPIRICAL RISK1 · FUZZY SETS: ABSTRACTION AXIOM, STATISTICAL INTERPRETATION, OBSERVATIONS ... · AN APPROACH TO COLLABORATIVE FILTERING BY ARTMAP NEURAL NETWORKS ·
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