scholarly journals Fuzzy Logic for Incidence Geometry

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Alex Tserkovny
Keyword(s):  
Fuzzy Logic ◽  
Spatial Reasoning ◽  
Geometric Reasoning ◽  
Conditional Inference ◽  
Incidence Geometry ◽  
Mathematical Framework ◽  
Human Language ◽  
Mathematical Apparatus ◽  
Reasoning System ◽  
Fuzzy Degree

The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid’s first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points.

scholarly journals Investigation on Agricultural Land Selection using Hybrid Fuzzy Logic System

2020 ◽  
Vol 21 (4) ◽  
pp. 569-582
Author(s):  
Sudhakar Sengan ◽  
Vijayakumar V ◽  
Sujatha Krishnamoorthy ◽  
Gunasekaran S ◽  
Sathiya Kumar C ◽  
...  
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Numbers ◽  
Agricultural Land ◽  
Test Results ◽  
Analytic Hierarchy ◽  
Fuzzy Degree ◽  
Hierarchy Process ◽  
Inherent Ambiguity ◽  
Different Levels ◽  
Logic System

For maintaining the horticultural generation, Land Selection Investigation (LSI) is essential. Though incorporates estimation of the criteria assortment from the soil, territory to financial, market, and foundation, and these components are considerably enigmatically characterized and described by their inherent ambiguity. Multi-criteria basic leadership systems like positioning, rating, and so on are utilized for reasonableness examination. Master learning and judgment by leaders at different levels is integrated into this process. In the field of farming sciences, the Fuzzy Logic (FL) strategy has been effectively used to take care of numerous issues. Fuzzy with AHP is a Hybrid Fuzzy Logic (HFL) methodology. The policies Analytic Hierarchy Process(AHP), Fuzzy Numbers, Fuzzy Degree Investigation, Alpha Cut, and Lambda capacity are associated with it. As expressed, the procedure of necessary leadership includes a scope of criteria and a considerable measure of master learning and decisions. The components result from impacts extraordinarily. The capacity of three methods to demonstrate the affectability of the necessary leadership procedure is researched. Alpha cut and lambda esteem give and encourage considerable affectability investigation. All techniques are actualized to examine the reasonableness of the crop in the Indian nation. Test results when performed on various datasets, demonstrate that the proposed procedure removes more highlights just as gives more exactness when  contrasted with existing techniques.

scholarly journals Assessment of Investment Attractiveness of Projects on the Basis of Environmental Factors

2019 ◽  
Vol 11 (9) ◽  
pp. 2544 ◽  
Author(s):  
Sayabek Ziyadin ◽  
Elena Streltsova ◽  
Alex Borodin ◽  
Nataliya Kiseleva ◽  
Irina Yakovenko ◽  
...  
Keyword(s):  
Fuzzy Logic ◽  
Decision Support ◽  
Environmental Factors ◽  
Mathematical Models ◽  
Mathematical Apparatus ◽  
Investment Projects ◽  
Environmental Criteria ◽  
Structured Knowledge ◽  
Matlab Package ◽  
The Impact

This article is devoted to the creation of intelligent modelling tools for decision support in the evaluation of intellectual projects submitted for financing, as based on qualitatively defined characteristics. The economic and mathematical models that form the basis of the toolkit are constructed using the mathematical apparatus of fuzzy logic, which allows for the description of poorly structured knowledge of specialists, as well as their application in solving questions about the extent of the impact of the proposed projects on the environment. The authors classify investment projects according to the degree of impact on the environment, the environmental criteria required by the investor for the evaluation of investment projects, and the formal formulation of the problem of evaluation of investment projects when taking into account the environmental factor. The toolkit was created based on the concept of intellectualization, where economic and mathematical models for the evaluation of investment projects are programmatically implemented via the tools and functions available in the MATLAB package.

scholarly journals The statistical nature of geometric reasoning

2017 ◽  
Author(s):  
Yuval Hart ◽  
Moira R. Dillon ◽  
Andrew Marantan ◽  
Anna L. Cardenas ◽  
Elizabeth Spelke ◽  
...  
Keyword(s):  
Dynamic Models ◽  
Physical World ◽  
Geometric Reasoning ◽  
Mathematical Framework ◽  
Global Orientation ◽  
Cognitive Studies ◽  
Statistical Dynamic ◽  
The Mean ◽  
Straight Lines ◽  
Triangle Completion

AbstractGeometric reasoning has an inherent dissonance: its abstract axioms and propositions refer to infinitesimal points and infinite straight lines while our perception of the physical world deals with fuzzy dots and curved stripes. How we use these disparate mechanisms to make geometric judgments remains unresolved. Here, we deploy a classically used cognitive geometric task - planar triangle completion - to study the statistics of errors in the location of the missing vertex. Our results show that the mean location has an error proportional to the side of the triangle, the standard deviation is sub-linearly dependent on the side length, and has a negative skewness. These scale-dependent responses directly contradict the conclusions of recent cognitive studies that innate Euclidean rules drive our geometric judgments. To explain our observations, we turn to a perceptual basis for geometric reasoning that balances the competing effects of local smoothness and global orientation of extrapolated trajectories. The resulting mathematical framework captures our observations and further predicts the statistics of the missing angle in a second triangle completion task. To go beyond purely perceptual geometric tasks, we carry out a categorical version of triangle completion that asks about the change in the missing angle after a change in triangle shape. The observed responses show a systematic scale-dependent discrepancy at odds with rule-based Euclidean reasoning, but one that is completely consistent with our framework. All together, our findings point to the use of statistical dynamic models of the noisy perceived physical world, rather than on the abstract rules of Euclid in determining how we reason geometrically.

scholarly journals THE PROBLEM OF OBJECTIVE ASSESSMENT OF THE STUDENT’S KNOWLEDGE

2021 ◽  
Vol 7 (73) (1) ◽  
pp. 77-85
Author(s):  
N. V. Apatova ◽  
A. I. Gaponov
Keyword(s):  
Fuzzy Logic ◽  
Knowledge Acquisition ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Educational Material ◽  
Specific Situation ◽  
Mathematical Apparatus ◽  
Subjective Factor ◽  
Hierarchy Analysis

In the modern pedagogical literature a large number of works are devoted to the issue of evaluating students mastered knowledge. Ensuring the quality of diagnostics of the level of knowledge acquisition by students of educational organizations is based on an adequate, reasonable, acceptable and accessible mathematical apparatus. The adequacy and validity of the mathematical apparatus allows you to significantly reduce the influence of the subjective factor on the assessment of knowledge acquisition and minimize objections to its application. On the other hand, acceptability makes it possible to use a specific situation under consideration as a diagnosis, taking into account only its inherent nuances. Accessibility also means the ability to use the proposed mathematical algorithm by teachers who have the necessary minimum of elements of the proposed mathematical apparatus. The article considers the possibility of determining the level of development of the studied topic by students on the basis of five factors of knowledge acquisition: 1. Understanding; 2. Recognition; 3.Reproduction; 4. Application; 5. Creativity. In this case, the calculations are performed by using a simplified method of hierarchy analysis and fuzzy set theory in order to reduce the subjectivity inherent in the rating system of evaluation, the use of elements of the hierarchy analysis method and fuzzy logic is proposed. The fuzzy set theory algorithm is implemented using the fuzzy Logic Toolbox application package of the MATLAB software environment. Using the method of hierarchy analysis is to aggregate scores based on the application of a matrix of paired comparisons. The synthesis of these methods allows us to obtain a fairly effective comparative assessment of students development of educational material. On the basis of the considered methodology for evaluating students assimilation of educational material, it is suggested that it is possible to reduce the influence of a subjective factor to a minimum.

scholarly journals FUZZY LOGIC APPARATUS AS A TOOL FOR ASSESSING THE EFFECTIVENESS OF DIGITALIZATION OF A COMPANY

2021 ◽  
pp. 36-41
Author(s):  
V. S. Kokhanova
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Classification ◽  
Estimation Methods ◽  
Mathematical Apparatus ◽  
A Company ◽  
Fuzzy Logical

In this article, the author gives an example of using the apparatus of fuzzy logic in assessing the effectiveness of digitalization of an enterprise, specifies indicators that can be used as criteria for building a system for assessing the effectiveness of digitalization, as well as provides an overview of existing developments. Within the framework of the article, the study outlines the directions of modification of classical estimation methods that are possible using the apparatus of fuzzy logic. The paper substantiates the choice of a universal fuzzy logic tool as a mathematical apparatus for forming an assessment: a system of fuzzy logical conclusions – standard five-level [0; 1]-classifiers. The possibility of fuzzy classification of properties, as well as qualimetry based on the aggregation of hierarchies of factors, will make it possible to assess the level of efficiency of enterprise digitalization by the degree of success. 

Fuzzy Analysis of Speech Metrics to Estimate Conductor Alertness

2009 ◽  
Author(s):  
Parham Shahidi ◽  
Steve C. Southward ◽  
Mehdi Ahmadian
Keyword(s):  
Mathematical Model ◽  
Fuzzy Logic ◽  
Rule Base ◽  
Mathematical Framework ◽  
Human Knowledge ◽  
Knowledge Based ◽  
Single Output ◽  
Output System ◽  
Alertness Level ◽  
Different Levels

A Fuzzy Logic-based algorithm has been developed for processing a series of speech metrics with the ultimate goal of estimating train conductor alertness. The output is a single metric, which directly quantifies the alertness level of the conductor. The metrics were selected based on their correlation to alertness through processed speech, but without any interpretation of the spoken words or phrases. Metrics that are used include: speech duration, silence duration, word production rate and word intensity. The assessment of these metrics is an experience and human knowledge based task, which generates the need for a mathematical model to accommodate this special circumstance. The algorithm developed here uses Fuzzy Logic to cast the human knowledge base into a mathematical framework for the alertness estimation analysis. The core of this fuzzy system is a rule base consisting of fuzzy IF-THEN rules, which are derived from the existing knowledge about the effects of sleep deprivation on alertness such as Furthermore, the rules were inferred from actual voice recordings that were taken on board a train. This data was then used to create a classification scheme to determine which pattern in the speech indicates different levels of alertness from anxiety to fatigue. The simplicity of the underlying mathematical model in this approach enables this system to compute and output an alertness metric in real-time. The nature of this algorithm allows for the use of an arbitrary number of rules to classify the alertness level and therefore provides the ability to continuously develop and extend the rule base as new knowledge emerges. The resulting algorithm is a fast, multi-input, single-output system that is able to quantify the train conductor’s alertness level anytime speech is produced.

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