Fuzzy Analogy Research Articles

Methodological issues of the fuzzy set theory (generalizing article)

The theory of fuzziness is an important area of modern theoretical and applied mathematics. The methodology of the theory of fuzziness is a doctrine of organizing activities in the field of development and application of the scientific results of this theory. We discuss some methodological issues of the theory of fuzziness, i.e., individual components of the methodology in the area under consideration. The theory of fuzziness is a science of pragmatic (fuzzy) numbers and sets. The ancient Greek philosopher Eubulides showed that the concepts «Heap» and «Bald» cannot be described using natural numbers. E. Borel proposed to define a fuzzy set using a membership function. A fundamentally important step was taken by L. A. Zadeh in 1965. He gave the basic definitions of the algebra of fuzzy sets and introduced the operations of intersection, product, union, sum, negation of fuzzy sets. The main thing he did was demonstration of the possibilities of expanding («doubling») mathematics: by replacing the numbers and sets used in mathematics with their fuzzy counterparts, we obtain new mathematical formulations. In the statistics of non-numerical data, methods of statistical analysis of fuzzy sets have been developed. Interval and triangular fuzzy numbers are often used specific types of membership functions. The theory of fuzzy sets in a certain sense is reduced to the theory of random sets. We think fuzzy and that is the only reason we understand each other. The paradox of the fuzzy theory is that it is impossible to consistently implement the thesis «Everything in the world is fuzzy». For ordinary fuzzy sets, the argument and values of the membership function are crisp. If they are replaced by fuzzy analogues, then their description will require their own clear arguments and membership functions, and so on ad infinitum. System fuzzy interval mathematics proceeds from the need to take into account the fuzziness of the initial data and the prerequisites of the mathematical model. One of the options for its practical implementation is an automated system-cognitive analysis and the intellectual system «Eidos».

A hybrid incomplete decision system using fuzzy sets and rough set theory with varying object sets and values

Researchers in science and engineering face various obstacles due to a lack of specific and full data. Many different approaches have been devised to deal with these restrictive requirements, but two notable schools of thought are the fuzzy set (FS) theory and the rough set (RS) theory, both of which have spawned many extensions and hybridizations. Although RS theory originated from an indiscernibility relation (also known as an equivalence relation in mathematics), emphasis rapidly shifted to similarity or coverings (and their fuzzy analogues). Many other hybrid schemes were suggested with this goal in mind. The gap between those concepts shrank because to this thorough analysis. Fuzzy set theory is a legitimate way to convey the ambiguity of assessment data, yet it is still inadequate for dealing with certain intricate problems in the actual world. In reality, decision makers will undoubtedly provide different kinds of ambiguous and nuanced assessments. Atanassov’s intuitionistic fuzzy set theory broadened the application of fuzzy set theory by imbuing it with an element of uncertainty. Sometimes in real life, you have to deal with a neutral element on top of the indeterminate one. Picture fuzzy sets were developed specifically for this purpose. Membership roles may be positive, neutral, or negative/refusal. In contrast, hesitant fuzzy sets and its hybrid models are useful when decision makers are on the fence about which option to choose. As a binary relation on a set, a graph is symmetric. It is a staple in mathematical modelling and is used in almost every scientific and technological discipline. Graph theory has been essential in the mathematical modelling and subsequent resolution of several real-world situations. Information about connections between things is often best represented using graph theory, which uses vertices to stand in for the items and edges for the relationships between them. The suggested dynamic algorithm is better to the static approach in dealing with the multidimensional dynamic changes of the hybrid incomplete decision system, according to a series of experiments carried out on nine UCI datasets.

MULTIVARIATE FUZZY APPROXIMATION BY NEURAL NETWORK OPERATORS ACTIVATED BY A GENERAL SIGMOID FUNCTION

Here is studied in detail the multivariate fuzzy approximation to the multivariate unit by multivariate fuzzy neural network operators activated by a general sigmoid function. These operators are multivariate fuzzy analogs of earlier studied multivariate Banach space valued ones. The derived results generalize earlier Banach space valued ones into the fuzzy level. Here the high order multivariate fuzzy pointwise and uniform convergences with rates to the multivariate fuzzy unit operator are given through multivariate fuzzy Jackson type inequalities involving the multivariate fuzzy moduli of continuity of the mth order (m ≥ 0) H-fuzzy partial derivatives, of the involved multivariate fuzzy number valued function. The treated operators are of averaged, quasi-interpolation, Kantorovich and quadrature types at the multivariate fuzzy setting.

IoT System Selection as a Fuzzy Multi-Criteria Problem.

This research aims to analyse the applications of IoT in agriculture and to compare the most widely used IoT platforms. The problem of determining the most appropriate IoT system depends on many factors, often expressed by incomplete and uncertain estimates. In order to find a feasible decision, this study develops a multi-criteria framework for IoT solution selection in a fuzzy environment. In the proposed framework, a new modification of the Multi-Attribute Border approximation Area Comparison (MABAC) method with a specific distance measure via intuitionistic fuzzy values has been presented as a decision analysis method. The new technique is more precise than existing crisp and fuzzy analogues, as it includes the three components of intuitionistic numbers (degree of membership, degree of non-membership and hesitancy degree) and the relationships between them. The effectiveness of the new decision-making framework has been verified through an illustrative example of ranking IoT platforms.

On chromatic number and perfectness of fuzzy graph

Perfect graphs have a significant role in graph theory in terms of structure as well as application. This article embarked a comprehensive study on perfect fuzzy graphs attempted to obtain the fuzzy analog of the famous weak and strong perfect graph theorems following due classification of fuzzy graphs in terms of perfectness. The inter-relationship between chromatic numbers of a fuzzy graph and its complement graph has been studied in detail deriving important theories and results. It has been shown that unlike crisp case, for fuzzy graphs there exists one and only one perfect fuzzy graph theorem satisfying both the conditions of strong and weak perfect graph theorems. A detailed study of the perfectness of different types of fuzzy graphs has been carried out comparing the results with those obtained on crisp graphs. It has been shown through illustrative examples how the perfectness of a fuzzy graph and that of its underlying crisp graph is independent of each other. Finally, the use of perfect fuzzy graph on application grounds has been evaluated by using it in analyzing how a huge percentage of population in a city is unknowingly living under a big threat due exposure to electromagnetic radiation emitted from cell-phone towers.

Research on the Trust Mechanism of Individual Consumers in Rural Financial Markets Based on the Dynamic CGE Model

In order to obtain the complete equilibrium state of rural financial market and ensure the stable development of rural financial consumer market, this paper introduces CGE model and analyzes the dynamic trust mechanism of individual consumers in rural financial market. In this paper, the single variable evolutionary fuzzy clustering algorithm is used to analyze the orthogonal eigenvector solutions of individual consumers; the big data of individual consumers under the mode of perceived trust is automatically clustered, so as to obtain the fuzzy analogy function of individual consumers in the rural financial market; and finally the prediction value of consumer trust is obtained. The results show that trust, customer satisfaction, and service quality are positively correlated. Under the same sample expectation constraints, the dynamic CGE model is more robust, and the individual consumer trust mechanism of rural financial market in the study area has higher advantages.

What Is the Uncertainty of the Result of Data Processing: Fuzzy Analogue of the Central Limit Theorem

What Is the Uncertainty of the Result of Data Processing: Fuzzy Analogue of the Central Limit Theorem

Research on Automation of Test Skill Evaluation Based on Fuzzy Controller

The fuzzy control system is composed of an integral part of modern intelligent automatic control, can control of precision is difficult to directly establish the mathematical model of the intelligent control system object data for effective fuzzy control, so fuzzy has wide application field, considering the basic features of fuzzy control arithmetic, more close to the parallel processing of the way of fuzzy data stream, so fuzzy control is more suitable for implementation by a special control circuit, not only can not only improve the speed of data processing, and it also can improve the control system running stability. With the improvement of programming logic and programmable ability of FPGA, FPGA has the necessary ability to implement ASIC directly and meet the requirements of system programming and design on chip. It has become the development trend of FPGA. The fuzzy analog controller can be used as a digital analog controller of a DC/DC fuzzy converter. In the absence of Matlab/Simulinkc environment, a DC/DC fuzzy converter can be modeled by using Maplecs toolbox. The simulation test results firstly verify the practical feasibility of the fuzzy analog controller. Then PLXILINXXC3S500EFPGA chip is used to realize the fuzzy simulation controller, and good simulation results are obtained.

A classification of invertible phases of bosonic quantum lattice systems in one dimension

We study invertible states of 1D bosonic quantum lattice systems. We show that every invertible 1D state is in a trivial phase: after tensoring with some unentangled ancillas, it can be disentangled by a fuzzy analog of a finite-depth quantum circuit. If an invertible state has symmetries, it may be impossible to disentangle it in a way that preserves the symmetries, even after adding unentagled ancillas. We show that in the case of a finite unitary symmetry G, the only obstruction is an index valued in degree-2 cohomology of G. We show that two invertible G-invariant states are in the same phase if and only if their indices coincide.

Clustering algorithm with strength of connectedness for m-polar fuzzy network models.

In this research study, we first define the strong degree of a vertex in an m-polar fuzzy graph. Then we present various useful properties and prove some results concerning this new concept, in the case of complete m-polar fuzzy graphs. Further, we introduce the concept of m-polar fuzzy strength sequence of vertices, and we also investigate it in the particular instance of complete m-polar fuzzy graphs. We discuss connectivity parameters in m-polar fuzzy graphs with precise examples, and we investigate the m-polar fuzzy analogue of Whitney's theorem. Furthermore, we present a clustering method for vertices in an m-polar fuzzy graph based on the strength of connectedness between pairs of vertices. In order to formulate this method, we introduce terminologies such as ϵA-reachable vertices in m-polar fuzzy graphs, ϵA-connected m-polar fuzzy graphs, or ϵA-connected m-polar fuzzy subgraphs (in case the m-polar fuzzy graph itself is not ϵA-connected). Moreover, we discuss an application for clustering different companies in consideration of their multi-polar uncertain information. We then provide an algorithm to clearly understand the clustering methodology that we use in our application. Finally, we present a comparative analysis of our research work with existing techniques to prove its applicability and effectiveness.

On nonlinear fuzzy set-valued $ \Theta $-contractions with applications

<abstract><p>Among various improvements in fuzzy set theory, a progressive development has been in process to investigate fuzzy analogues of fixed point theorems of the classical fixed point results. In this direction, taking the ideas of $ \theta $-contractions as well as Feng-Liu's approach into account, some new fuzzy fixed point results for nonlinear fuzzy set-valued $ \theta $-contractions in the framework of metric-like spaces are introduced in this paper without using the usual Pompeiu-Hausorff distance function. Our established concepts complement, unify and generalize a few important fuzzy and classical fixed point theorems in the corresponding literature. A handful of these special cases of our notions are pointed and analyzed. Some of the main results herein are further applied to derive their analogues in metric-like spaces endowed with partial ordering and binary relations. Comparisons and nontrivial examples are given to authenticate the hypotheses and significance of the obtained ideas.</p></abstract>

How to Describe Conditions Like 2-out-of-5 in Fuzzy Logic: A Neural Approach

In many medical applications, we diagnose a disease and/or apply a certain remedy if, e.g., two out of five conditions are satisfied. In the fuzzy case, i.e., when we only have certain degrees of confidence that each of n statement is satisfied, how do we estimate the degree of confidence that k out of n conditions are satisfied? In principle, we can get this estimate if we use the usual methodology of applying fuzzy techniques: we represent the desired statement in terms of “and” and “or,” and use fuzzy analogues of these logical operations. The problem with this approach is that for large n, it requires too many computations. In this paper, we derive the fastest-to-compute alternative formula. In this derivation, we use the ideas from neural networks.

Programmable Photoelectric Memristor Gates for In Situ Image Compression

Integrated circuits designed to perform mathematical operations, such as Fourier transforms and matrix multiplications, in artificial visual perception and intelligent image processing are mainly constructed of conventional logic gates. However, Boolean logic is probably not the most optimal approach for brain‐inspired computing due to the fuzzy nature of biologic neural networks. This work demonstrates an application based on programmable fuzzy‐logic gates capable of combined photoelectric computations. Such an apparatus may be used to perform image compression immediately upon acquisition without having the need to rely on interaction between separate processor and sensor modules. It is based on resistive memory devices capable of state transitions in response to both electronic and light stimulations. Material nonimplication and logical true operations are first presented. A more complex functionality for material nonimplication of a logic conjunction is then demonstrated. These gates are then used as building blocks in the design and simulation of a configurable matrix multiplication unit that effectively implements in situ image compression. A membership function (FUZZIFY) that may be used to map strict logic levels to incremental fuzzy analog ones is also shown. Finally, an approach for integrating conventional logic with a fuzzy computation is discussed.

Bipolar Fuzzy Relations

We introduce the concepts of a bipolar fuzzy reflexive, symmetric, and transitive relation. We study bipolar fuzzy analogues of many results concerning relationships between ordinary reflexive, symmetric, and transitive relations. Next, we define the concepts of a bipolar fuzzy equivalence class and a bipolar fuzzy partition, and we prove that the set of all bipolar fuzzy equivalence classes is a bipolar fuzzy partition and that the bipolar fuzzy equivalence relation is induced by a bipolar fuzzy partition. Finally, we define an ( a , b ) -level set of a bipolar fuzzy relation and investigate some relationships between bipolar fuzzy relations and their ( a , b ) -level sets.

Fuzzy Analogical Gate to Select the Best Design of Heat Exchanger Network

This article shows a systematic method to choose the optimal minimum temperature in order to get a flexible HEN and more operable by utilizing the fuzzy analogical gate way for the tradeoff between two cost capital and operating for a given minimum temperature difference. By follow, three steps to choose the best minimum approach temperature 1) obtain minimum utilities target 2) obtain of the area of all HEN 3) fuzzy analogical gates to select the best minimum temperature difference. The recommended method was be conducted on two case studies well known in published literature yielded an optimum solution that is consistent with a different approach. It is clear the fuzzy analogical gate performance is completely hopeful; it is simple and has ability to be applied by manual calculations.

A Note on Strong Axiomatization of Gödel Justification Logic

Justification logics are special kinds of modal logics which provide a framework for reasoning about epistemic justifications. For this, they extend classical boolean propositional logic by a family of necessity-style modal operators “t : ”, indexed over t by a corresponding set of justification terms, which thus explicitly encode the justification for the necessity assertion in the syntax. With these operators, one can therefore not only reason about modal effects on propositions but also about dynamics inside the justifications themselves. We replace this classical boolean base with Gödel logic, one of the three most prominent fuzzy logics, i.e. special instances of many-valued logics, taking values in the unit interval [0, 1], which are intended to model inference under vagueness. We extend the canonical possible-world semantics for justification logic to this fuzzy realm by considering fuzzy accessibility- and evaluation-functions evaluated over the minimum t-norm and establish strong completeness theorems for various fuzzy analogies of prominent extensions for basic justification logic.

Analogy-Based Approaches to Improve Software Project Effort Estimation Accuracy

Abstract In the discipline of software development, effort estimation renders a pivotal role. For the successful development of the project, an unambiguous estimation is necessitated. But there is the inadequacy of standard methods for estimating an effort which is applicable to all projects. Hence, to procure the best way of estimating the effort becomes an indispensable need of the project manager. Mathematical models are only mediocre in performing accurate estimation. On that account, we opt for analogy-based effort estimation by means of some soft computing techniques which rely on historical effort estimation data of the successfully completed projects to estimate the effort. So in a thorough study to improve the accuracy, models are generated for the clusters of the datasets with the confidence that data within the cluster have similar properties. This paper aims mainly on the analysis of some of the techniques to improve the effort prediction accuracy. Here the research starts with analyzing the correlation coefficient of the selected datasets. Then the process moves through the analysis of classification accuracy, clustering accuracy, mean magnitude of relative error and prediction accuracy based on some machine learning methods. Finally, a bio-inspired firefly algorithm with fuzzy analogy is applied on the datasets to produce good estimation accuracy.

Pythagorean Dombi fuzzy graphs

Pythagorean fuzzy graph, a broadly used extension of fuzzy and intuitionistic fuzzy graph, is helpful in representing structural relationships between several objects where the relation between these objects is vague, while the Dombi operators with operational parameters have excellent flexibility. Utilizing these two concepts, this research paper proposes the novel concept of Pythagorean Dombi fuzzy graphs (PDFGs). Basically, graph terminology is employed for introducing Pythagorean fuzzy analogs of various fundamental graphical ideas using Dombi operator. Further, under Pythagorean Dombi fuzzy environment, regular, totally regular, strongly regular and biregular graphs are defined with appropriate illustration and some of their crucial properties are examined. Meanwhile, the notion of edge regularity of PDFG is also initiated with substantial characteristics. Finally, a numerical example related to evaluation of appropriate ETL software for a business intelligence project is presented to better understand PDFGs.

Empirical evaluation of an entropy‐based approach to estimation variation of software development effort

AbstractAs effort estimation has gained increasing attention, most of the techniques proposed have focused on the accuracy of effort estimates. Yet no clear conclusions have been drawn on which techniques perform best in all contexts. We propose an entropy‐based approach to effort estimate variation caused by measurement and model error sources whatever the effort estimation technique used. The proposed approach was empirically evaluated by exploring three entropy formulae, four interpolation methods, and two analogy‐based effort estimation approaches (crisp and fuzzy analogy) over seven datasets using the Jackknife evaluation method.The obtained results show that the three entropy formulae have in general the same positive influence on the performance of the entropy‐based approach measured in terms of absolute error of effort deviation. In addition, the spline interpolation outperformed all other interpolation methods, using any of the entropy formulae. Moreover, achievement percentages of the best variants of our approach closely approximated those of the Gaussian distribution confirming that the Gaussian distribution is useful for characterizing effort estimate variation.

Evaluating filter fuzzy analogy homogenous ensembles for software development effort estimation

AbstractResearchers have developed and evaluated many techniques to deliver accurate estimates of the effort required to complete a new software program. Among these, analogy has emerged as a very promising technique, in particular the fuzzy analogy estimation technique that uses the fuzzy logic concepts in order to deal with both categorical and numerical data. The aim of this paper is twofold: (1) evaluate the impact of 3 filters on the predictive ability of single and ensemble fuzzy analogy techniques and (2) assess whether filters could be a source of diversity for fuzzy analogy ensembles. Moreover, it compares the filter single and ensemble fuzzy analogy techniques with fuzzy analogy ensembles built without using feature selection over 6 datasets. The overall results suggest that (1) more accurate estimates are generated when filters were used with single and ensemble fuzzy analogy techniques, (2) filter single fuzzy analogy techniques outperformed filter fuzzy analogy ensembles, and (3) fuzzy analogy ensembles without feature selection were more accurate than filter single and ensemble techniques. Therefore, though the use of feature selection techniques led single and ensemble fuzzy analogy to generate accurate estimations, they failed to be a source of diversity for fuzzy analogy ensembles. Hence, constructing fuzzy analogy homogenous ensembles that combine single fuzzy analogy techniques with different parameter configurations still generate better accuracy than filter fuzzy analogy ensembles. However, further empirical evaluations of filter/wrappers fuzzy analogy ensembles are required in order to confirm or refute these findings.