• Annals of Fuzzy Mathematics and Informatics
• /
• v.16 no.3
• /
• pp.333-336
• /
• 2018

One of the well known results in general topology says that every compact subset of a Hausdorff space is closed. This result in soft topology is not true in general as demonstrated throughout this note. We begin this investigation by showing that [Theorem 3.34, p.p.23] which proposed by Varol and $Ayg{\ddot{u}}n$ [7] is invalid in general, by giving a counterexample. Then we derive under what condition this result can be generalized in soft topology. Finally, we evidence that [Example 3.22, p.p. 20] which introduced in [7] is false, and we make a correction for this example to satisfy a condition of soft Hausdorffness.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.1 no.1
• /
• pp.9-25
• /
• 1991

This tutorial paper has been written for biologists, physicians or beginners in fuzzy sets theory and applications. This field is introduced in the framework of medical diagnosis problems. The paper describes and illustrates with practical examples, a general methodology of special interest in the processing of borderline cases, that allows a graded assignment of diagnoses to patients. A pattern of medical knowledge consists of a tableau with linguistic entries or of fuzzy propositions. Relationships between symptoms and diagnoses are interpreted as labels of fuzzy sets. It is shown how possibility measures (soft matching) can be used and combined to derive diagnoses after measurements on collected data. The concepts and methods are illustrated in a biomedical application on inflammatory protein variations. In the case of poor diagnostic classifications, it is introduced appropriate ponderations, acting on the characterizations of proteins, in order to decrease their relative influence. As a consequence, when pattern matching is achieved, the final ranking of inflammatory syndromes assigned to a given patient might change to better fit the actual classification. Defuzzification of results (i.e. diagnostic groups assigned to patients) is performed as a non fuzzy sets partition issued from a "separating power", and not as the center of gravity method commonly employed in fuzzy control. It is then introduced a model of fuzzy connectionist expert system, in which an artificial neural network is designed to build the knowledge base of an expert system, from training examples (this model can also be used for specifications of rules in fuzzy logic control). Two types of weights are associated with the connections: primary linguistic weights, interpreted as labels of fuzzy sets, and secondary numerical weights. Cell activation is computed through MIN-MAX fuzzy equations of the weights. Learning consists in finding the (numerical) weights and the network topology. This feed forward network is described and illustrated in the same biomedical domain as in the first part.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.10 no.4
• /
• pp.296-302
• /
• 2010

This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies) introduced by Ying [16, (I)]. It investigates topological notions defined by means of regular open sets when these are planted into the frame-work of Ying's fuzzifying topological spaces (in ${\L}$ukasiewwicz fuzzy logic). The concept of fuzzifying nearly compact spaces is introduced and some of its properties are obtained. We use the finite intersection property to give a characterization of fuzzifying nearly compact spaces. Furthermore, we study the image of fuzzifying nearly compact spaces under fuzzifying completely continuous functions, fuzzifying almost continuity and fuzzifying R-map.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.63 no.8
• /
• pp.1080-1084
• /
• 2014

This paper addresses a design technique for formation tracking controllers of discrete-time Takagi-Sugeno fuzzy multi-agent systems based on consensus. The interconnection topology among the agents is expressed as a digraph. The design condition is represented in terms of linear matrix inequalities. Numerical example demonstrates the effectiveness of the proposed method.

• Journal of Power Electronics
• /
• v.16 no.2
• /
• pp.564-571
• /
• 2016

This study proposes an adaptive neuro-fuzzy inference system (ANFIS)-based rotor position controller for brushless direct current (BLDC) motors to improve the control performance of the drive under transient and steady-state conditions. The dynamic response of a BLDC motor to the proposed ANFIS controller is considered as standard reference input. The effectiveness of the proposed controller is compared with that of the proportional integral derivative (PID) controller and fuzzy PID controller. The proposed controller solves the problem of nonlinearities and uncertainties caused by the reference input changes of BLDC motors and guarantees a fast and accurate dynamic response with an outstanding steady-state performance. Furthermore, the ANFIS controller provides low torque ripples and high starting torque. The detailed study includes a MATLAB-based simulation and an experimental prototype to illustrate the feasibility of the proposed topology.

• Journal of Power Electronics
• /
• v.16 no.2
• /
• pp.654-665
• /
• 2016

The pumping of electric power from photovoltaic (PV) farms is normally carried out using transformers, which require heavy mounting structures and are thus costly, less efficient, and bulky. Therefore, transformerless schemes are developed for the injection of power into the grid. Compared with the H4 inverter topology, the H6 topology is a better choice for pumping PV power into the grid because of the reduced common mode current. This paper presents how the perturb and observe (P&O) algorithm for maximum power point tracking (MPPT) can be implemented in the H6 inverter topology along with the improved sinusoidal current injected to the grid at unity power factor with the average current mode control technique. On the basis of the P&O MPPT algorithm, a power reference for the present insolation level is first calculated. Maintaining this power reference and referring to the AC sine wave of bus bars, a sinusoidal current at unity power factor is injected to the grid. The proportional integral (PI) controller and fuzzy logic controller (FLC) are designed and implemented. The FLC outperforms the PI controller in terms of conversion efficiency and injected power quality. A simulation in the MATLAB/SIMULINK environment is carried out. An experimental prototype is built to validate the proposed idea. The dynamic and steady-state performances of the FLC controller are found to be better than those of the PI controller. The results are presented in this paper.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.12 no.1
• /
• pp.66-76
• /
• 2012

In this paper, we introduce the concept of ordinary smooth topology on a set X by considering the gradation of openness of ordinary subsets of X. And we obtain the result [Corollary 2.13] : An ordinary smooth topology is fully determined its decomposition in classical topologies. Also we introduce the notion of ordinary smooth [resp. strong and weak] continuity and study some its properties. Also we introduce the concepts of a base and a subbase in an ordinary smooth topological space and study their properties. Finally, we investigate some properties of an ordinary smooth subspace.

• Communications of the Korean Mathematical Society
• /
• v.19 no.1
• /
• pp.143-153
• /
• 2004

In [3] and [6] the concepts of smooth closure, smooth interior, smooth ${\alpha}-closure$ and smooth ${\alpha}-interior$ of a fuzzy set were introduced and some of their properties were obtained. In this paper, we introduce the concepts of several types of weak smooth compactness and weak smooth ${\alpha}-compactness$ in terms of these concepts introduced in [3] and [61 and investigate some of their properties.

• Korean Journal of Mathematics
• /
• v.14 no.2
• /
• pp.233-240
• /
• 2006

In this paper we introduce the concepts of several types of $weak^*$ quasi-smooth ${\alpha}$-compactness in terms of the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set in smooth topological spaces and investigate some of their properties.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.58 no.6
• /
• pp.1230-1237
• /
• 2009

In this paper, we develop a design methodology of Granular-based Radial Basis Function Neural Networks(GRBFNN) by context-based clustering. In contrast with the plethora of existing approaches, here we promote a development strategy in which a topology of the network is predominantly based upon a collection of information granules formed on a basis of available experimental data. The output space is granulated making use of the K-Means clustering while the input space is clustered with the aid of a so-called context-based fuzzy clustering. The number of information granules produced for each context is adjusted so that we satisfy a certain reconstructability criterion that helps us minimize an error between the original data and the ones resulting from their reconstruction involving prototypes of the clusters and the corresponding membership values. In contrast to "standard" Radial Basis Function neural networks, the output neuron of the network exhibits a certain functional nature as its connections are realized as local linear whose location is determined by the values of the context and the prototypes in the input space. The other parameters of these local functions are subject to further parametric optimization. Numeric examples involve some low dimensional synthetic data and selected data coming from the Machine Learning repository.