• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.4
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• pp.341-346
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• 2002

Type-1 fuzzy set is used to show the uncertainty in a given value. But there are many situations where it needs to be extended to type-2 fuzzy set because it can be also difficult to determine the crisp membership function itself. Type-2 fuzzy systems have the advantage that they are more expressive and powerful than type-1 fuzzy systems, but they require many operations defined for type-1 fuzzy sets need to be extended in the domain of type-2 fuzzy sets. In this paper, comparison and ranking methods for type-2 fuzzy sets are proposed. It is based on the satisfaction function that produces the comparison results considering the actual values of the given type-2 fuzzy sets with their possibilities. Some properties of the proposed method are also analyzed.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.933-947
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• 2022

In this research, we presented the type 2 fuzzy transportation problem with additional constraints and solved by our proposed genetic algorithm model, and the results are verified using the softwares, genetic algorithm tool in Matlab and Lingo. The goal of our approach is to minimize the cost in solving a transportation problem with an additional constraint (TPAC) using the genetic algorithm (GA) based type 2 fuzzy parameter. We reduced the type 2 fuzzy set (T₂FS) into a type 1 fuzzy set (T₁FS) using a critical value-based reduction method (CVRM). Also, we use the centroid method (CM) to obtain the corresponding crisp value for this reduced fuzzy set. To achieve the best solution, GA is applied to TPAC in type 2 fuzzy parameters. A real-life situation is considered to illustrate the method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.5
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• pp.705-711
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• 2013

In this paper, we introduce an design of multi-output fuzzy neural networks based on Interval Type-2 fuzzy set. The proposed Interval Type-2 fuzzy set-based fuzzy neural networks with multi-output (IT2FS-based FNNm) comprise the network structure generated by dividing the input space individually. The premise part of the fuzzy rules of the network reflects the individuality of the division space for the entire input space and the consequent part of the fuzzy rules expresses three types of polynomial functions with interval sets such as constant, linear, and modified quadratic inference for pattern recognition. The learning of fuzzy neural networks is realized by adjusting connections of the neurons in the consequent part of the fuzzy rules, and it follows a back-propagation algorithm. In addition, in order to optimize the network, the parameters of the network such as apexes of membership functions, uncertainty factor, learning rate and momentum coefficient were automatically optimized by using real-coded genetic algorithm. The proposed model is evaluated with the use of numerical experimentation.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.11a
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• pp.19-22
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• 2006

Type-2 fuzzy 이론은 기존의 퍼지 이론보다 패턴의 불확실성에 대한 제어를 더 향상시킬 수 있다. 반면에 계산 량이 커지는 문제점 때문에 본 논문에서는 type-2 fuzzy set 대신에 secondary membership이 interval의 형태를 갖는 interval type-2 fuzzy set을 기존의 radial basis function(RBF) neural network에 적용시킨 interval type-2 fuzzy RBF neural network를 제안한다. 제안한 알고리즘은 interval type-2 fuzzy membership function에 의하여 패턴들의 불확실성을 좀 더 잘 제어하여 기존의 RBF neural network의 성능을 향상시킬 수 있다. 본 논문에서는 제안한 알고리즘의 타당성을 보이기 위하여 여러 데이터 집합에 대한 분류 결과를 보인다.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.6
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• pp.842-848
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• 2008

This paper deal with uncertainty problem by using Type-2 fuzzy logic set for nonlinear system modeling. We design Type-2 fuzzy logic system in which the antecedent and the consequent part of rules are given as Type-2 fuzzy set and also analyze the performance of the ensuing nonlinear model with uncertainty. Here, the apexes of the antecedent membership functions of rules are decided by C-means clustering algorithm and the apexes of the consequent membership functions of rules are learned by using back-propagation based on gradient decent method. Also, the parameters related to the fuzzy model are optimized by means of particle swarm optimization. The proposed model is demonstrated with the aid of two representative numerical examples, such as mathematical synthetic data set and Mackey-Glass time series data set and also we discuss the approximation as well as generalization abilities for the model.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.05a
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• pp.265-268
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• 2002

In this paper we introduce the concepts of type-2 fuzzy set-valued mappings and quasi-convex fuzzy mappings on L-L fuzzy numbers and discuss some properties of these mappings.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.16 no.4
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• pp.225-237
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• 2016

In conventional transportation problem (TP), all the parameters are always certain. But, many of the real life situations in industry or organization, the parameters (supply, demand and cost) of the TP are not precise which are imprecise in nature in different factors like the market condition, variations in rates of diesel, traffic jams, weather in hilly areas, capacity of men and machine, long power cut, labourer's over time work, unexpected failures in machine, seasonal changes and many more. To counter these problems, depending on the nature of the parameters, the TP is classified into two categories namely type-2 and type-4 fuzzy transportation problems (FTPs) under uncertain environment and formulates the problem and utilizes the trapezoidal fuzzy number (TrFN) to solve the TP. The existing ranking procedure of Liou and Wang (1992) is used to transform the type-2 and type-4 FTPs into a crisp one so that the conventional method may be applied to solve the TP. Moreover, the solution procedure differs from TP to type-2 and type-4 FTPs in allocation step only. Therefore a simple and efficient method denoted by PSK (P. Senthil Kumar) method is proposed to obtain an optimal solution in terms of TrFNs. From this fuzzy solution, the decision maker (DM) can decide the level of acceptance for the transportation cost or profit. Thus, the major applications of fuzzy set theory are widely used in areas such as inventory control, communication network, aggregate planning, employment scheduling, and personnel assignment and so on.

• Journal of the Korea Management Engineers Society
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• v.23 no.4
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• pp.87-103
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• 2018

This paper introduces the method to develop two main types of the fuzzy OEE (Overall Equipment Effectiveness) models via triangular membership function for measuring uncertainty. The fuzzy OEE includes model type 1 and model type 2. The model type 1 is used when the theoretical machine speed only reflects the time loss whereas model type 2 is used when the actual machine speed reflects both time and speed loss. Model type 2 has shown to perform a lower availability rate and a higher performance rate compared to model type 1. In addition, the fuzzy UPH (Unit Per Hour) which is derived from using the fuzzy OEE is presented to satisfy demand uncertainty. The fuzzy UPH can easily measure the fuzzy tact time and cycle time by reciprocating itself. Finally, this study demonstrates the fuzzy OEE models using IVIFS (Interval-Valued Intuitionistic Fuzzy Set) based on the characterization via membership function, non-membership function and hesitant function. For the purpose of analyzing the fuzzy system OEE, the OEE for each machine of plant structure is considered triangular interval-valued intuitionistic fuzzy number. Regardless of plant structure, the validity degree of fuzzy membership function of system OEE decreases when the number of machine with worst value of the validity degree increases. Corresponding examples are presented in this paper for practitioner to understand the applicability and practicability of the proposed fuzzy OEE methods.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.05a
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• pp.9-12
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• 2000

In this paper, we are interested in counting the number of elements of a type two fuzzy set. Using concepts of type-two fuzzy sets, we can obtain some properties of these concepts and some results of possibility of type-two fuzzy sets.

• Journal of the Korean Institute of Intelligent Systems
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• v.27 no.2
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• pp.99-105
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• 2017

Type-2 fuzzy sets are preferred over type-1 sets as they are capable of addressing uncertainty more efficiently. The fuzzifier values play pivotal role in managing these uncertainties; still selecting appropriate value of fuzzifiers has been a tedious task. Generally, based on observation particular value of fuzzifier is chosen from a given range of values. In this paper we have tried to adaptively compute suitable fuzzifier values of interval type-2 possibilistic fuzzy c-means (IT2 PFCM) for a given data. Information is extracted from individual data points using histogram approach and this information is further processed to give us the two fuzzifier values $m_1$, $m_2$. These obtained values are bounded within some upper and lower bounds based on interval type-2 fuzzy sets.