A New Method for Parameterization of General Type-2 Fuzzy Sets

Castro, Juan R.; Sánchez, Martínez; González, Claudia I.; Melín, Patricia; Castillo, Oscar

doi:10.1080/16168658.2018.1509519

Cited by 24 publications

(20 citation statements)

References 42 publications

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“…A more complex approach is represented by IT2FS, where the concept of uncertainty in the form of intervals is introduced. Although computationally complex compared to T1FS, they derive an improvement in the general fuzzy model by being more resistant to external noise, as reported by Castro et al [2]; Puška et al [3]; Eren [4]; Tavossi et al [5].…”

Section: Introductionmentioning

confidence: 94%

Type-2 Fuzzy Expert System Approach for Decision-Making of Financial Assets and Investing under Different Uncertainty

Janková

Dostál

2021

Mathematical Problems in Engineering

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Extensive research results of stock market time series using classical fuzzy sets (type-1) are available in the literature. However, type-1 fuzzy sets cannot fully capture the uncertainty associated with stock market developments due to their limited descriptiveness. This paper fills a scientific gap and focuses on type-2 fuzzy logic applied to stock markets. Type-2 fuzzy sets may include additional uncertainty resulting from unclear, uncertain, or inaccurate financial data through which model inputs are calculated. Here we propose four methods based on type-2 fuzzy logic, which differ in the level of uncertainty contained in fuzzy sets and compared with the type-1 fuzzy model. The case study aims to create a model to support investment decisions in Exchange-Traded Funds (ETFs) listed on international equity markets. The created models of type-2 fuzzy logic are compared with the classic type-1 fuzzy logic model. Based on the results of the comparison, it can be said that type-2 fuzzy logic with dual fuzzy sets is able to better describe data from financial time series and provides more accurate outputs. The results reflect the capability and effectiveness of the approach proposed in this document. However, the performance of type-2 fuzzy logic models decreases with the inclusion of increasing uncertainty in fuzzy sets. For further research, it would be appropriate to examine the different levels of uncertainty in the input parameters themselves and monitor the performance of such a modified model.

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Section: Introductionmentioning

confidence: 94%

Type-2 Fuzzy Expert System Approach for Decision-Making of Financial Assets and Investing under Different Uncertainty

Janková

Dostál

2021

Mathematical Problems in Engineering

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“…Equation (21) defines the composition; the symbol represents the meet operator of the GT2 FS and is used to represent the join. 5) To obtain the GT2 FSI, finally, we calculate the supreme of the σ α i using Equation (22).…”

Section: )mentioning

confidence: 99%

“…In general, information aggregation is an important and necessary process to perform any decision-making task; nevertheless, this can be applied to any problem when we need to aggregate different information sources or different criteria. Implementing the GT2 FS theory [ 18 , 19 , 20 ] is possible to generate powerful aggregation techniques with the capability of handling the uncertainty information present in any image processing system [ 21 , 22 , 23 ]; being this one of the main motivations in developing this proposal.…”

Section: Introductionmentioning

confidence: 99%

“…One of the main drawbacks that we have when obtaining an interval, is to determine which of the values represents the best solution. For this work, one of the approximations that we use is to calculate the average of each one of the intervals and, in the end, to select the supreme of all of them to represent the solution set expressed in Equation (22). For this particular edge detection application, the main goal was to determine whether the pixel corresponds to an edge.…”

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confidence: 99%

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General Type-2 Fuzzy Sugeno Integral for Edge Detection

et al. 2019

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A type-2 fuzzy edge detection method is presented in this paper. The general process consists of first obtaining the image gradients in the four directions—horizontal, vertical, and the two diagonals—and this technique is known as the morphological gradient. After that, the general type-2 fuzzy Sugeno integral (GT2 FSI) is used to integrate the four image gradients. In this second step, the GT2 FSI establishes criteria to determine at which level the obtained image gradient belongs to an edge during the process; this is calculated assigning different general type-2 fuzzy densities, and these fuzzy gradients are aggregated using the meet and join operators. The gradient integration using the GT2 FSI provides a methodology for achieving more robust edge detection, even more if we are working with blurry images. The experimental evaluations are performed on synthetic and real images, and the accuracy is quantified using Pratt’s Figure of Merit. The results values demonstrate that the proposed edge detection method outperforms other existing algorithms.

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“…The first mentioned fuzzy sets are considered to be a very simplified form of representation of linguistic variables, which is able to integrate exclusively a certain degree of uncertainty according to [4,5], while type-2 interval fuzzy sets are able to integrate uncertainty in the form of intervals, thus not limiting the level of uncertainty. Although IT2FS are more computationally intensive and more complex to design, according to [6], these sets are better able to deal with the additional noise and the nonlinear and chaotic environment of input data from various disciplines.…”

Section: Introductionmentioning

confidence: 99%

Comparison Uncertainty of Different Types of Membership Functions in T2FLS: Case of International Financial Market

Janková

Rakovská

2022

Applied Sciences

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This article deals with the determination and comparison of different types of functions of the type-2 interval of fuzzy logic, using a case study on the international financial market. The model is demonstrated on the time series of the leading stock index DJIA of the US market. Type-2 Fuzzy Logic membership features are able to include additional uncertainty resulting from unclear, uncertain or inaccurate financial data that are selected as inputs to the model. Data on the financial situation of companies are prone to inaccuracies or incomplete information, which is why the type-2 fuzzy logic application is most suitable for this type of financial analysis. This paper is primarily focused on comparing and evaluating the performance of different types of type-2 fuzzy membership functions with integrated additional uncertainty. For this purpose, several model situations differing in shape and level or degree of uncertainty of membership functions are constructed. The results of this research show that type-2 fuzzy sets with dual membership functions is a suitable expert system for highly chaotic and unstable international stock markets and achieves higher accuracy with the integration of a certain level of uncertainty compared to type-1 fuzzy logic.

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A New Method for Parameterization of General Type-2 Fuzzy Sets

Cited by 24 publications

References 42 publications

Type-2 Fuzzy Expert System Approach for Decision-Making of Financial Assets and Investing under Different Uncertainty

Type-2 Fuzzy Expert System Approach for Decision-Making of Financial Assets and Investing under Different Uncertainty

General Type-2 Fuzzy Sugeno Integral for Edge Detection

Comparison Uncertainty of Different Types of Membership Functions in T2FLS: Case of International Financial Market

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