An approach to Fuzzy clustering of the iris petals by using Ac-means Analysis

This paper proposes a definition of a fuzzy partition element based on the homomorphism between type-1 fuzzy sets and the three-valued Kleene algebra. A new clustering method based on the C-means algorithm, using the defined partition, is presented in this paper, which will be validated with the traditional iris clustering problem by measuring its petals.

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Parameter Prediction Based on Type-2 Fuzzy Clustering

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488518500393 ◽

2018 ◽

Vol 26 (06) ◽

pp. 877-892 ◽

Cited By ~ 1

Author(s):

Türkan Erbay Dalkiliç ◽

Seda Sağirkaya

Keyword(s):

Fuzzy Logic ◽

Regression Analysis ◽

Fuzzy Clustering ◽

Alternative Methods ◽

Data Set ◽

Clustering Problem ◽

Fuzzy Clustering Method ◽

Parameter Prediction

In regression analysis, the data have different distributions which requires to go beyond the classical analysis during the prediction process. In such cases, the analysis method based on fuzzy logic is preferred as alternative methods. There are couple important steps in the regression analysis based on fuzzy logic. One of them is identification of the clusters that generate the data set, the other is the degree of memberships that are determined the grades of the contributions of the data contained in these clusters. In this study, parameter prediction based on type-2 fuzzy clustering is discussed. Firstly, type-1 fuzzy clustering problem was solved by the fuzzy c-means (FCM) method when the fuzzifier index is equal to two. Then the fuzzifier index m is defined as interval number. The membership degrees to the sets are determined by type-2 fuzzy clustering method. Membership degree obtained as a result of clustering based on type-1 and type-2 fuzzy logic are used as weight and parameter prediction using these membership degrees that determined by the proposed algorithm. Finally, the prediction result of the type-1 and type-2 fuzzy clustering parameter is compared with the error criterion based on the difference between observed values and the predicted values.

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Clustering within the Framework of Hesitant Fuzzy Sets

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.668-669.1143 ◽

2014 ◽

Vol 668-669 ◽

pp. 1143-1146

Author(s):

Yi Zhi Wang ◽

Ying Jun Zhang ◽

Lan Dong

Keyword(s):

Fuzzy Sets ◽

Correlation Coefficient ◽

Matrix Composition ◽

Clustering Method ◽

Hesitant Fuzzy Sets ◽

Correlation Relation ◽

Numerical Example ◽

Clustering Problem ◽

Fuzzy Environment ◽

Relation Matrix

In this paper, we propose a variety of correlation coefficient measures for hesitant fuzzy sets (HFSs) and investigate their properties. Moreover, we utilize the concepts of correlation relation matrix, composition matrix and equivalent correlation relation matrix to deal with the clustering problem under hesitant fuzzy environment. Finally, a numerical example is utilized to validate the proposed correlation coefficient measures and the clustering method.

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DPFCM: A novel distributed picture fuzzy clustering method on picture fuzzy sets

Expert Systems with Applications ◽

10.1016/j.eswa.2014.07.026 ◽

2015 ◽

Vol 42 (1) ◽

pp. 51-66 ◽

Cited By ~ 93

Author(s):

Le Hoang Son

Keyword(s):

Fuzzy Sets ◽

Fuzzy Clustering ◽

Clustering Method ◽

Fuzzy Clustering Method ◽

Picture Fuzzy Sets

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Combined Probabilistic and Possibilistic Used to a Build Type-2 Fuzzy Clustering Algorithm Model

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.284-287.3060 ◽

2013 ◽

Vol 284-287 ◽

pp. 3060-3069

Author(s):

Leehter Yao ◽

Kuei Sung Weng

Keyword(s):

Fuzzy Sets ◽

Membership Function ◽

Fuzzy Clustering ◽

Clustering Algorithm ◽

Fuzzy Clustering Algorithm ◽

Noise Data ◽

Membership Value ◽

Will Force

In a noise environment probabilistic fuzzy clustering will force the noise into one or more clusters, seriously influencing the main dataset structure. We extend Type-1 membership values to Type-2 by assigning a possibilistic-membership function to each Type-1 membership value. The idea in building the Type-2 fuzzy sets is based simply on the fact that, for the same Type-1 membership value, the secondary membership function should make the larger possibility value greater than the smaller possibility value. This paper presents an efficient combined probabilistic and possibilistic method for building Type-2 fuzzy sets. Utilizing this concept we present a Type-2 FCM (T2FCM) that is an extension of the conventional FCM. The experimental results show that the T2FCM is less susceptible to noise than the Type-1 FCM. The T2FCM can ignore the inlier and outlier interrupt. The clustering results show the robustness of the proposed T2FCM because a reasonable amount of noise data does not affect its clustering performance.

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Triangular Interval Type-2 Interpolative Fuzzy Reasoning

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.198-199.261 ◽

2012 ◽

Vol 198-199 ◽

pp. 261-266

Author(s):

Yang Chen ◽

Tao Wang

Keyword(s):

Fuzzy Sets ◽

Fuzzy Inference ◽

Fuzzy Reasoning ◽

Membership Functions ◽

Inference Models ◽

Definition Of ◽

Interval Type ◽

Triangular Type

This paper first gives the definition of interval type-2 fuzzy sets,then investigates interval type-2 interpolative fuzzy reasoning under Triangular type membership functions. Two interpolative fuzzy reasoning algorithms responding to interval type-2 fuzzy inference models in the line of type-1 interpolative fuzzy reasoning algorithms are proposed.

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Genetic fuzzy clustering for the definition of fuzzy sets

Proceedings of 6th International Fuzzy Systems Conference ◽

10.1109/fuzzy.1997.619790 ◽

2002 ◽

Cited By ~ 9

Author(s):

J.R. Velasco ◽

S. Lopez ◽

L. Magdalena

Keyword(s):

Fuzzy Sets ◽

Fuzzy Clustering ◽

Definition Of

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An interval type-2 hesitant fuzzy best-worst method

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202801 ◽

2021 ◽

pp. 1-28

Author(s):

Ashraf Norouzi ◽

Hossein Razavi hajiagha

Keyword(s):

Decision Making ◽

Fuzzy Sets ◽

Group Decision Making ◽

Group Decision ◽

Fuzzy Ahp ◽

Uncertain Data ◽

Interval Type ◽

Best Worst Method

Multi criteria decision-making problems are usually encounter implicit, vague and uncertain data. Interval type-2 fuzzy sets (IT2FS) are widely used to develop various MCDM techniques especially for cases with uncertain linguistic approximation. However, there are few researches that extend IT2FS-based MCDM techniques into qualitative and group decision-making environment. The present study aims to adopt a combination of hesitant and interval type-2 fuzzy sets to develop an extension of Best-Worst method (BWM). The proposed approach provides a flexible and convenient way to depict the experts’ hesitant opinions especially in group decision-making context through a straightforward procedure. The proposed approach is called IT2HF-BWM. Some numerical case studies from literature have been used to provide illustrations about the feasibility and effectiveness of our proposed approach. Besides, a comparative analysis with an interval type-2 fuzzy AHP is carried out to evaluate the results of our proposed approach. In each case, the consistency ratio was calculated to determine the reliability of results. The findings imply that the proposed approach not only provides acceptable results but also outperforms the traditional BWM and its type-1 fuzzy extension.

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