Hesitant fuzzy sets and their variants
Lubna Shafi; Shilpi Jain; Praveen Agarwal; Pervaiz Iqbal; Aadil Rashid Sheergojri
Abstract
Fuzzy time series forecasting is an approach for dealing with uncertainty in time series data that uses fuzzy logic. The hesitant fuzzy set theory emphasizes the chances of capturing fuzziness and uncertainty due to randomness better than the classic fuzzy set theory. This study aims to improve the previously ...
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Fuzzy time series forecasting is an approach for dealing with uncertainty in time series data that uses fuzzy logic. The hesitant fuzzy set theory emphasizes the chances of capturing fuzziness and uncertainty due to randomness better than the classic fuzzy set theory. This study aims to improve the previously identified hesitant fuzzy time series forecasting models by including various degrees of hesitation to improve forecasting performance. The goal is to deal with the issue of identifying a common membership grade when several fuzzification methods are available to fuzzify time series data.The proposed method utilizes trapezoidal and bell-shaped fuzzy membership functions for constructing hesitant fuzzy sets.Ahesitant fuzzy weighted averaging operator is then applied to the hesitant fuzzy elements to create fuzzy logical relations.The suggested technique is employed to forecast enrollment in the University of Alabama and cancer incidence rates in India. The efficiency of the proposed forecasting approach is determined by rigorously comparing it to various computational fuzzy time series forecasting methods in terms of error measurements like root mean square error, average forecasting error, and mean absolute deviation. The validity of the proposed forecasting model is verified by using correlation coefficients, coefficients of determination, tracking signals, and performance parameters. The significance of improved accuracy in forecasted results is confirmed as well using the two-tailed t-test. The results of the study revealed that the enhanced hesitant fuzzy time series model is more effective and accurate in forecasting the university enrolment of Alabama and the cancer incidence rates of India.
Complex Fuzzy Sets and their variants
Rubeena Khaliq; Pervaiz Iqbal; Shahid Ahmad Bhat; Ram Singh; Shilpi Jain; Praveen Agarwal
Abstract
In this present study, the tumor growth model using the Gompertz equation with the Allee effect is developed under a fuzzy environment using the Generalized Hukuhara Derivative (GHD) approach. To capture the tumor growth patterns with the Allee threshold, the parameters present in the model vary ...
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In this present study, the tumor growth model using the Gompertz equation with the Allee effect is developed under a fuzzy environment using the Generalized Hukuhara Derivative (GHD) approach. To capture the tumor growth patterns with the Allee threshold, the parameters present in the model vary from time to time, and in real life, it is very difficult to estimate the exact cell count. In this vague situation, the initial condition, coefficient, and both together are taken as the fuzzy number. In this paper, the GHD approach is used to solve the fuzzy tumor growth model in which four different cases are considered with respect to (i)-gH differentiability and (ii)-gH differentiability concept. The main objective of this study is to present a significant reduction in uncertainty while modeling the tumor growth in a fuzzy environment with the Allee effect. Finally, the proposed model and technique are illustrated by numerical simulation and analysis of tumor growth is conducted.
