scholarly journals Measuring the Directional or Non-directional Distance Between Type-1 and Type-2 Fuzzy Sets With Complex Membership Functions

2019 ◽  
Vol 27 (7) ◽  
pp. 1506-1515 ◽  
Author(s):  
Josie McCulloch ◽  
Christian Wagner
Keyword(s):  
Fuzzy Sets ◽  
Membership Functions

Triangular Interval Type-2 Interpolative Fuzzy Reasoning

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.

An interval type-2 hesitant fuzzy best-worst method

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.

New Negations on the Membership Functions of Type-2 Fuzzy Sets

2019 ◽  
Vol 27 (7) ◽  
pp. 1397-1406 ◽  
Author(s):  
Carmen Torres-Blanc ◽  
Susana Cubillo ◽  
Pablo Hernandez-Varela
Keyword(s):  
Fuzzy Sets ◽  
Membership Functions

scholarly journals Optimal Design of Interval Type-2 Fuzzy Heart Rate Level Classification Systems Using the Bird Swarm Algorithm

Algorithms ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 206 ◽  
Author(s):  
Ivette Miramontes ◽  
Juan Guzman ◽  
Patricia Melin ◽  
German Prado-Arechiga
Keyword(s):  
Heart Rate ◽  
Fuzzy Systems ◽  
Membership Functions ◽  
Classification Rate ◽  
Heart Rate Level ◽  
Swarm Algorithm ◽  
Bird Swarm Algorithm ◽  
Interval Type

In this paper, the optimal designs of type-1 and interval type-2 fuzzy systems for the classification of the heart rate level are presented. The contribution of this work is a proposed approach for achieving the optimal design of interval type-2 fuzzy systems for the classification of the heart rate in patients. The fuzzy rule base was designed based on the knowledge of experts. Optimization of the membership functions of the fuzzy systems is done in order to improve the classification rate and provide a more accurate diagnosis, and for this goal the Bird Swarm Algorithm was used. Two different type-1 fuzzy systems are designed and optimized, the first one with trapezoidal membership functions and the second with Gaussian membership functions. Once the best type-1 fuzzy systems have been obtained, these are considered as a basis for designing the interval type-2 fuzzy systems, where the footprint of uncertainty was optimized to find the optimal representation of uncertainty. After performing different tests with patients and comparing the classification rate of each fuzzy system, it is concluded that fuzzy systems with Gaussian membership functions provide a better classification than those designed with trapezoidal membership functions. Additionally, tests were performed with the Crow Search Algorithm to carry out a performance comparison, with Bird Swarm Algorithm being the one with the best results.

scholarly journals Automatic Methods for Generation of Type-1 and Interval Type-2 Fuzzy Membership Functions

2015 ◽  
Vol 11 (9) ◽  
pp. 976-987 ◽  
Author(s):  
Andréia Alves dos Santos Schwaab ◽  
Silvia Modesto Nassar ◽  
Paulo José de Freitas Filho
Keyword(s):  
Fuzzy Membership ◽  
Membership Functions ◽  
Fuzzy Membership Functions ◽  
Automatic Methods ◽  
Interval Type

Analysis of Data Generated From Multidimensional Type-1 and Type-2 Fuzzy Membership Functions

2018 ◽  
Vol 26 (2) ◽  
pp. 681-693 ◽  
Author(s):  
Desh Raj ◽  
Aditya Gupta ◽  
Bhuvnesh Garg ◽  
Kenil Tanna ◽  
Frank Chung-Hoon Rhee
Keyword(s):  
Fuzzy Membership ◽  
Membership Functions ◽  
Fuzzy Membership Functions

scholarly journals Uncertainty in Interval Type-2 Fuzzy Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Sadegh Aminifar ◽  
Arjuna Marzuki
Keyword(s):  
Fuzzy Systems ◽  
System Response ◽  
Membership Functions ◽  
Degree Reduction ◽  
Word Meanings ◽  
Lower Complexity ◽  
Interval Type

This paper studies uncertainty and its effect on system response displacement. The paper also describes how IT2MFs (interval type-2 membership functions) differentiate from T1MFs (type-1 membership functions) by adding uncertainty. The effect of uncertainty is modeled clearly by introducing a technique that describes how uncertainty causes membership degree reduction and changing the fuzzy word meanings in fuzzy logic controllers (FLCs). Several criteria are discussed for the measurement of the imbalance rate of internal uncertainty and its effect on system behavior. Uncertainty removal is introduced to observe the effect of uncertainty on the output. The theorem of uncertainty avoidance is presented for describing the role of uncertainty in interval type-2 fuzzy systems (IT2FSs). Another objective of this paper is to derive a novel uncertainty measure for IT2MFs with lower complexity and clearer presentation. Finally, for proving the affectivity of novel interpretation of uncertainty in IT2FSs, several investigations are done.

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