Distinguishability of interval type-2 fuzzy sets data by analyzing upper and lower membership functions

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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Properties of interval type-2 fuzzy sets in decision support systems

Bulletin of the National Technical University «KhPI» Series New solutions in modern technologies ◽

10.20998/2413-4295.2021.04.10 ◽

2021 ◽

pp. 75-81

Author(s):

Alexander Zakovorotniy ◽

Artem Kharchenko

Keyword(s):

Fuzzy Sets ◽

Fuzzy Inference ◽

Systems Design ◽

Membership Functions ◽

Fuzzy Inference Systems ◽

Footprint Of Uncertainty ◽

Expert Assessments ◽

Interval Type ◽

Inference Systems

Definitions and methods of designing interval type-2 fuzzy sets in fuzzy inference systems for control problems of complex technical objects in conditions of uncertainty are considered. The main types of uncertainties, that arise when designing fuzzy inference systems and depend on the number of expert assessments, are described. Methods for assessing intra-uncertainty and inter-uncertainty are proposed, taking into account the different number of expert assessments at the stage of determining the types and number of membership functions. Factors influencing the parameters and properties of interval type-2 fuzzy during experimental studies are determined. Such factors include the number of experiments performed, external factors, technical parameters of the control object, and the reliability of the components of the computer system decision support system. The properties of the lower and upper membership functions of interval type-2 fuzzy sets are investigated on the example of the Gaussian membership function, which is one of the most used in the problems of fuzzy inference systems design. The main features and differences in the methods of determining the lower and upper membership functions of interval type-2 fuzzy sets for different types of uncertainties are taken into account. Methods for determining the footprint of uncertainty, as well as the dependence of its size on the number of expert assessments, are considered. The footprint of uncertainty is characterized by the lower and upper membership functions, and its size directly affects the accuracy of the obtained solutions. Methods for determining interval type-2 fuzzy sets using regulation factors of membership function parameters for intra-uncertainty and weighting factors of membership functions for inter-uncertainties have been developed. The regulation factor of the function parameters can be used to describe the lower and upper membership functions while determining the size of the footprint of uncertainty. Complex interval type-2 sets are determined to take into account inter-uncertainties in the problems of fuzzy inference systems design.

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An Entropy of Interval Type-2 Fuzzy Sets

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.321-324.1999 ◽

2013 ◽

Vol 321-324 ◽

pp. 1999-2003 ◽

Cited By ~ 2

Author(s):

Gao Zheng ◽

Shi Wei Yin

Keyword(s):

Fuzzy Sets ◽

Fuzzy Set ◽

Fuzzy Entropy ◽

Calculation Formula ◽

Membership Functions ◽

Axiomatic Definition ◽

Fuzzy Degree ◽

Interval Type

The entropy shows the fuzzy degree of a fuzzy set (FS) and can be used in various areas. Aiming at the characteristics of the fuzzy entropy and type-2 fuzzy sets (IT2 FSs), we introduce a new entropy of IT2 FSs in this paper. At first, we select an axiomatic definition for it. Then, considering a fact that the operations of IT2 FSs depend on the upper membership functions (UMFs) and lower membership functions (LMFs), we propose a calculation formula and verify it accords with the four axioms of the selected definition. Finally, we use an example to illuminate its reasonable performance.

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Hazard identification, risk assessment and control for dam construction safety using an integrated BWM and MARCOS approach under interval type-2 fuzzy sets environment

Automation in Construction ◽

10.1016/j.autcon.2021.103699 ◽

2021 ◽

Vol 127 ◽

pp. 103699

Author(s):

Erkan Celik ◽

Muhammet Gul

Keyword(s):

Risk Assessment ◽

Fuzzy Sets ◽

Construction Safety ◽

Hazard Identification ◽

Dam Construction ◽

Interval Type ◽

And Control

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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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Design of back propagation optimized Nagar-Bardini structure-based interval type-2 fuzzy logic systems for fuzzy identification

Transactions of the Institute of Measurement and Control ◽

10.1177/01423312211006635 ◽

2021 ◽

pp. 014233122110066

Author(s):

Yang Chen ◽

Jiaxiu Yang

Keyword(s):

Fuzzy Logic ◽

Back Propagation ◽

Membership Functions ◽

Identification Problems ◽

Fuzzy Logic Systems ◽

Fuzzy Identification ◽

Logic Systems ◽

Academic Topic ◽

Interval Type

In recent years, fuzzy identification based on system identification theory has become a hot academic topic. Interval type-2 fuzzy logic systems (IT2 FLSs) have become a rising technology. This paper designs a type of Nagar-Bardini (NB) structure-based singleton IT2 FLSs for fuzzy identification problems. The antecedents of primary membership functions of IT2 FLSs are chosen as Gaussian type-2 primary membership functions with uncertain standard deviations. Then, the back propagation algorithms are used to tune the parameters of IT2 FLSs according to the chain rule of derivation. Compared with the type-1 fuzzy logic systems, simulation studies show that the proposed IT2 FLSs can obtain better abilities of generalization for fuzzy identification problems.

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