scholarly journals INTRODUCING TYPE-2 FUZZY SETS FOR IMAGE TEXTURE MODELING

2010 ◽  
Vol 09 (03) ◽  
pp. 171-185
Author(s):  
JESÚS CHAMORRO-MARTÍNEZ ◽  
PEDRO MARTÍNEZ-JIMÉNEZ ◽  
DANIEL SÁNCHEZ
Keyword(s):  
Fuzzy Sets ◽  
Human Perception ◽  
Image Texture ◽  
Membership Functions ◽  
Texture Modeling ◽  
Reference Set ◽  
Texture Property

In this paper, the texture property "coarseness" is modeled by means of type-2 fuzzy sets, relating representative coarseness measures (our reference set) with the human perception of this texture property. The type-2 approach allows to face both the imprecision in the interpretation of the measure value and the uncertainty about the coarseness degree associated with a measure value. In our study, a wide variety of measures is analyzed, and assessments about coarseness perception are collected from pools. This information is used to obtain type-2 fuzzy sets where the secondary fuzzy sets are modeled by means of triangular membership functions fitted to the collected data.

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

Interval Type-2 Fuzzy Sets Constructed From Several Membership Functions: Application to the Fuzzy Thresholding Algorithm

2013 ◽  
Vol 21 (2) ◽  
pp. 230-244 ◽  
Author(s):  
Miguel Pagola ◽  
Carlos Lopez-Molina ◽  
Javier Fernandez ◽  
Edurne Barrenechea ◽  
Humberto Bustince
Keyword(s):  
Fuzzy Sets ◽  
Membership Functions ◽  
Thresholding Algorithm ◽  
Interval Type ◽  
Fuzzy Thresholding

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.

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

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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