An overview and a derivation of interval type-2 fussy logic system (IT2 FLS), which can handle rule’s uncertainties on continuous domain, having good number of applications in real world. This work fo-cused on the performance of an IT2 FLS that involves the operations of a fuzzification, inference, and output processing. The output processing consists of Type-Reduction (TR) and defuzzification. This work made IT2 FLS much more accessible to FLS modellers, because it provides mathematical formulation for calculating the de-rivatives. Presenting extend to representation of T2 FSs on continuous domain and using it to derive formulas for operations, we developed and extended the derivation of the union of two IT2 FSs to the derivation of the intersection and union of N-IT2 FSs that is based on various concepts. The derivation of all the formulas that are related with an IT2 and these formulas depend on continuous domain with multiple rules. Each rule has multiple antecedents that are activated by a crisp number with T2 singleton fuzzification (SF). Then, we have shown how those results can be extended to T2 non-singleton fuzzification (NSF). We are derived the relation-ship between the consequent and the domain of uncertainty (DOU) of the T2 fired output FS. As well as, provide the derivation of the general form at continuous domain to calculate the different kinds of type-reduced. We have also applied an IT2 FLS to medical application of Heart Diseases (HDs) and an IT2 provide rather modest performance improvements over the T1 predictor. Finally, we made a comparison of HDs result between IT2 FLS using the IT2FLS in MATLAB and the IT2 FLS in Visual C# models with T1 FISs (Mamdani, and Takagi-Sugeno).
Inhaltsverzeichnis (Table of Contents)
- 1. INTRODUCTION
- 2. INTERVAL TYPE-2 FUZZY SETS
- 3. SET-THEORETIC OPERATIONS ON TYPE-2 FUZZY SETS
- 3.1 Derivation the intersection of N-T2 FSs depending on the concept of the embedded IT2 FSs
- 3.2 Derivation the intersection of N-T2 FSs depending on the concept of the Extension Principle
- 3.3 Derivation the meet operations of N-T2 FSs depending on the concept of the secondary MF
- 4. INTERVAL TYPE-2 FUZZY LOGIC SYSTEM
- 4.1 Type-2 Singleton Fuzzification Model
- 4.2 Type-2 Non-singleton Fuzzification Model
- 5. THE OUTPUT PROCESSING
Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)
This paper introduces a new class of fuzzy logic systems - interval type-2 fuzzy logic systems (IT2 FLS) - which can handle uncertainties in rules on a continuous domain. The work explores the performance of IT2 FLS by focusing on the operations of fuzzification, inference, and output processing, including type-reduction and defuzzification. The paper aims to provide a mathematical formulation for calculating derivatives, extending the representation of T2 fuzzy sets on continuous domains and deriving formulas for operations.
- Modeling uncertainties in rules on a continuous domain
- Performance analysis of IT2 FLS with focus on fuzzification, inference, and output processing
- Mathematical formulation for calculating derivatives of IT2 FLS
- Extension of T2 fuzzy set representation to continuous domains
- Derivation of formulas for set-theoretic operations on IT2 fuzzy sets
Zusammenfassung der Kapitel (Chapter Summaries)
- Introduction: This chapter introduces the concept of interval type-2 fuzzy logic systems (IT2 FLS) and their potential applications in handling uncertainties in rules. It highlights the challenges associated with using general type-2 fuzzy sets and emphasizes the practical advantages of IT2 FLS.
- Interval Type-2 Fuzzy Sets: This chapter defines IT2 fuzzy sets and related concepts, providing a framework for communicating about these sets. It explains the concept of fuzzing type-1 membership functions and introduces the notion of embedded IT2 fuzzy sets.
- Set-Theoretic Operations on Type-2 Fuzzy Sets: This chapter focuses on deriving formulas for the intersection and union of N-IT2 fuzzy sets. It explores two key concepts: embedded IT2 fuzzy sets and the Extension Principle. Additionally, it derives formulas for the meet and join operations.
- Interval Type-2 Fuzzy Logic System: This chapter describes the structure of an IT2 FLS, outlining its components: rules, fuzzifier, inference system, and output processing. It delves into two models of fuzzification: type-2 singleton fuzzification and type-2 non-singleton fuzzification, presenting derivations of related formulas.
- The Output Processing: This chapter explains the concept of type-reduction and its role in computing the centroid of an IT2 fuzzy set. It discusses the derivation of the general form for continuous domain to calculate different types of type-reduced sets, drawing on previous work by Karnik et al. (2004).
Schlüsselwörter (Keywords)
The paper focuses on the development and application of interval type-2 fuzzy logic systems (IT2 FLS) for handling uncertainties in rules on a continuous domain. The key themes include type-1 fuzzy logic systems, type-2 fuzzy sets, type-2 membership functions, interval type-2 fuzzy systems, footprint of uncertainties, type-reduction, and the application to heart diseases.
- Quote paper
- R.W. Hndoosh (Author), M.S. Saroa (Author), S. Kumar (Author), 2015, Modelling of an Interval Type-2 Fussy Logic System (IT2 FLS) on Continuous Domain with Medical Application, Munich, GRIN Verlag, https://www.grin.com/document/296058
