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Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications

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A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (30 June 2017) | Viewed by 77922

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Prof. Dr. Oscar Castillo

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Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana 22414, Mexico
Interests: type-2 fuzzy logic; fuzzy control; neuro-fuzzy; genetic-fuzzy hybrid approaches
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Special Issue Information

Dear Colleagues,

Recent developments in fuzzy logic have presented new theories, concepts and algorithms, extending the original ideas of the pioneering work of Prof. Zadeh. Traditional fuzzy logic, now called type-1 fuzzy logic, has been widely applied in many real world problems with relative success, ranging from control, pattern recognition, robotics, time series prediction and economics. However, complex problems usually involve high degrees of uncertainty that cannot be handled with the traditional type-1 fuzzy logic. In this case, extensions to type-1, like interval type-2 fuzzy logic, general type-2 fuzzy logic, intuitionistic fuzzy logic and other similar approaches have been recently proposed to tackle more complex real world problem. The present Special issue is dedicated to the new theories, concepts and algorithms that have been developed to consider situations and problems under high degrees of uncertainty. The topics include, but not limited to, new theories and algorithms in the following areas:

Interval Type-2 Fuzzy Logic
General Type-2 Fuzzy Logic
Intuitionistic Fuzzy Logic
Type-2 Fuzzy Systems
Intuitionistic Fuzzy Systems
Fuzzy Differential Equations
Algorithms for designing optimal fuzzy systems
Hybrid models including fuzzy with bio-inspired computing, or evolutionary and swarm intelligence
Applications of the above models to problems in any area

Prof. Dr. Oscar Castillo
Guest Editor

Manuscript Submission Information

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Keywords

Type-2 Fuzzy Logic
Intuitionistic Fuzzy Logic
Extensions to Type-1 Fuzzy Logic

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Published Papers (12 papers)

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619 KiB

Open AccessArticle

Type-1 Fuzzy Sets and Intuitionistic Fuzzy Sets

by Krassimir T. Atanassov

Algorithms 2017, 10(3), 106; https://doi.org/10.3390/a10030106 - 13 Sep 2017

Cited by 38 | Viewed by 8304

Abstract

A comparison between type-1 fuzzy sets (T1FSs) and intuitionistic fuzzy sets (IFSs) is made. The operators defined over IFSs that do not have analogues in T1FSs are shown, and such analogues are introduced whenever possible. Full article

(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)

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4449 KiB

Open AccessArticle

Comparative Study of Type-2 Fuzzy Particle Swarm, Bee Colony and Bat Algorithms in Optimization of Fuzzy Controllers

by Frumen Olivas, Leticia Amador-Angulo, Jonathan Perez, Camilo Caraveo, Fevrier Valdez and Oscar Castillo

Algorithms 2017, 10(3), 101; https://doi.org/10.3390/a10030101 - 28 Aug 2017

Cited by 59 | Viewed by 7330

Abstract

In this paper, a comparison among Particle swarm optimization (PSO), Bee Colony Optimization (BCO) and the Bat Algorithm (BA) is presented. In addition, a modification to the main parameters of each algorithm through an interval type-2 fuzzy logic system is presented. The main aim of using interval type-2 fuzzy systems is providing dynamic parameter adaptation to the algorithms. These algorithms (original and modified versions) are compared with the design of fuzzy systems used for controlling the trajectory of an autonomous mobile robot. Simulation results reveal that PSO algorithm outperforms the results of the BCO and BA algorithms. Full article

(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)

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4758 KiB

Open AccessArticle

Hybrid Learning for General Type-2 TSK Fuzzy Logic Systems

by Mauricio A. Sanchez, Juan R. Castro, Violeta Ocegueda-Miramontes and Leticia Cervantes

Algorithms 2017, 10(3), 99; https://doi.org/10.3390/a10030099 - 25 Aug 2017

Cited by 19 | Viewed by 6262

Abstract

This work is focused on creating fuzzy granular classification models based on general type-2 fuzzy logic systems when consequents are represented by interval type-2 TSK linear functions. Due to the complexity of general type-2 TSK fuzzy logic systems, a hybrid learning approach is proposed, where the principle of justifiable granularity is heuristically used to define an amount of uncertainty in the system, which in turn is used to define the parameters in the interval type-2 TSK linear functions via a dual LSE algorithm. Multiple classification benchmark datasets were tested in order to assess the quality of the formed granular models; its performance is also compared against other common classification algorithms. Shown results conclude that classification performance in general is better than results obtained by other techniques, and in general, all achieved results, when averaged, have a better performance rate than compared techniques, demonstrating the stability of the proposed hybrid learning technique. Full article

(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)

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889 KiB

Open AccessArticle

Transformation-Based Fuzzy Rule Interpolation Using Interval Type-2 Fuzzy Sets

by Chengyuan Chen and Qiang Shen

Algorithms 2017, 10(3), 91; https://doi.org/10.3390/a10030091 - 15 Aug 2017

Cited by 9 | Viewed by 5812

Abstract

In support of reasoning with sparse rule bases, fuzzy rule interpolation (FRI) offers a helpful inference mechanism for deriving an approximate conclusion when a given observation has no overlap with any rule in the existing rule base. One of the recent and popular FRI approaches is the scale and move transformation-based rule interpolation, known as T-FRI in the literature. It supports both interpolation and extrapolation with multiple multi-antecedent rules. However, the difficult problem of defining the precise-valued membership functions required in the representation of fuzzy rules, or of the observations, restricts its applications. Fortunately, this problem can be alleviated through the use of type-2 fuzzy sets, owing to the fact that the membership functions of such fuzzy sets are themselves fuzzy, providing a more flexible means of modelling. This paper therefore, extends the existing T-FRI approach using interval type-2 fuzzy sets, which covers the original T-FRI as its specific instance. The effectiveness of this extension is demonstrated by experimental investigations and, also, by a practical application in comparison to the state-of-the-art alternative approach developed using rough-fuzzy sets. Full article

(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)

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2842 KiB

Open AccessArticle

A New Meta-Heuristics of Optimization with Dynamic Adaptation of Parameters Using Type-2 Fuzzy Logic for Trajectory Control of a Mobile Robot

by Camilo Caraveo, Fevrier Valdez and Oscar Castillo

Algorithms 2017, 10(3), 85; https://doi.org/10.3390/a10030085 - 26 Jul 2017

Cited by 39 | Viewed by 7509

Abstract

Fuzzy logic is a soft computing technique that has been very successful in recent years when it is used as a complement to improve meta-heuristic optimization. In this paper, we present a new variant of the bio-inspired optimization algorithm based on the self-defense mechanisms of plants in the nature. The optimization algorithm proposed in this work is based on the predator-prey model originally presented by Lotka and Volterra, where two populations interact with each other and the objective is to maintain a balance. The system of predator-prey equations use four variables (α, β, λ, δ) and the values of these variables are very important since they are in charge of maintaining a balance between the pair of equations. In this work, we propose the use of Type-2 fuzzy logic for the dynamic adaptation of the variables of the system. This time a fuzzy controller is in charge of finding the optimal values for the model variables, the use of this technique will allow the algorithm to have a higher performance and accuracy in the exploration of the values. Full article

(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)

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4717 KiB

Open AccessArticle

Fuzzy Fireworks Algorithm Based on a Sparks Dispersion Measure

by Juan Barraza, Patricia Melin, Fevrier Valdez and Claudia I. Gonzalez

Algorithms 2017, 10(3), 83; https://doi.org/10.3390/a10030083 - 21 Jul 2017

Cited by 21 | Viewed by 6001

Abstract

The main goal of this paper is to improve the performance of the Fireworks Algorithm (FWA). To improve the performance of the FWA we propose three modifications: the first modification is to change the stopping criteria, this is to say, previously, the number of function evaluations was utilized as a stopping criteria, and we decided to change this to specify a particular number of iterations; the second and third modifications consist on introducing a dispersion metric (dispersion percent), and both modifications were made with the goal of achieving dynamic adaptation of the two parameters in the algorithm. The parameters that were controlled are the explosion amplitude and the number of sparks, and it is worth mentioning that the control of these parameters is based on a fuzzy logic approach. To measure the impact of these modifications, we perform experiments with 14 benchmark functions and a comparative study shows the advantage of the proposed approach. We decided to call the proposed algorithms Iterative Fireworks Algorithm (IFWA) and two variants of the Dispersion Percent Iterative Fuzzy Fireworks Algorithm (DPIFWA-I and DPIFWA-II, respectively). Full article

(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)

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4833 KiB

Open AccessArticle

Optimization of Intelligent Controllers Using a Type-1 and Interval Type-2 Fuzzy Harmony Search Algorithm

by Cinthia Peraza, Fevrier Valdez and Patricia Melin

Algorithms 2017, 10(3), 82; https://doi.org/10.3390/a10030082 - 20 Jul 2017

Cited by 38 | Viewed by 6033

Abstract

This article focuses on the dynamic parameter adaptation in the harmony search algorithm using Type-1 and interval Type-2 fuzzy logic. In particular, this work focuses on the adaptation of the parameters of the original harmony search algorithm. At present there are several types of algorithms that can solve complex real-world problems with uncertainty management. In this case the proposed method is in charge of optimizing the membership functions of three benchmark control problems (water tank, shower, and mobile robot). The main goal is to find the best parameters for the membership functions in the controller to follow a desired trajectory. Noise experiments are performed to test the efficacy of the method. Full article

(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)

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8040 KiB

Open AccessArticle

Design of an Optimized Fuzzy Classifier for the Diagnosis of Blood Pressure with a New Computational Method for Expert Rule Optimization

by Juan Carlos Guzman, Patricia Melin and German Prado-Arechiga

Algorithms 2017, 10(3), 79; https://doi.org/10.3390/a10030079 - 14 Jul 2017

Cited by 27 | Viewed by 7069

Abstract

A neuro fuzzy hybrid model (NFHM) is proposed as a new artificial intelligence method to classify blood pressure (BP). The NFHM uses techniques such as neural networks, fuzzy logic and evolutionary computation, and in the last case genetic algorithms (GAs) are used. The main goal is to model the behavior of blood pressure based on monitoring data of 24 h per patient and based on this to obtain the trend, which is classified using a fuzzy system based on rules provided by an expert, and these rules are optimized by a genetic algorithm to obtain the best possible number of rules for the classifier with the lowest classification error. Simulation results are presented to show the advantage of the proposed model. Full article

(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)

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3785 KiB

Open AccessArticle

New Methodology to Approximate Type-Reduction Based on a Continuous Root-Finding Karnik Mendel Algorithm

by Emanuel Ontiveros-Robles, Patricia Melin and Oscar Castillo

Algorithms 2017, 10(3), 77; https://doi.org/10.3390/a10030077 - 5 Jul 2017

Cited by 62 | Viewed by 6524

Abstract

Interval Type-2 fuzzy systems allow the possibility of considering uncertainty in models based on fuzzy systems, and enable an increase of robustness in solutions to applications, but also increase the complexity of the fuzzy system design. Several attempts have been previously proposed to reduce the computational cost of the type-reduction stage, as this process requires a lot of computing time because it is basically a numerical approximation based on sampling, and the computational cost is proportional to the number of samples, but also the error is inversely proportional to the number of samples. Several works have focused on reducing the computational cost of type-reduction by developing strategies to reduce the number of operations. The first type-reduction method was proposed by Karnik and Mendel (KM), and then was followed by its enhanced version called EKM. Then continuous versions were called CKM and CEKM, and there were variations of this and also other types of variations that eliminate the type-reduction process reducing the computational cost to a Type-1 defuzzification, such as the Nie-Tan versions and similar enhancements. In this work we analyzed and proposed a variant of CEKM by viewing this process as solving a root-finding problem, in this way taking advantage of existing numerical methods to solve the type-reduction problem, the main objective being eliminating the type-reduction process and also providing a continuous solution of the defuzzification. Full article

(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)

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660 KiB

Open AccessArticle

An Easily Understandable Grey Wolf Optimizer and Its Application to Fuzzy Controller Tuning

by Radu-Emil Precup, Radu-Codrut David, Alexandra-Iulia Szedlak-Stinean, Emil M. Petriu and Florin Dragan

Algorithms 2017, 10(2), 68; https://doi.org/10.3390/a10020068 - 10 Jun 2017

Cited by 53 | Viewed by 6202

Abstract

This paper proposes an easily understandable Grey Wolf Optimizer (GWO) applied to the optimal tuning of the parameters of Takagi-Sugeno proportional-integral fuzzy controllers (T-S PI-FCs). GWO is employed for solving optimization problems focused on the minimization of discrete-time objective functions defined as the weighted sum of the absolute value of the control error and of the squared output sensitivity function, and the vector variable consists of the tuning parameters of the T-S PI-FCs. Since the sensitivity functions are introduced with respect to the parametric variations of the process, solving these optimization problems is important as it leads to fuzzy control systems with a reduced process parametric sensitivity obtained by a GWO-based fuzzy controller tuning approach. GWO algorithms applied with this regard are formulated in easily understandable terms for both vector and scalar operations, and discussions on stability, convergence, and parameter settings are offered. The controlled processes referred to in the course of this paper belong to a family of nonlinear servo systems, which are modeled by second order dynamics plus a saturation and dead zone static nonlinearity. Experimental results concerning the angular position control of a laboratory servo system are included for validating the proposed method. Full article

(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)

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400 KiB

Open AccessArticle

Revised Gravitational Search Algorithms Based on Evolutionary-Fuzzy Systems

by Danilo Pelusi, Raffaele Mascella and Luca Tallini

Algorithms 2017, 10(2), 44; https://doi.org/10.3390/a10020044 - 21 Apr 2017

Cited by 25 | Viewed by 4902

Abstract

The choice of the best optimization algorithm is a hard issue, and it sometime depends on specific problem. The Gravitational Search Algorithm (GSA) is a search algorithm based on the law of gravity, which states that each particle attracts every other particle with a force called gravitational force. Some revised versions of GSA have been proposed by using intelligent techniques. This work proposes some GSA versions based on fuzzy techniques powered by evolutionary methods, such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO) and Differential Evolution (DE), to improve GSA. The designed algorithms tune a suitable parameter of GSA through a fuzzy controller whose membership functions are optimized by GA, PSO and DE. The results show that Fuzzy Gravitational Search Algorithm (FGSA) optimized by DE is optimal for unimodal functions, whereas FGSA optimized through GA is good for multimodal functions. Full article

(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)

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809 KiB

Open AccessArticle

Reliable Portfolio Selection Problem in Fuzzy Environment: An m_λ Measure Based Approach

by Yuan Feng, Li Wang and Xinhong Liu

Algorithms 2017, 10(2), 43; https://doi.org/10.3390/a10020043 - 18 Apr 2017

Cited by 1 | Viewed by 4437

Abstract

This paper investigates a fuzzy portfolio selection problem with guaranteed reliability, in which the fuzzy variables are used to capture the uncertain returns of different securities. To effectively handle the fuzziness in a mathematical way, a new expected value operator and variance of [...] Read more.

m_{λ}

measure that is a linear combination of the possibility measure and necessity measure to balance the pessimism and optimism in the decision-making process. To formulate the reliable portfolio selection problem, we particularly adopt the expected total return and standard variance of the total return to evaluate the reliability of the investment strategies, producing three risk-guaranteed reliable portfolio selection models. To solve the proposed models, an effective genetic algorithm is designed to generate the approximate optimal solution to the considered problem. Finally, the numerical examples are given to show the performance of the proposed models and algorithm. Full article

(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)

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