A survey of Type-2 fuzzy logic controller design using nature inspired optimization

Abstract

In this paper, we are presenting a survey of research works dealing with Type-2 fuzzy logic controllers designed using optimization algorithms inspired on natural phenomena. Also, in this review, we analyze the most popular optimization methods used to find the important parameters on Type-1 and Type-2 fuzzy logic controllers to improve on previously obtained results. To this end have included a summary of the results obtained from the web of science database to observe the recent trend of using optimization methods in the area of optimal type-2 fuzzy logic control design. Also, we have made a comparison among countries of the network of researchers using optimization methods to analyze the distribution and impact of the papers.

Keywords

Nature inspired optimization Type-2 fuzzy logic fuzzy control

1 Introduction

Swarm intelligence is inspired on the study of nature and social species, which enables the design of powerful optimization methods. For example, choreography on school of fish led to the design of the particle swarm optimization algorithm, and studies of the foraging behavior of ants resulted in ant colony optimization algorithms. The main problem in algorithmic development is the design of models to solve complex problems. In this regard, enormous successes have been achieved through the modeling of biological and swarm intelligence, resulting in systems called “intelligent systems”. These intelligent methods include artificial neural networks, evolutionary computation, swarm intelligence, artificial immune systems, and fuzzy systems.

In recent years, there has been an increasing interest in optimizing fuzzy controllers with nature inspired approaches [1]. Therefore, in this paper, a survey about the nature optimization methods used for optimization on Type-1 and Type-2 fuzzy logic controllers is presented. The main idea is to review the most important optimization methods that have been applied in the control area. In Table 1 a summary of the most well-known nature based intelligence optimization methods is presented. However, in this paper we present only the methods used for optimization of the most important parameters in controllers based on fuzzy logic. Also, a brief description of the different methods cited in each analyzed work is mentioned, for example, particle swarm optimization (PSO), genetic algorithms (GA), ant colony optimization (ACO), etc. The main contribution in this paper is to show the importance that optimization methods have been receiving attention for optimizing type-1 and type-2 fuzzy logic controllers, since they improve the results in several applications.

Table 1
Nature intelligence based optimization methods

Method Author Reference

Water cycle algorithm Eskander et al. [35]

Egyptian Vulture Sur et al. [36]

Intelligent water drop Shah-Hosseini [37]

Great salmon run Mozzaffari [38]

Japanese tree frogs calling Hernandez and Blum [39]

Dolphin echolocation Kave and Farhoudi [40]

Roach infestation algorithm Havens [41]

Flower pollination algorithm Yang [42]

Bat algorithm Yang [6]

Particle swarm optimization Kennedy and Eberhart [3]

Genetic algorithms Holland [7]

Paddy field algorithm Premaratne et al. [43]

Atmosphere clouds model Yan and Hao [44]

Plants swarm algorithm Caraveo et al. [45]

Ant colony optimization Dorigo and Blum [2]

Shuffled frog leaping algorithm Eusuff et al. [46]

Fast bacterial swarming algorithm Chu et al. [47]

Ant lion optimizer Ali et al. [48]

Black hole Hatamlou [49]

Differential evolution Storn and Price [50]

Termite colony optimization Hedayatzadeh et al. [51]

River formation dynamics Rabanal et al. [52]

Marriage in honey bees Abbass [53]

Monkey search Mucherino and Seref [54]

Firefly algorithm Yang [55]

Brain storm optimization Shi [56]

Method	Author	Reference
Water cycle algorithm	Eskander et al.	[35]
Egyptian Vulture	Sur et al.	[36]
Intelligent water drop	Shah-Hosseini	[37]
Great salmon run	Mozzaffari	[38]
Japanese tree frogs calling	Hernandez and Blum	[39]
Dolphin echolocation	Kave and Farhoudi	[40]
Roach infestation algorithm	Havens	[41]
Flower pollination algorithm	Yang	[42]
Bat algorithm	Yang	[6]
Particle swarm optimization	Kennedy and Eberhart	[3]
Genetic algorithms	Holland	[7]
Paddy field algorithm	Premaratne et al.	[43]
Atmosphere clouds model	Yan and Hao	[44]
Plants swarm algorithm	Caraveo et al.	[45]
Ant colony optimization	Dorigo and Blum	[2]
Shuffled frog leaping algorithm	Eusuff et al.	[46]
Fast bacterial swarming algorithm	Chu et al.	[47]
Ant lion optimizer	Ali et al.	[48]
Black hole	Hatamlou	[49]
Differential evolution	Storn and Price	[50]
Termite colony optimization	Hedayatzadeh et al.	[51]
River formation dynamics	Rabanal et al.	[52]
Marriage in honey bees	Abbass	[53]
Monkey search	Mucherino and Seref	[54]
Firefly algorithm	Yang	[55]
Brain storm optimization	Shi	[56]

This paper is organized as follows: Section 2 presents the literature review that was analyzed in this research. In Section 3 a review of type-1 and type-2 fuzzy logic control using optimization methods is presented and finally in Section 4 the conclusions about this work are described.

2 Brief description of optimization methods

Nowadays, the use of bio inspired algorithms has become very popular because with them we are able to solve a variety of complex optimization problems.

Therefore, in this Section we are presenting a brief description about the optimization methods mentioned in the reviewed papers.

2.1 Ant colony optimization

The ACO metaheuristic is inspired by observing the behavior of real ant colonies, which have an interesting feature; they know how to find the shortest paths between the nest and food. On their way the ants deposit a substance called pheromone, and this trail allows the ants back to their nest from the food; they use the evaporation of pheromone to avoid an unlimited increase of pheromone trails and allow forgetting the bad decisions [2].

2.1.1 Particle swarm optimization

PSO is an optimization method proposed by Eberhart and Kennedy in 1995, inspired by the social behavior of bird flocking or fish schooling [3]. The algorithm is initialized with a population of random solutions and searches for optima by updating the position of particles in the iterations. In PSO, the individual particles fly through the search space by following the current optimal particles [4].

2.2 Bee colony optimization (BCO)

In nature, bees would perform a dancing ceremony, which would notify other bees about the quantity of food they have collected, and the closeness of the path to the nest. In BCO, the artificial bees publicize the quality of the solutions, i.e. the objective function value. During the backward pass, every bee decides with a certain probability whether to abandon the created partial solution and become an again uncommitted follower, or dance and thus recruit the nest mates before returning to the created partial solution. During the second forward pass the bees expand previously created partial solutions, by a predefined number of nodes, and after that perform again the backward pass and return to the hive [5].

2.3 Bat algorithm

The Bat algorithm (BA) is a bio-inspired algorithm developed by Yang in 2010. BA has been found to be very efficient according to [6]. If we idealize some of the echolocation characteristics of micro bats, we can develop various bat-inspired algorithms or bat algorithms. All bats use echolocation to sense distance, ant they also ‘know’ the difference between food/prey and background barriers in some unknown way.

2.4 Genetic algorithms

Holland, from the University of Michigan initiated his work on genetic algorithms at the beginning of the 1960s. His first achievement was the publication of Adaptation in Natural and Artificial System in 1975.

He had two goals in mind: to improve the understanding of natural adaptation process, and to design artificial systems having properties similar to natural systems [7].

2.4.1 Firefly algorithm

Firefly algorithm is classified as a swarm intelligent, metaheuristic and nature-inspired, and it was developed by Yang in 2008 by animating the characteristic behaviors of fireflies. In fact, the population of fireflies show characteristic luminary flashing activities to function as attracting the partners, communication, and risk warning for predators [8].

2.4.2 Cuckoo search algorithm

The Cuckoo Search algorithm is a recently developed meta-heuristic optimization algorithm, which is used for solving problems. This is a nature-inspired metaheuristic algorithm, which is based on the brood parasitism of some cuckoo species, along with Levy flights random walks. Normally, the parameters of the cuckoo search are kept constant for certain duration, these results into a decrease of the efficiency of the algorithm [9].

3 Type-2 fuzzy logic

Type-2 fuzzy logic emerges as a tool that contains a set of mathematical concepts and methodologies to handle the implied uncertainty contained in the fuzzy sets that describe the linguistic values of fuzzy variables. Type-2 fuzzy logic generalizes the conventional Type-1 fuzzy logic; it can model in a better way the concepts embedded on the rule-based fuzzy systems. In Fig. 1, the Temperature variable contains three linguistic values: Cold, Warm, and Hot. In the case of Type 2, the boundary to delimit the concepts is given through a footprint that describes the uncertainty implied in them, different from the Type-1 fuzzy set in which the boundary is well-defined.

Fig. 1

Fuzzy sets in type-1 and type-2 versions.

A type-2 fuzzy set Ã is defined by a tuple as follows: $\tilde{A} = {\begin{matrix} ((x, u), μ_{\tilde{A}} (x, u)) | \forall x \in X, \\ \forall u \in J_{x} \subseteq [0, 1], 0 \leq μ_{\tilde{A}} (x, u) \leq 1 \end{matrix}}$ (1) where X is the domain of the fuzzy variable, and u belongs to the interval called the primary member- ship, that is u ∈ J_x ⊆ [0, 1], $μ_{\tilde{A}} (x, u)$ is a 2-dimension membership function for defining the secondary membership [10 –13]. If $μ_{\tilde{A}} (x, u) = 1$ for all (x, u) in a fuzzy set then the type-2 fuzzy set is called interval type-2 fuzzy set.

In general, a fuzzy rule l in a Mamdani fuzzy system can be expressed as: $R^{l} : if x_{1} is F_{1}^{l} and x_{2} is F_{2}^{l} then y^{l} = G^{l}$ (2)

If one or some fuzzy sets in the rule-based are type-2 then the fuzzy system is Type-2. Figure 2 depicts the basic components of a Type-2 fuzzy system. The fuzzifier operation maps crisp values to Type-2 fuzzy sets, the rules block contains a set of fuzzy rules, and they can be expressed as in Equation 2. In inference block, rules are processed using the mathematics of type-2 fuzzy sets, and this block generated an induced type-2 fuzzy set. Finally, the induced type-2 fuzzy set can be quantified to map it to a type-1 fuzzy set or a crisp value in the output processor.

Fig. 2

Type-2 fuzzy system.

4 Literature review

In this Section a detailed review about the analyzed methods is presented.

In [14] the authors proposed a comparative study of the conventional mathematical and fuzzy logic controllers for velocity regulation. In this case, the authors only made a comparison with different PID controllers without optimization methods. However, the authors have proposed in the future to work with optimization methods to improve the obtained results.

In [15] a type-2 fuzzy neural network (T2FNN) and its learning method using Grey wolf optimizer (GWO) for system identification was proposed. The structure of T2FNN is a combination between a type-2 fuzzy logic system with human-like IF-THEN rule thinking properties and neural networks (NN) with learning and optimization capability. To validate in the best way their approach, the authors made a comparison with Particle swarm optimization (PSO) and Genetic Algorithms (GA). Also, in [16] an optimal tuning of fuzzy parameters for structural motion control is presented. In this case, the main aim of the authors was to optimize the fuzzy logic controller (FLC) using multiverse optimizer (MVO). The performance of the MVO system is compared with the various classical and advanced optimization algorithms. On other hand, Qian et al. [17] proposed a fuzzy controller for transport control of double pendulum type systems and used GA for tuning of the FLC parameters. Marinaki et al. [18] developed a new method inspired on PSO, with a different velocity equation, for the calculation of the parameters in active control systems with a FLC.

In [19], a novel nature-inspired population-based discrete optimization technique, namely binary bat algorithm (BBA), is proposed for the first time to solve load frequency control (LFC) problem in power system. In another work Caraveo et al. [20], presented a modification of a bio-inspired algorithm based on the bee behavior for optimizing fuzzy controllers. The experimental results were compared with the traditional bee colony optimization in the optimal design of fuzzy controllers.

In [21] a new methodology for FLC parameter optimization using Cuckoo search was presented, includ-ing the rule base as another degree of freedom, in such a way that a better solution for the problem to be optimized is more feasible to achieve. In [22] the authors used the search group algorithm (SGA) and introduced an adaptive parameter control using fuzzy logic, namely fuzzy SGA (FSGA), for enhancing the solution quality of the basic SGA. In the proposed method a fuzzy system was used to dynamically adjust the control parameter value with respect to normalized iteration and normalized error value, which are the inputs of the system.

In [23], a new variant of the algorithm proposed in [22] using Type-2 fuzzy logic for the dynamic adjustment of parameters used to optimize the trajectory of a mobile robot was proposed. The main goal in this work was that the robot can follow a given reference path with a minimum error.

Also, in [24] a work for finding the optimal path planning of mobile robot in unknown static and dynamic environments using Fuzzy-Wind Driven Optimization algorithm singleton type-1 fuzzy logic system (T1-SFLS) controller and Fuzzy-WDO hybrid was presented. The WDO (Wind Driven Optimization) algorithm is used to optimize and tune the input/output membership function parameters of the fuzzy controller.

In [25], a migrant-inspired path planning algorithm for the obstacle avoidance was developed, where the design of an FLC to adjust the dominant ratio of the PSO algorithm and the PFN method for improving the convergence speed; the experimental results were compared with other methods.

In [26], the lightning search algorithm (LSA) was developed to enhance the performance of the trial-and error procedure in obtaining the MFs used in the conventional FLC. LSA is a novel controller for the three-phase PV inverter. The proposed approach aims to solve the problem of nature-inspired technique formulated to solve both single-modal and multi-modal optimization trial-and-error procedure in obtaining MFs used in the conventional FLC.

Also, many authors have been studying several optimization methods to solve different problems; for example, in [27], the authors present an overview on recent developments in machine learning, data mining and evolving soft computing techniques for fault diagnosis and on nature-inspired optimal control. The generic theory was discussed along with illustrative industrial process applications that include a real liquid level control application, wind turbines and a nonlinear servo system. In [28] an attempt to propose an intelligent control system which takes the form of a fractional order fuzzy proportional–integral–derivative (FOFPID) controller was investigated as a solution to deal with the complex dynamic nature of the distillation column. In [29] the authors suggests a synergy of fuzzy logic and nature-inspired optimization in terms of the nature- inspired optimal tuning of the input membership functions of a class of Takagi- Sugeno-Kang (TSK) fuzzy models dedicated to Antilock Braking Systems. Also, in [30] two new strategies for navigation of a swarm of robots for target/mission focused applications including landmine detection and firefighting was presented. The first method presents an embedded fuzzy logic approach in the PSO algorithm and the second method presents a swarm of fuzzy logic controllers, one on each robot. The framework of both strategies were inspired by natural swarms, such as the school of fish or the flock of birds. In this Section, we observed some works where the researchers have been using optimization methods to improve the experimental results on the controllers using type-1 and type-2 fuzzy logic or optimization methods can be used without fuzzy rules. However, is necessary to identify when is better to use type-1 fuzzy logic than type-2 fuzzy logic. Finally, in [31] was introduced a new hybrid approach that combines ant system optimization and fuzzy logic concept to facilitate the multi-objective HPSP optimization, such as the maks-pean, and the processors workload. Based on the concept of the ant system and fuzzy controller, we automatically control the ant system parameters evolution for the multi-objective Heterogeneous processors system using ant system and fuzzy logic controller optimization. Therefore, we have made a review with recent works using both types of fuzzy logic. Finally, in [32] the parameter adaptation was focused on managing the weights of neural networks using type-2 fuzzy inference systems optimized with bio-inspired methods. This is important due to the fact that the weights affect the performance of the learning process of the neural network [33, 34] and the use of type-2 fuzzy weights can be important in the training phase for managing uncertainty in real world data.

5 A review with Type-1 and Type-2 fuzzy logic using optimization methods

In this section, we are presenting a survey of recent works using type-1 and type-2 fuzzy logic using optimization methods to improve the experimental results. In the literature review, we presented some works in a general form using optimization methods, where some papers use, type-1 and type-2 fuzzy logic with optimization algorithms and other works only used optimization without fuzzy logic. Based on the search in web of science “fuzzy logic controller nature inspired optimization”, we found 15 works mentioning the above keywords. In Fig. 3, we can observe that India has 3 works, while other countries only have 2 and 1 paper related with this topic.

Fig. 3

TOPIC in web of science: (fuzzy logic controller nature inspired optimization).

The network of researchers according to this search is presented in Fig. 4.

Fig. 4

Network of researchers in the world working with the topic ‘fuzzy logic controller nature inspired optimization’.

On other hand, if the search is “type 2 fuzzy logic controller optimization” on web of science. We found, 199 works, where Mexico has the first place in this topic with 49 (24.623 %) of 199 papers. However, we present only the first 20 references [45 , 57–75] according to web of science (see Fig. 6). The rest of papers can be reviewed with the above search. The network of researchers for Mexican papers is presented in Fig. 5.

Fig. 5

Network of researchers in Mexico working with the topic ‘type 2 fuzzy logic controller optimization’.

Fig. 6

Citation report for 49 results from Web of Science Core Collection.

The second place is taken by Peoples R China with 16.583 % and Iran with 15.075 %. The rest of countries have less than 10% with the analyzed search. In Fig. 7, is presented a graphic by countries with this topic.

Fig. 7

TOPIC in web of science (type 2 fuzzy logic controller optimization).

Also, we performed a search in web of science with the topic “fuzzy logic controller optimization”, and were 1471 papers found in total to observe the difference with the topic “type-2 fuzzy logic controller optimization”. In Fig. 9 is presented a plot, where India is leading with 215 papers (14.548 %) of 1471. However, we present only the first 15 references according to web of science [76 –94] (view Fig. 8), followed by Peoples R China with 12.101 % and Iran with 11.081 %. USA, Mexico and other countries have less than 10% of papers.

Fig. 8

Citation report for 215 results from Web of Science Core Collection.

Fig. 9

TOPIC web of science (fuzzy logic controller optimization).

The complete network considering all countries with the topic “type-2 fuzzy logic controller optimization” is shown in Fig. 10.

Fig. 10

Network working with the topic ‘type 2 fuzzy logic controller optimization’.

Figure 11 shows the complete network with the topic ‘fuzzy logic controller optimization’.

Fig. 11

Network working with the topic ‘fuzzy logic controller optimization’.

6 Conclusions

After finishing the review we can notice that many works using nature inspired optimization methods on type-1 or type-2 fuzzy logic controller design have been proposed. We can conclude the importance of the optimization methods to achieve the best results in real problems. Nowadays, control systems are very complex, and tuning of several parameters is needed, and is difficult to the users are test and error every time run the system. Therefore, the use of optimization methods based on nature is a good alternative to improve the results with a low computational cost as can be seen in this review. Also, with this survey we can observe that the use of type-1 and type-2 fuzzy systems is becoming more popular, the authors are using fuzzy rules to improve the results combining optimization methods based on nature. With the results obtained from web of science, we have observed how the trend is to use optimization methods every day because the researchers have been achieving good results applying bio-inspired methods. Also, nowadays we can find in the literature hybrid methods to improve the results. Also, as a future work we can explore more optimization methods using other type of parameter adaptation or can be included in the survey hybrid methods with parameter adaptation using fuzzy logic to compare the performance among the methods. Other advantage of making this type of reviews is the motivation for the authors to use techniques to change dynamically the parameters achieving the best results with the optimization methods.

Footnotes

Acknowledgments

The authors would like to thank CONACYT and Tecnológico Nacional de Mexico/Tijuana Institute of Technology for the support during this research work.

References

Valdez

, A review of optimization swarm intelligence inspired algorithms with type-2 fuzzy logic parameter adaptation, Soft Computing (2019). 10.1007/s00500-019-04290-y.

Dorigo

and Blum

, Ant colony optimization theory: A survey, Theoretical Computer Science 344(2) (2005), 243–278. 10.1016/j.tcs.2005.05.020.

Kennedy

and Eberhart

, Particle swarm optimization, in: Proceedings of ICNN’ 95 - International Conference on Neural Networks 4, 1995. 10.1109/ICNN.1995.488968.

Angeline

P.J.

, Using selection to improve particle swarm optimization, in: 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360), (1998), pp. 84–89. 10.1109/ICEC.1998.699327.

Lucic

and Teodorovic'

, Bee system: Modeling combinatorial optimization transportation engineering problems by swarm intelligence, Preprints of the TRISTAN IV Triennial Symposium on Transportation Analysis (2001), 441–445.

Yang

X.S.

, A new metaheuristic bat-inspired algorithm, in: Nature inspired cooperative strategies for optimization, Springer, 2010, pp. 65–74.

Holland

J.H.

, Genetic Algorithms and Adaptation, in: Adaptive Control of Ill-Defined Systems. NATO Conference Series (II Systems Science), Vol. 16, S.O.G.., R.E.L.. and A.M.A.., eds, Springer, 1984.

Lindfield

and Penny

, Chapter 10 - Recent Developments and Comparative Studies, Academic Press, Boston, 2017, pp. 185–194. 10.1016/B978-0-12-803636-5.00010-4.

Joshi

A.S.

, Kulkarni

, Kakandikar

G.M.

and Nandedkar

V.M.

, Cuckoo Search Optimization- A Review, Materials Today: Proceedings 4(8) (2017), 7262–7269. 10.1016/j.matpr.2017.07.055.

10.

Gaxiola

, Melin

, Valdez

, Castro

J.R.

and Castillo

, Op- timization of type-2 fuzzy weights in backpropagation learning for neural networks using GAs and PSO, Appl Soft Comput 38 (2016), 860–871. 10.1016/j.asoc.2015.10.027.

11.

Gaxiola

, Melin

, Valdez

and Castillo

, Interval type-2 fuzzy weight adjustment for backpropagation neural networks with application in time series prediction, Inf Sci 260 (2014), 1–14. 10.1016/j.ins.2013.11.006.

12.

Mendel

J.M.

, Type-2 Fuzzy Sets as Well as Computing with Words, IEEE Comp Int Mag 14(1) (2019), 82–95. 10.1109/MCI.2018.2881646.

13.

and Mendel

J.M.

, Similarity Measures for Closed General Type-2 Fuzzy Sets: Overview, Comparisons, and a Geo- metric Approach, IEEE Trans Fuzzy Systems 27(3) (2019), 515–526. 10.1109/TFUZZ.2018.2862869.

14.

Valdez

, Castillo

, Caraveo

and Peraza

, Comparative Study of the Conventional Mathematical and Fuzzy Logic Controllers for Velocity Regulation, Axioms 8(2) (2019), 53. 10.3390/axioms8020053.

15.

Mao Suprapto

W.-L.

, Hung

C.-W.

, et al., Type-2 fuzzy neural network using grey wolf optimizer learning algorithm for nonlinear system identification, Microsystem Technologies 24 (2018), 4075–4075. 10.1007/s00542-017-3636-x.

16.

Azizi

, Ghasemi

S.A.M.

, Ejlali

R.G.

and Talatahari

, Optimal tuning of fuzzy parameters for structural motion control using multiverse optimizer, The Structural Design of Tall and Special Buildings 28(13) (2019), 1652. 10.1002/tal.1652.

17.

Qian

, Tong

and Lee

S.G.

, Fuzzy-logic-based control of payloads subjected to double-pendulum motion in overhead cranes, Automation in Construction 65 (2016), 133–143.

18.

Marinaki

, Marinakis

and Stavroulakis

, Fuzzy control optimized by a Multi-Objective Particle Swarm Optimization algorithm for vibration suppression of smart structures, Structural and Multidisciplinary Optimization 43 (2011), 29–42. 10.1007/s00158-010-0552-4.

19.

Guha

, Roy

P.K.

, Banerjee

, et al., Binary Bat Algorithm Applied to Solve MISO-Type PID-SSSC-Based Load Frequency Control Problem, Iranian Journal of Science and Technology, Transactions of Electrical Engineering 43(2) (2019), 323–342. 10.1007/s40998-018-0106-0.

20.

Caraveo

, Valdez

and Castillo

, Optimization of fuzzy controller design using a new bee colony algorithm with fuzzy dynamic parameter adaptation, Appl Soft Comput 43 (2016), 131–142. 10.1016/j.asoc.2016.02.033.

21.

García-Gutiérrez

, Arcos-Aviles

, Carrera

, Gispert

, Motoasca

, Ayala

and Ibarra

, Fuzzy Logic Controller Parameter Optimization Using Metaheuristic Cuckoo Search Algorithm for a Magnetic Levitation System, Applied Sciences 9 (2019), 2458. 10.3390/app9122458.

22.

Noorbin

S.F.H.

and Alfi

, Adaptive parameter control of search group algorithm using fuzzy logic applied to networked control systems, Soft Computing 22(23) (2018), 7939–7960. 10.1007/s00500-017-2742-0.

23.

Caraveo

, Valdez

and Castillo

, A New Meta-Heuristics of Optimization with Dynamic Adaptation of Parameters Using Type-2 Fuzzy Logic for Trajectory Control of a Mobile Robot, Algorithms 10(3) (2017), 85. 10.3390/a10030085.

24.

Pandey

and Parhi

D.R.

, Optimum path planning of mobile robot in unknown static and dynamic environments using Fuzzy-Wind Driven Optimization algorithm, Defence Technology 13(1) (2017), 47–58. 10.1016/j.dt.2017.01.001.

25.

Kuo

P.-H.

, Li

T.-H.S.

, Chen

G.-Y.

, Ho

Y.-F.

and Lin

C.-J.

, A migrant-inspired path planning algorithm for obstacle run using particle swarm optimization, potential field navigation, and fuzzy logic controller, The Knowledge Engineering Review 32 (2017), 5. 10.1017/S0269888916000151.

26.

Mutlag

, Mohamed

and Shareef

, A Nature-Inspired Optimization-Based Optimum Fuzzy Logic Photovoltaic Inverter Controller Utilizing an eZdsp F5 Board, Energies 9 (2016), 120. 10.3390/en9030120.

27.

Precup

R.-E.

, Angelov

, Costa

B.S.J.

and Sayed-Mouchaweh

, An overview on fault diagnosis and nature- inspired optimal control of industrial process applications, Computers in Industry 74 (2015), 75–94. 10.1016/j.compind.2015.03.001.

28.

Mishra

, Kumar

and Rana

K.P.S.

, A fractional order fuzzy PID controller for binary distillation column control, Expert Systems with Applications 42(22) (2015), 8533–8549. 10.1016/j.eswa.2015.07.008.

29.

Precup

R.-E.

, Sabau

M.-C.

and Petriu

E.M.

, Nature-inspired optimal tuning of input membership functions of Takagi- Sugeno-Kang fuzzy models for Anti-lock Braking Systems, Applied Soft Computing 27 (2015), 575–589. https://doi.org/ 10.1016/j.asoc.2014.07.004.

30.

Venayagamoorthy

G.K.

, Grant

L.L.

and Doctor

, Collective robotic search using hybrid techniques: Fuzzy logic and swarm intelligence inspired by nature, Engineering Applications of Artificial Intelligence 22(3) (2009), 431–441. 10.1016/j.engappai.2008.10.002.

31.

Liouane

, Yahia

and Borne

, Multi-objective Scheduling onto Heterogeneous Processors System Using Ant System & Fuzzy Logic Controller, Studies in Informatics and Control 17 (2008).

32.

Gaxiola

, Melin

, Valdez

, Castro

J.R.

and Castillo

, Optimization of type-2 fuzzy weights in backpropagation learning for neural networks using GAs and PSO, Applied Soft Computing 38 (2016), 860–871. 10.1016/j.asoc.2015.10.027.

33.

Ahmadi

M.A.

, Connectionist approach estimates gas–oil relative permeability in petroleum reservoirs: Application to reservoir simulation, Fuel 140 (2015), 429–439. 10.1016/j.fuel.2014.09.058.

34.

Ahmadi

M.A.

and Golshadi

, Neural network based swarm concept for prediction asphaltene precipitation due to natural depletion, Journal of Petroleum Science and Engineering 98-99 (2012), 40–49. 10.1016/j.petrol.2012.08.011.

35.

Sadollah

, Eskandar

, Lee

H.M.

, Yoo

D.G.

and Kim

J.H.

, Water cycle algorithm: A detailed standard code, SoftwareX 5 (2016), 37–43. 10.1016/j.softx.2016.03.001.

36.

Sur

, Sharma

and Shukla

, Egyptian Vulture Optimization Algorithm - A New Nature Inspired Meta-heuristics for Knapsack Problem, in: The 9th International Conference on Computing and Information Technology (IC2IT2013). Advances in Intelligent Systems and Computing, Vol. 209, M.P..,U.H.. and B.S.., eds, Springer, 2013.

37.

Shah-Hosseini

, Intelligent water drops algorithm, International Journal of Intelligent Computing and Cybernetics 1(2) (2008), 193–212. 10.1108/17563780810874717.

38.

Fathi

and Mozaffari

, TGSR: the great salmon run optimization algorithm, Int J Computer Applications in Technology 49 (2014), 192–192.

39.

Hernández

and Blum

, Distributed Graph Coloring: An Approach Based on the Calling Behavior of Japanese Tree Frogs, Swarm Intelligence 6(2) (2012), 117–150. 10.1007/s11721-012-0067-2.

40.

Kaveh

and Farhoudi

, A new optimization method: Dolphin echolocation, Advances in Engineering Software 59 (2013), 53–70. 10.1016/j.advengsoft.2013.03.004.

41.

Havens

T.C.

, Spain

C.J.

, Salmon

N.G.

and Keller

J.M.

, Roach Infestation Optimization, in: 2008 IEEE Swarm Intelligence Symposium, 2008, pp. 1–7. 10.1109/SIS.2008.4668317.

42.

Yang

X.S.

, Flower pollination algorithm for global optimization, in: Unconventional computation and natural computation, Springer, 2012, pp. 240–249.

43.

Premaratne

, Samarabandu

and Sidhu

, A new biologically inspired optimization algorithm, in: 2009 International Conference on Industrial and Information Systems (ICIIS), 2009, pp. 279–284. 10.1109/ICI-INFS.2009.5429852.

44.

Gao-Wei

and Zhanju

, A Novel Atmosphere Clouds ModelOptimizationAlgorithm, in: 2012 International Conference on Computing, Measurement, Control and Sensor Net- work, 2012, pp. 217–220. 10.1109/CMCSN.2012.117.

45.

Caraveo

, Valdez

and Castillo

, A new optimization meta-heuristic algorithm based on self-defense mechanism of the plants with three reproduction operators, Soft Comput 22(15) (2018), 4907–4920. 10.1007/s00500-018-3188-8.

46.

Eusuff

, Lansey

and Pasha

, Shuffled frog-leaping algorithm: a memetic meta-heuristic for discrete optimization, Engineering Optimization 38(2) (2006), 129–154. 10.1080/03052150500384759.

47.

Chu

, Mi

, Liao

, Ji

and Wu

Q.H.

, A Fast Bacterial Swarming Algorithm for high-dimensional function optimization, IEEE Congress on Evolutionary Computation (2008), 3135–3140.

48.

Ali

E.S.

, Elazim

S.M.A.

and Abdelaziz

A.Y.

, Ant Lion Optimization Algorithm for optimal location and sizing of renew- able distributed generations, Renewable Energy 101 (2017), 1311–1324. 10.1016/j.renene.2016.09.023.

49.

Hatamlou

, Black hole: A new heuristic optimization approach for data clustering, Information Sciences 222 (2013), 175–184. 10.1016/j.ins.2012.08.023.

50.

Storn

and Price

K.V.

, Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces, Journal of Global Optimization 11 (1997), 341–359.

51.

Hedayatzadeh

, Salmasi

, Keshtgari

, Reza

and Ziarati

, Termite Colony Optimization: A Novel Approach for Optimizing Continuous Problems, 2010. 10.1109/IRANIANCEE.2010.5507009.

52.

Rabanal

, Rodríguez

and Rubio

, Solving Dynamic TSP by Using River Formation Dynamics, in: 2008 Fourth International Conference on Natural Computation, Vol. 1, 2008, pp. 246–250. 10.1109/ICNC.2008.760.

53.

Abbass

H.A.

, MBO: marriage in honey bees optimization a Haplometrosis polygynous swarming approach, in: Proceed- ings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546), Vol. 1, 2001. 10.1109/CEC.2001.934391.

54.

Mucherino

and Seref

, Monkey search: A novel meta-heuristic search for global optimization, AIP Conference Proceedings 953 (2007). 10.1063/1.2817338.

55.

Yang

X.-S.

, Firefly Algorithms for Multimodal Optimization, 2010. 10.1007/978-3-642-04944-6_14.

56.

Shi

, Brain Storm Optimization Algorithm, in: Advances in Swarm Intelligence, Y. Tan, Y. Shi, Y. Chai and G.Wang, eds, Springer Berlin Heidelberg, Berlin, Heidelberg, 2011, pp. 303– 309.

57.

Bernal

, Castillo

, Soria

and Valdez

, Optimization of Fuzzy Controller Using Galactic Swarm Optimization with Type-2 Fuzzy Dynamic Parameter Adjustment, Axioms 8(1) (2019), 26–26. 10.3390/axioms8010026.

58.

Olivas

, Valdez

, Melin

, Sombra

and Castillo

, Interval type-2 fuzzy logic for dynamic parameter adaptation in a modified gravitational search algorithm, Information Sciences 476 (2019), 159–175. 10.1016/j.ins.2018.10.025.

59.

Castillo

, Melin

, Valdez

, Soria

, Ontiveros

, Peraza

RoblesC.

and Ochoa

, Shadowed Type-2 Fuzzy Systems for Dynamic Parameter Adaptation in Harmony Search and Differential Evolution Algorithms, Algorithms 12(1) (2019), 17–17. 10.3390/a12010017.

60.

Castillo

and Amador-Angulo

, A generalized type-2 fuzzy logic approach for dynamic parameter adaptation in bee colony optimization applied to fuzzy controller design, Information Sciences 460-461 (2018), 476–496. 10.1016/j.ins.2017.10.032.

61.

Olivas

, Valdez

and Castillo

, Comparison of Bio-Inspired Methods with Parameter Adaptation Through Interval Type-2 Fuzzy Logic, in: Fuzzy Logic Augmentation of Neural and Optimization Algorithms: Theoretical Aspects and Real Applications, O. Castillo, P. Melin and J. Kacprzyk, eds, Springer International Publishing, Cham, 2018, pp. 39–53. 10.1007/978-3-319-71008-2_4.

62.

Ontiveros

, Melin

and Castillo

, Impact Study of the Footprint of Uncertainty in Control Applications Based on Interval Type-2 Fuzzy Logic Controllers, in: Fuzzy Logic Augmentation of Neural and Optimization Algorithms: Theoretical Aspects and Real Applications, O. Castillo, P. Melin and J. Kacprzyk, eds, Springer International Publishing, Cham, 2018, pp. 181–197. 10.1007/978-3-319-71008-2_15.

63.

Cervantes

, Castillo

, Hidalgo

and Martinez-Soto

, Fuzzy Dynamic Adaptation of Gap Generation and Mutation in Genetic Optimization of Type 2 Fuzzy Controllers, Advances in Operations Research 2018 (2018), 1–13. 10.1155/2018/9570410.

64.

Peraza

, Valdez

, Castro

J.R.

and Castillo

, Fuzzy Dynamic Parameter Adaptation in the Harmony Search Algorithm for the Optimization of the Ball and Beam Controller, Adv Operations Research 2018 (2018). 10.1155/2018/3092872.

65.

Amador-Angulo

and Castillo

, A new fuzzy bee colony optimization with dynamic adaptation of parameters using interval type-2 fuzzy logic for tuning fuzzy controllers, Soft Computing 22(2) (2018), 571–594. 10.1007/s00500-016-2354-0.

66.

Olivas

, Amador-Angulo

, Pérez

, Caraveo

, Valdez

and Castillo

, Comparative Study of Type-2 Fuzzy Particle Swarm, Bee Colony and Bat Algorithms in Optimization of Fuzzy Controllers, Algorithms 10(3) (2017), 101. 10.3390/a10030101.

67.

Ontiveros-Robles

, Melin

and Castillo

, New Methodology to Approximate Type-Reduction Based on a Continuous Root-Finding Karnik Mendel Algorithm, Algorithms 10(3) (2017), 77. 10.3390/a10030077.

68.

Peraza

, Valdez

and Melin

, Optimization of Intelligent Controllers Using a Type-1 and Interval Type-2 Fuzzy Harmony Search Algorithm, Algorithms 10(3) (2017), 82. 10.3390/a10030082.

69.

Olivas

, Valdez

, Castillo

, González

C.I.

, Martinez

G.E.

and Melin

, Ant colony optimization with dynamic parameter adaptation based on interval type-2 fuzzy logic systems, Appl Soft Comput 53 (2017), 74–87. 10.1016/j.asoc.2016.12.015.

70.

Pérez

, Valdez

, Castillo

, Melin

, González

C.I.

and Martinez

, Interval type-2 fuzzy logic for dynamic parameter adaptation in the bat algorithm, Soft Comput 21(3) (2017), 667–685. 10.1007/s00500-016-2469-3.

71.

Madera

, Castillo

, Garcia-Valdez

and Mancilla

, Bidding Strategies Based on Type-1 and Interval Type-2 Fuzzy Systems for Google AdWords Advertising Campaigns, Vol. 667, 2017, pp. 99–113. 10.1007/978-3-319-47054-2_6.

72.

de la O

, Castillo

and Soria

, Optimization of Reactive Control for Mobile Robots Based on the CRA Using Type-2 Fuzzy Logic, in: Nature-Inspired Design of Hybrid Intelligent Systems, P. Melin, O. Castillo and J. Kacprzyk, eds, Springer International Publishing, Cham, 2017, pp. 505–515. 10.1007/978-3-319-47054-2_33.

73.

Angulo

G.A.

, Mendoza

, Castro

, Rodríguez-Díaz

, Melin

and Castillo

, Fuzzy Sets in Dynamic Adaptation of Parameters of a Bee Colony Optimization for Controlling the Trajectory of an Autonomous Mobile Robot, Sensors 16 (2016), 1458. 10.3390/s16091458.

74.

Castillo

, Cervantes

, Soria

, Sanchez

and Castro

J.R.

, A generalized type-2 fuzzy granular approach with applications to aerospace, Information Sciences 354 (2016), 165–177. 10.1016/j.ins.2016.03.001.

75.

Tai

, El-Sayed

A.-R.

, Biglarbegian

, González

, Castillo

and Mahmud

, Review of Recent Type-2 Fuzzy Controller Applications, Algorithms 9 (2016), 39. 10.3390/a9020039.

76.

Sharma

, Bhasin

, Gaur

and Joshi

, A switching- based collaborative fractional order fuzzy logic controllers for robotic manipulators, Applied Mathematical Modelling 73 (2019), 228–246. 10.1016/j.apm.2019.03.041.

77.

Chintu

J.M.R.

, Sahu

R.K.

and Panda

, Adaptive differential evolution tuned hybrid fuzzy PD-PI controller for automatic generation control of power systems, International Journal of Ambient Energy 0(0) (2019), 1–16. 10.1080/01430750.2019.1653986.

78.

Singh

, Tiwari

, Shah

, Niazi

K.R.

, Meena

and Ratra

, Voltage stability index and APFC for performance improvement of modern power systems with intense renewables, The Journal of Engineering (2019). 10.1049/joe.2018.9375.

79.

Rath

, Parhi

, Das

, Kumar

, Muni

and Salony

, Path optimization for navigation of a humanoid robot using hybridized fuzzy-genetic algorithm, International Journal of Intelligent Unmanned Systems 7 (2019). 10.1108/IJIUS-11-2018-0032.

80.

Ramya

, Balaji

and Kamaraj

, Adaptive MF tuned fuzzy logic speed controller for BLDC motor drive using ANN and PSO technique, The Journal of Engineering 2019(17) (2019), 3947–3950. 10.1049/joe.2018.8179.

81.

Guha

, Roy

P.K.

and Banerjee

, Binary Bat Algorithm Applied to Solve MISO-Type PID-SSSC-Based Load Frequency Control Problem, Iranian Journal of Science and Technology, Transactions of Electrical Engineering 43(2) (2019), 323–342. 10.1007/s40998-018-0106-0.

82.

Jadhav

S.H.

and Sarwadnya

R.V.

, A Brawny hybrid FOFPID in MODA controller in HEVs, Energy Sources, Part A: Recovery, Utilization, and Environmental Effects 0(0) (2019), 1–18. 10.1080/15567036.2019.1602199.

83.

Bensam

and Pandi

, A hybrid MWOAL approach for fast and efficient maximum power point tracking in wind energy conversion systems, Journal of Renewable and Sustainable Energy 11 (2019), 033302. 10.1063/1.5080784.

84.

Piraisoodi

, Irudhayarajan

and Kappuva

, Multi-objective robust fuzzy fractional order proportional-integral-derivative controller design for nonlinear hydraulic turbine governing system using evolutionary computation techniques, Expert Systems 36 (2018), 12366. 10.1111/exsy.12366.

85.

Shankar

and Devi

R.P.K.

, Choice of Frequency Ratio and Its Optimization for PWM Inverter Harmonic Distortion Control, Journal of Control Engineering and AP- Plied Informatics 21(1) (2019), 31–41.

86.

Patle

B.K.

, Parhi

D.R.K.

, Jagadeesh

and Kashyap

S.K.

, Application of probability to enhance the performance of fuzzy based mobile robot navigation, Applied Soft Computing 75 (2019), 265–283. 10.1016/j.asoc.2018.11.026.

87.

Palwalia

, Sharma

and Shrivastava

, Distributed generation integration optimization using fuzzy logic controller, AIMS Energy 7 (2019), 337–348. 10.3934/energy.2019.3.337.

88.

Neelamsetti

and Gandhi

, Implementation of fuzzy logic controller in power system applications, Journal of Intelligent & Fuzzy Systems 36 (2019), 1–12. 10.3233/JIFS-169971.

89.

Ramya

K.C.

, Kumar

, Irfan

, Mesforush

, Mohana-sundaram

and Vijayakumar

, Fuzzy based hybrid incorporating wind solar energy source by reduced harmonics, Journal of Intelligent & Fuzzy Systems 36 (2019), 1–10. 10.3233/JIFS-169982.

90.

Singh

, Nasiruddin

, Sharma

and Saxena

, Implicit control of eddy current braking system using fuzzy logic controller (FLC) and particle swarm optimisation (PSO), Journal of Discrete Mathematical Sciences and Cryptography 22 (2019), 253–275. 10.1080/09720529.2019.1582871.

91.

Talib

and Darus

I.M.

, Intelligent fuzzy logic with fire-fly algorithm and particle swarm optimization for semi-active suspension system using magneto-rheological damper, Journal of Vibration and Control 23 (2015). 10.1177/1077546315580693.

92.

Yassine

A.M.

, Tadeo

, Mezghani

, Mami Allani

, et al., FPGA Implementation of a Robust MPPT of a Photovoltaic System Using a Fuzzy Logic... FPGA Implementation of a Robust MPPT of a Photovoltaic System Using a Fuzzy Logic Controller Based on Incremental and Conductance Algorithm, Vol 9 (2019).

93.

Azizi

, Ejlali

R.G.

, Ghasemi

S.A.M.

and Talatahari

, Upgraded Whale Optimization Algorithm for fuzzy logic based vibration control of nonlinear steel structure, Engineering Structures 192 (2019), 53–70. 10.1016/j.engstruct.2019.05.007.

94.

, Li

, Yan

and Feng

, A hybrid priority-based genetic algorithm for simultaneous pickup and delivery problems in reverse logistics with time windows and multiple decision-makers, Soft Computing 23(15) (2019), 6697–6714. 10.1007/s00500-019-03754-5.