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International Journal of Trend in Scientific Research and Development (IJTSRD)
Volume 6 Issue 2, January-February 2022 Available Online: www.ijtsrd.com e-ISSN: 2456 – 6470
@ IJTSRD | Unique Paper ID – IJTSRD49287 | Volume – 6 | Issue – 2 | Jan-Feb 2022 Page 672
An Overview of Hard Computing
Matthew N. O. Sadiku1
, Uwakwe C. Chukwu2
, Abayomi Ajayi-Majebi3
, Sarhan M. Musa1
1
Roy G. Perry College of Engineering, Prairie View A&M University, Prairie View, TX, USA
2
Department of Engineering Technology, South Carolina State University, Orangeburg, SC, USA
3
Department of Manufacturing Engineering, Central State University, Wilberforce, OH, USA
ABSTRACT
Computing refers to the process of accomplishing a particular task
with the help of a computer or a computing device. Hard computing
is the traditional computing algorithm, which processes functions and
data with a verifiable output. It requires an analytical, precisely stated
model. Hard computing is deterministic and precise. It may also be
regarded as a heterogeneous collection of traditional computing
methods. This paper presents hard computing, the differences
between hard computing and soft computing, and their fusion.
KEYWORDS: hard computing, soft computing, fusion, hybrid mode
How to cite this paper: Matthew N. O.
Sadiku | Uwakwe C. Chukwu | Abayomi
Ajayi-Majebi | Sarhan M. Musa "An
Overview of Hard Computing"
Published in
International
Journal of Trend in
Scientific Research
and Development
(ijtsrd), ISSN:
2456-6470,
Volume-6 | Issue-2,
February 2022, pp.672-676, URL:
www.ijtsrd.com/papers/ijtsrd49287.pdf
Copyright © 2022 by author (s) and
International Journal of Trend in
Scientific Research and Development
Journal. This is an
Open Access article
distributed under the
terms of the Creative Commons
Attribution License (CC BY 4.0)
(http://creativecommons.org/licenses/by/4.0)
INTRODUCTION
We are in the era of computing. Computing is
experiencing its most exciting moments in history,
permeating nearly all areas of human activities.
Computing is any activity that involves using
computers. It is any goal-oriented activity requiring
the use of computers. It includes designing and
building hardware and software systems for a wide
range of purposes. It has resulted in deep changes in
infrastructures and development practices of
computing. It is a critically important, integral
component of modern life. In this era of computing,
the type of computing one uses can make a big
difference. Problem-solving technologies can be of
two types: hard computing and soft computing [1].
Figure 1 compares hard computing and soft
computing [2].
Traditional or hard computing techniques are based
on principles of precision, uncertainty and rigor. The
problems based on analytical model can be easily
solved using such techniques. The analytical models
are precise because they require perfect knowledge.
The terms “hard computing” and “soft computing”
were coined by Lofti A. Zadeh in 1991. Since then,
the area has experienced rapid development. Soft
Computing became a discipline within computer
science in the early 1990s. The terms “machine
intelligence” and “computational intelligence” have
been used to have close meaning as soft computing
[3]. Soft computing approaches include neural
networks, probabilistic models, evolutionary
algorithms, artificial neural networks, fuzzy logic
swarm intelligence, etc.
HARD COMPUTING
One may regard the whole history of computer
science as a record of continuous attempts to
discover, study, and implement computing ideas.
Computing technology greatly affects nearly every
aspect of our modern life including education,
entertainment, transportation, communication,
economy, medicine, engineering, and science. The
history of computing is one of punctuated
equilibrium, bringing new and unexpected changes.
IJTSRD49287
International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470
@ IJTSRD | Unique Paper ID – IJTSRD49287 | Volume – 6 | Issue – 2 | Jan-Feb 2022 Page 673
Mainframes gave birth to minicomputers, which gave
birth to workstations, which gave birth to personal
computers, which gave birth to smartphones.
Hard computing (HC) is a traditional computing
approach. It emphasizes precision, certainty, and
rigor, while soft computing requires that computation,
reasoning, and decision making exploit the tolerance
for imprecision and uncertainty wherever possible. It
is a conventional computing approach which requires
precisely stated analytical model and takes very large
computation time. Hard computing or traditional
computing is fast, efficient, and reliable with
deterministic outcomes. It is the sequential kind of
computing that provides precise and certain solutions.
Hard computing methods are typically easier to apply.
Also the stability of resulting solutions is highly
predictable and the computational burden of practical
algorithms is typically low. HC often takes a lot of
computation time. It strictly follows known steps to
solve a task as opposed to soft computing which is
heuristic Today, we have microwave ovens, washing
machines, cameras, and many other products that
manifest an impressive capability to reason, make
intelligent decisions, adapt to changes in the operating
conditions, and learn from experience [4].
HARD COMPUTING VERSUS SOFT
COMPUTING
The traditional hard computing is an ancient approach
which came before soft computing. The principles of
hard computing are precision, certainty and rigor. The
input data should be exact and the output will be
precise and verifiable. Hard computing is used in
solving the deterministic problems, prototyping, and
modeling. Applications of hard computing include
mobile robot coordination and forecasting
combinational problems.
Soft computing (SC) refers to a collection of
computational techniques in computer science,
artificial intelligence, and machine learning. It differs
from the conventional hard computing as it can
handle uncertainty, imprecision easily. While
conventional hard computing is based on crisp values
and binary numbers, SC uses soft values and fuzzy
sets. Soft computing techniques solve the real-life,
non-linear problems which involve uncertain,
imprecise and approximate solutions of a problem.
Both hard computing and soft computing are
illustrated in Figure 2 [5]. The major differences
between hard computing and soft computing are
summarized as follows [6]:
Hard Computing:
It requires a precise state analytic model.
It relies on binary logic and predefined
instructions.
Its features include precision and categoricity.
It has a deterministic nature.
It works on exact data.
It is used to perform sequential computations.
It produces precise, accurate results.
The programs have to be written.
It is settled in nature.
It cannot handle imprecision and partial truth
It does not suitable for real-world problems.
It consumes a large amount of computation time
and cost.
Soft Computing:
It can be associated with being liberal with
inexactness, uncertainty, partial truth, and
approximation.
It is based on the model of the human mind or
human intelligence.
It depends on formal logic and probabilistic
reasoning.
It consists of approximation and dispositionality.
It has a stochastic nature.
It generally works on ambiguous and noisy data.
It can be used to perform parallel computations.
It results in approximate results.
It can come out with its own programs.
It incorporates randomness in its computations.
It uses multivalued logic.
The differences between soft computing and hard
computing are summarized in Table 1 [7]. The fusion
of the two is considered next.
FUSION OF SOFT COMPUTING AND HARD
COMPUTING
In general, it is irrelevant to ask whether one should
prefer SC over HC or vice-versa. As the soft
computing community is not looking for perfect
solutions but competitive ones instead, there exists an
implicit commitment to benefit from the fusion of
various methodologies. A fusion of soft computing
and hard computing appears to be a natural and
practical choice. There exists a large amount of
applications where SC is used together with HC;
these kind of approaches aim at technically and
economically competitive systems, products, and
services.
Proper fusion of soft computing technology with
conventional hard computing technology is key to
success [8]. In the fusion of SC and HC, the roles
between different methodologies should be assigned
based on their individual characteristics. SC aims to
exploit tolerance for imprecision, uncertainty, and
partial truth to achieve robustness, tractability, and
low total cost. HC techniques are typically easier to
International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470
@ IJTSRD | Unique Paper ID – IJTSRD49287 | Volume – 6 | Issue – 2 | Jan-Feb 2022 Page 674
analyze, their stability is highly predictable, and the
computational burden of algorithms is either low or
moderate. A typical example of a fusion of hard
computing and soft computing is shown in Figure 3
[9].
There are two obvious alternatives to form hybrid
cascades of soft computing and hard computing
algorithms, SC-HC or HCSC, depending on the
sequential order of those functional blocks. In SC and
HC type systems, the soft computing and hard
computing constituents both have their independent
roles, and there is a loose union, with no explicit
connection between them. Although the hard
computing and soft computing research communities
are somewhat separated, many SC-oriented
researchers and engineers are openly favoring the
various fusion opportunities. The unfortunate
separation is clearly hindering the industrial
acceptance of SC [10].
A trend in the fusion of soft computing and hard
computing is the simultaneous partnership of HC and
multiple SC methodologies. The conventional HC
techniques and the emerging SC should be regarded
as complementing methodologies. Fusion of soft and
hard computing techniques are also useful in
applications such as robotics and a nonlinear tracking
system. The fusion of individual soft computing
methodologies has been advantageous in numerous
applications such as providing intelligent behavior.
The integration can improve the control performance
of nonlinear systems. The integration could be closely
or loosely.
CONCLUSION
Hard computing is the conventional methodology,
which relies on the principles of accuracy, certainty,
and inflexibility. Conversely, soft computing is an
emerging modern approach premised on the idea of
the approximation, uncertainty, and flexibility. Hard
computing is based on a crisp system and binary
logic, while soft computing is based on fuzzy logic
and probabilistic reasoning. Hard computing performs
sequential computations, while soft computing
performs parallel computations on the data. Soft
computing approach is probabilistic in nature whereas
hard computing is deterministic. Soft computing and
hard computing are being used together in various
industries. The traditional HC techniques and the
emerging SC should be seen as complementary
methodologies. More information about hard
computing can be found in the books in [11-13] and
the following related journals:
Soft Computing
Applied Soft Computing
REFERENCES
[1] D Morgan, “Hard computing v/s soft
computing,”
https://www.techyv.com/article/hard-
computing-vs-soft-computing/
[2] B. Xavier, and P. B. Dahikar, “A
comprehensive study on the significance of soft
computing in healthcare systems,”
International Journal of Engineering Research
& Technology, vol. 4, no. v2, February 2015,
pp. 278-281.
[3] M. N. O. Sadiku, Y. Wang, S. Cui, S. M. Musa,
“Soft computing: An introduction,”
International Journal of Advanced Research in
Computer Science and Software Engineering,
vol. 8, no. 6, June 2018, pp. 63-65.
[4] L. A. Zadeh, “Fuzzy logic, neural networks,
and soft computing,” Communications of the
ACM, vol. 37, no. 3, March 1994, pp. 77-84.
[5] “Difference between soft computing and hard
computing,”
https://techdifferences.com/difference-between-
soft-computing-and-hard-computing.html
[6] A. Diwan, “Difference between soft computing
and hard computing,” April 2021,
https://www.tutorialspoint.com/difference-
between-soft-computing-and-hard-computing
[7] “Soft computing vs. hard computing:
Difference explained,”
https://wisdomplexus.com/blogs/soft-
computing-vs-hard-
computing/#:~:text=Hard%20computing%20rel
ies%20on%20binary,logic%2C%20and%20use
s%20multivalued%20logic.
[8] A. Kamiya et al., “Fusion of soft computing
and hard computing for large-scale plants: A
general model,” Applied Soft Computing, vol.
5, 2005, pp. 265–279.
[9] S. J. Ovaska et al., “Fusion of soft computing
and hard computing techniques: A review of
applications,” Proceedings of the IEEE SMC'99
Conference Proceedings. 1999 IEEE
International Conference on Systems, Man, and
Cybernetics, October 1999.
[10] S. J. Ovaska, A. Kamiya, and Y. Q. Chen,
“Fusion of soft computing and hard computing:
Computational structures and characteristic
features,” IEEE Transactions on Systems, Man,
and Cybernetics—Part C: Applications and
Reviews, vol. 36, no. 3, May 2006, pp. 439-448.
International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470
@ IJTSRD | Unique Paper ID – IJTSRD49287 | Volume – 6 | Issue – 2 | Jan-Feb 2022 Page 675
[11] J. Pejaś et al. (eds.), Advances in Soft and Hard
Computing. Springer, 2019.
[12] G. C. Buttazzo, Hard Real-Time Computing
Systems: Predictable Scheduling Algorithms
and Applications. Springer Science & Business
Media, 2011.
[13] S. J. Ovaska (ed.), Computationally Intelligent
Hybrid Systems; The Fusion of Soft Computing
and Hard Computing. John Wiley & Sons,
2005.
Figure 1 Comparing hard computing with soft computing [1].
Table 1 The differences between soft computing and hard computing [7].
Figure 2 Hard computing and soft computing [5].
International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470
@ IJTSRD | Unique Paper ID – IJTSRD49287 | Volume – 6 | Issue – 2 | Jan-Feb 2022 Page 676
Figure 3 Fusion of hard computing and soft computing methodologies [9].

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An Overview of Hard Computing

  • 1. International Journal of Trend in Scientific Research and Development (IJTSRD) Volume 6 Issue 2, January-February 2022 Available Online: www.ijtsrd.com e-ISSN: 2456 – 6470 @ IJTSRD | Unique Paper ID – IJTSRD49287 | Volume – 6 | Issue – 2 | Jan-Feb 2022 Page 672 An Overview of Hard Computing Matthew N. O. Sadiku1 , Uwakwe C. Chukwu2 , Abayomi Ajayi-Majebi3 , Sarhan M. Musa1 1 Roy G. Perry College of Engineering, Prairie View A&M University, Prairie View, TX, USA 2 Department of Engineering Technology, South Carolina State University, Orangeburg, SC, USA 3 Department of Manufacturing Engineering, Central State University, Wilberforce, OH, USA ABSTRACT Computing refers to the process of accomplishing a particular task with the help of a computer or a computing device. Hard computing is the traditional computing algorithm, which processes functions and data with a verifiable output. It requires an analytical, precisely stated model. Hard computing is deterministic and precise. It may also be regarded as a heterogeneous collection of traditional computing methods. This paper presents hard computing, the differences between hard computing and soft computing, and their fusion. KEYWORDS: hard computing, soft computing, fusion, hybrid mode How to cite this paper: Matthew N. O. Sadiku | Uwakwe C. Chukwu | Abayomi Ajayi-Majebi | Sarhan M. Musa "An Overview of Hard Computing" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-6 | Issue-2, February 2022, pp.672-676, URL: www.ijtsrd.com/papers/ijtsrd49287.pdf Copyright © 2022 by author (s) and International Journal of Trend in Scientific Research and Development Journal. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) (http://creativecommons.org/licenses/by/4.0) INTRODUCTION We are in the era of computing. Computing is experiencing its most exciting moments in history, permeating nearly all areas of human activities. Computing is any activity that involves using computers. It is any goal-oriented activity requiring the use of computers. It includes designing and building hardware and software systems for a wide range of purposes. It has resulted in deep changes in infrastructures and development practices of computing. It is a critically important, integral component of modern life. In this era of computing, the type of computing one uses can make a big difference. Problem-solving technologies can be of two types: hard computing and soft computing [1]. Figure 1 compares hard computing and soft computing [2]. Traditional or hard computing techniques are based on principles of precision, uncertainty and rigor. The problems based on analytical model can be easily solved using such techniques. The analytical models are precise because they require perfect knowledge. The terms “hard computing” and “soft computing” were coined by Lofti A. Zadeh in 1991. Since then, the area has experienced rapid development. Soft Computing became a discipline within computer science in the early 1990s. The terms “machine intelligence” and “computational intelligence” have been used to have close meaning as soft computing [3]. Soft computing approaches include neural networks, probabilistic models, evolutionary algorithms, artificial neural networks, fuzzy logic swarm intelligence, etc. HARD COMPUTING One may regard the whole history of computer science as a record of continuous attempts to discover, study, and implement computing ideas. Computing technology greatly affects nearly every aspect of our modern life including education, entertainment, transportation, communication, economy, medicine, engineering, and science. The history of computing is one of punctuated equilibrium, bringing new and unexpected changes. IJTSRD49287
  • 2. International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD49287 | Volume – 6 | Issue – 2 | Jan-Feb 2022 Page 673 Mainframes gave birth to minicomputers, which gave birth to workstations, which gave birth to personal computers, which gave birth to smartphones. Hard computing (HC) is a traditional computing approach. It emphasizes precision, certainty, and rigor, while soft computing requires that computation, reasoning, and decision making exploit the tolerance for imprecision and uncertainty wherever possible. It is a conventional computing approach which requires precisely stated analytical model and takes very large computation time. Hard computing or traditional computing is fast, efficient, and reliable with deterministic outcomes. It is the sequential kind of computing that provides precise and certain solutions. Hard computing methods are typically easier to apply. Also the stability of resulting solutions is highly predictable and the computational burden of practical algorithms is typically low. HC often takes a lot of computation time. It strictly follows known steps to solve a task as opposed to soft computing which is heuristic Today, we have microwave ovens, washing machines, cameras, and many other products that manifest an impressive capability to reason, make intelligent decisions, adapt to changes in the operating conditions, and learn from experience [4]. HARD COMPUTING VERSUS SOFT COMPUTING The traditional hard computing is an ancient approach which came before soft computing. The principles of hard computing are precision, certainty and rigor. The input data should be exact and the output will be precise and verifiable. Hard computing is used in solving the deterministic problems, prototyping, and modeling. Applications of hard computing include mobile robot coordination and forecasting combinational problems. Soft computing (SC) refers to a collection of computational techniques in computer science, artificial intelligence, and machine learning. It differs from the conventional hard computing as it can handle uncertainty, imprecision easily. While conventional hard computing is based on crisp values and binary numbers, SC uses soft values and fuzzy sets. Soft computing techniques solve the real-life, non-linear problems which involve uncertain, imprecise and approximate solutions of a problem. Both hard computing and soft computing are illustrated in Figure 2 [5]. The major differences between hard computing and soft computing are summarized as follows [6]: Hard Computing: It requires a precise state analytic model. It relies on binary logic and predefined instructions. Its features include precision and categoricity. It has a deterministic nature. It works on exact data. It is used to perform sequential computations. It produces precise, accurate results. The programs have to be written. It is settled in nature. It cannot handle imprecision and partial truth It does not suitable for real-world problems. It consumes a large amount of computation time and cost. Soft Computing: It can be associated with being liberal with inexactness, uncertainty, partial truth, and approximation. It is based on the model of the human mind or human intelligence. It depends on formal logic and probabilistic reasoning. It consists of approximation and dispositionality. It has a stochastic nature. It generally works on ambiguous and noisy data. It can be used to perform parallel computations. It results in approximate results. It can come out with its own programs. It incorporates randomness in its computations. It uses multivalued logic. The differences between soft computing and hard computing are summarized in Table 1 [7]. The fusion of the two is considered next. FUSION OF SOFT COMPUTING AND HARD COMPUTING In general, it is irrelevant to ask whether one should prefer SC over HC or vice-versa. As the soft computing community is not looking for perfect solutions but competitive ones instead, there exists an implicit commitment to benefit from the fusion of various methodologies. A fusion of soft computing and hard computing appears to be a natural and practical choice. There exists a large amount of applications where SC is used together with HC; these kind of approaches aim at technically and economically competitive systems, products, and services. Proper fusion of soft computing technology with conventional hard computing technology is key to success [8]. In the fusion of SC and HC, the roles between different methodologies should be assigned based on their individual characteristics. SC aims to exploit tolerance for imprecision, uncertainty, and partial truth to achieve robustness, tractability, and low total cost. HC techniques are typically easier to
  • 3. International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD49287 | Volume – 6 | Issue – 2 | Jan-Feb 2022 Page 674 analyze, their stability is highly predictable, and the computational burden of algorithms is either low or moderate. A typical example of a fusion of hard computing and soft computing is shown in Figure 3 [9]. There are two obvious alternatives to form hybrid cascades of soft computing and hard computing algorithms, SC-HC or HCSC, depending on the sequential order of those functional blocks. In SC and HC type systems, the soft computing and hard computing constituents both have their independent roles, and there is a loose union, with no explicit connection between them. Although the hard computing and soft computing research communities are somewhat separated, many SC-oriented researchers and engineers are openly favoring the various fusion opportunities. The unfortunate separation is clearly hindering the industrial acceptance of SC [10]. A trend in the fusion of soft computing and hard computing is the simultaneous partnership of HC and multiple SC methodologies. The conventional HC techniques and the emerging SC should be regarded as complementing methodologies. Fusion of soft and hard computing techniques are also useful in applications such as robotics and a nonlinear tracking system. The fusion of individual soft computing methodologies has been advantageous in numerous applications such as providing intelligent behavior. The integration can improve the control performance of nonlinear systems. The integration could be closely or loosely. CONCLUSION Hard computing is the conventional methodology, which relies on the principles of accuracy, certainty, and inflexibility. Conversely, soft computing is an emerging modern approach premised on the idea of the approximation, uncertainty, and flexibility. Hard computing is based on a crisp system and binary logic, while soft computing is based on fuzzy logic and probabilistic reasoning. Hard computing performs sequential computations, while soft computing performs parallel computations on the data. Soft computing approach is probabilistic in nature whereas hard computing is deterministic. Soft computing and hard computing are being used together in various industries. The traditional HC techniques and the emerging SC should be seen as complementary methodologies. More information about hard computing can be found in the books in [11-13] and the following related journals: Soft Computing Applied Soft Computing REFERENCES [1] D Morgan, “Hard computing v/s soft computing,” https://www.techyv.com/article/hard- computing-vs-soft-computing/ [2] B. Xavier, and P. B. Dahikar, “A comprehensive study on the significance of soft computing in healthcare systems,” International Journal of Engineering Research & Technology, vol. 4, no. v2, February 2015, pp. 278-281. [3] M. N. O. Sadiku, Y. Wang, S. Cui, S. M. Musa, “Soft computing: An introduction,” International Journal of Advanced Research in Computer Science and Software Engineering, vol. 8, no. 6, June 2018, pp. 63-65. [4] L. A. Zadeh, “Fuzzy logic, neural networks, and soft computing,” Communications of the ACM, vol. 37, no. 3, March 1994, pp. 77-84. [5] “Difference between soft computing and hard computing,” https://techdifferences.com/difference-between- soft-computing-and-hard-computing.html [6] A. Diwan, “Difference between soft computing and hard computing,” April 2021, https://www.tutorialspoint.com/difference- between-soft-computing-and-hard-computing [7] “Soft computing vs. hard computing: Difference explained,” https://wisdomplexus.com/blogs/soft- computing-vs-hard- computing/#:~:text=Hard%20computing%20rel ies%20on%20binary,logic%2C%20and%20use s%20multivalued%20logic. [8] A. Kamiya et al., “Fusion of soft computing and hard computing for large-scale plants: A general model,” Applied Soft Computing, vol. 5, 2005, pp. 265–279. [9] S. J. Ovaska et al., “Fusion of soft computing and hard computing techniques: A review of applications,” Proceedings of the IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics, October 1999. [10] S. J. Ovaska, A. Kamiya, and Y. Q. Chen, “Fusion of soft computing and hard computing: Computational structures and characteristic features,” IEEE Transactions on Systems, Man, and Cybernetics—Part C: Applications and Reviews, vol. 36, no. 3, May 2006, pp. 439-448.
  • 4. International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD49287 | Volume – 6 | Issue – 2 | Jan-Feb 2022 Page 675 [11] J. Pejaś et al. (eds.), Advances in Soft and Hard Computing. Springer, 2019. [12] G. C. Buttazzo, Hard Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications. Springer Science & Business Media, 2011. [13] S. J. Ovaska (ed.), Computationally Intelligent Hybrid Systems; The Fusion of Soft Computing and Hard Computing. John Wiley & Sons, 2005. Figure 1 Comparing hard computing with soft computing [1]. Table 1 The differences between soft computing and hard computing [7]. Figure 2 Hard computing and soft computing [5].
  • 5. International Journal of Trend in Scientific Research and Development @ www.ijtsrd.com eISSN: 2456-6470 @ IJTSRD | Unique Paper ID – IJTSRD49287 | Volume – 6 | Issue – 2 | Jan-Feb 2022 Page 676 Figure 3 Fusion of hard computing and soft computing methodologies [9].