متن لاتین و ترجمه فارسی Hybrid Soft Computing Systems سیستمهای هیبریدی
21 صفحه فایل ورد (متن انگلیسی)
30 صفحه فایل ورد (ترجمه فارسی متن)
Hybrid Soft Computing Systems: Where Are We Going?
Piero P. Bonissone1
Abstract.
Soft computing is an association of
computing methodologies that includes fuzzy logic, neuro-computing,
evolutionary computing,and probabilistic computing. After a brief
overview of Soft Computing components, we will analyze some of its most
synergistic combinations. We will emphasize the development of smart
algorithm-controllers, such as the use of fuzzy logic to control the
parameters of evolutionary computing and, conversely, the application of
evolutionary algorithms to tune fuzzy controllers. We will focus on
three real-world applications of soft computing that leverage the
synergism created by hybrid systems.
1 SOFT COMPUTING OVERVIEW
Soft computing (SC) is a term originally
coined by Zadeh to denote systems that “… exploit the tolerance for
imprecision, uncertainty, and partial truth to achieve tractability,
robustness, low solution cost, and better rapport with reality" [1].
Traditionally SC has been comprised by four technical disciplines. The
first two, probabilistic reasoning (PR) and fuzzy logic (FL) reasoning
systems, are based on knowledge-driven reasoning. The other two technical disciplines, neuro computing (NC) and evolutionary computing (EC), are data-driven search
and optimization approaches [2]. Although we have not reached a
consensus regarding the scope of SC or the nature of this association
[3], the emergence of this new discipline is undeniable [4]. This paper
is the reduced version of a much more extensive coverage of this topic,
which can be found in [5].
2 SC COMPONENTS AND TAXONOMY
2.1 Fuzzy Computing
The treatment of imprecision and vagueness
can be traced back to the work of Post, Kleene, and Lukasiewicz,
multiple-valued logicians who in the early 1930's proposed the use of
three-valued logic systems (later followed by infinite-valued logic) to
represent undetermined, unknown, or other possible intermediate
truth-values between the classical Boolean true and false values [6]. In
1937, the philosopher Max Black suggested the use of a consistency
profile to represent vague concepts [7]. While vagueness relates to
ambiguity, fuzziness addresses the lack of sharp set-boundaries. It was
not until 1965, when Zadeh proposed a complete theory of fuzzy sets (and
its isomorphic fuzzy logic), that we were able to represent and
manipulate ill-defined concepts [8].
1GE Corporate Research and Development, One Research Circle, Niskayuna, NY 12309, USA. email: bonissone@crd.ge.com
In a narrow sense, fuzzy logic could be considered a fuzzification of Lukasiewicz
Aleph-1 multiple-valued logic [9]. In the
broader sense, however, this narrow interpretation represents only one
of FL’s four facets [10]. More specifically, FL has a logical facet,
derived from its multiple-valued logic genealogy; a set-theoretic facet,
stemming from the representation of sets with ill-defined boundaries; a
relational facet, focused on the representation and use of fuzzy
relations; and an epistemic facet, covering the use of FL to fuzzy
knowledge based systems and data bases. A comprehensive review of fuzzy
logic and fuzzy computing can be found in [11]. Fuzzy logic gives us a
language, with syntax and local semantics, in which we can translate
qualitative knowledge about the problem to be solved. In particular, FL
allows us to use linguistic variables to model dynamic systems. These
variables take fuzzy values that are characterized by a label (a
sentence generated from the syntax) and a meaning (a membership function
determined by a local semantic procedure). The meaning of a linguistic
variable may be interpreted as an elastic constraint on its value. These
constraints are propagated by fuzzy inference operations, based on the
generalized modus-ponens. This reasoning mechanism, with its
interpolation properties, gives FL a robustness with respect to
variations in the system's parameters, disturbances, etc., which is one
of FL's main characteristics [12].
2.2 Probabilistic Computing
Rather than retracing the history of
probability, we will focus on the development of probabilistic computing
(PC) and illustrate the way it complements fuzzy computing. As depicted
in Figure 1, we can divide probabilistic computing into two classes:
single-valued and interval-valued systems. Bayesian belief networks
(BBNs), based on the original work of Bayes [13], are a typical example
of single-valued probabilistic reasoning systems. They started with
approximate methods used in first-generation expert systems, such as
MYCIN’s confirmation theory [14] and PROSPECTOR’s modified Bayesian rule
[15], and evolved into formal methods for propagating probability
values over networks [16-17]. In general, probabilistic reasoning
systems have exponential complexity, when we need to compute the joint
probability distributions for all the variables used in a model. Before
the advent of BBNs, it was customary to avoid such computational
problems by making unrealistic, global assumptions of conditional
independence. By using BBNs we can decrease this complexity by encoding
domain knowledge as structural information: the presence or lack of
conditional dependency between two variables is indicated by the
presence or lack of a link connecting the nodes representing such
variables in the network topology. For specialized topologies (trees,
poly-trees, directed acyclic graphs), efficient propagation algorithms
have been proposed by Kim and Pearl [18]. However, the complexity of
multiple–connected BBNs is still exponential in the number of nodes of
the largest sub-graph. When a graph decomposition is not possible, we
resort to approximate methods, such as clustering and bounding
conditioning, and simulation techniques, such as logic samplings and
Markov simulations. Dempster-Shafer (DS) systems are a typical example
of intervalvalued probabilistic reasoning systems. They provide lower
and upper probability bounds instead of a single value as in most BBN
cases. The DS theory was developed independently by Dempster [19] and
Shafer [20]. Dempster proposed a calculus for dealing with
interval-valued probabilities induced by multiple-valued mappings.
Shafer, on the other hand, started from an axiomatic approach and
defined a calculus of belief functions. His purpose was to compute the
credibility (degree of belief) of statements made by different sources,
taking into account the sources’ reliability. Although they started from
different semantics, both calculi were identical. Probabilistic
computing provides a way to evaluate the outcome of systems affected by
randomness (or other types of probabilistic uncertainty). PC’s basic
inferential mechanism - conditioning - allows us to modify previous
estimates of the system's outcome based on new evidence.
2.2.1 Comparing Probabilistic and Fuzzy Computing.
In this brief review of fuzzy and
probabilistic computing, we would like to emphasize that randomness and
fuzziness capture two different types of uncertainty. In randomness, the
uncertainty is derived from the non-deterministic membership of a point
from a sample space (describing the set of possible values for the
random variable), into a well-defined region of that space (describing
the event). A probability value describes the tendency or frequency with
which the random variable takes values inside the region. In fuzziness,
the uncertainty is derived from the deterministic but partial
membership of a point (from a reference space) into an imprecisely
defined region of that space. The region is represented by a fuzzy set.
The characteristic function of the fuzzy set maps every point from such
space into the real-valued interval [0,1], instead of the set {0,1}. A
partial membership value does not represent a frequency. Rather, it
describes the degree to which that particular element of the universe of
discourse satisfies the property that characterizes the fuzzy set. In
1968, Zadeh noted the complementary nature of these two concepts, when
he introduced the probability measure of a fuzzy event [21]. In 1981,
Smets extended the theory of belief functions to fuzzy sets by defining
the belief of a fuzzy event [22]. These are the first two cases of
hybrid systems illustrated in Figure 1.
2.3 Neural Computing
The genealogy of neural networks (NN) could
be traced back to 1943, when McCulloch and Pitts showed that a network
of binary decision units (BDNs) could implement any logical function
[23]. Building upon this concept, Rosenblatt proposed a one-layer
feedforward network, called a perceptron, and demonstrated that it could
be trained to classify patterns [24-26]. Minsky and Papert [27] proved
that single-layer perceptrons could only provide linear partitions of
the decision space. As such they were not capable of separating
nonlinear or non-convex regions. This caused the NN community to focus
its efforts on the development of multilayer NNs that could overcome
these limitations. The training of these networks, however, was still
problematic. Finally, the introduction of backpropagation (BP),
independently developed by Werbos [28], Parker [29], and LeCun [30],
provided a sound theoretical way to train multi-layered, feed-forward
networks with nonlinear activation functions. In 1989, Hornik et al.
proved that a three-layer NN (with one input layer, one hidden layer of
squashing units, and one output layer of linear units) was a universal
functional approximator [31]. Topologically, NNs are divided into
feedforward and recurrent networks. The feedforward networks include
single- and multiplelayer perceptrons, as well as radial basis functions
(RBF) networks [32]. The recurrent networks cover competitive networks,
selforganizing maps (SOMs) [33], Hopfield nets [34], and adaptive
resonance theory (ART) models [35]. While feed-forward NNs are used in
supervised mode, recurrent NNs are typically geared toward unsupervised
learning, associative memory, and self-organization. In the context of
this paper, we will only consider feed-forward NNs. Given the functional
equivalence already proven between RBF and fuzzy systems [36] we will
further limit our discussion to multi-layer feed-forward networks. A
comprehensive current review of neuro-computing can be found in [37].
Feedforward multilayer NNs are computational structures that
can be trained to learn patterns from
examples. They are composed of a network of processing units or neurons.
Each neuron performs a weighted sum of its input, using the resulting
sum as the argument of a non-linear activation function. Originally the
activation functions were sharp thresholds (or Heavyside) functions,
which evolved to piecewise linear saturation functions, to
differentiable saturation functions (or sigmoids), and to Gaussian
functions (for RBFs). By using a training set that samples the relation
between inputs and outputs, and a learning method that trains their
weight vector to minimize a quadratic error function, neural networks
offer the capabilities of a supervised learning algorithm that performs
fine-granule local optimization.
2.4 Evolutionary Computing
Evolutionary computing (EC) algorithms
exhibit an adaptive behavior that allows them to handle non-linear, high
dimensional problems without requiring differentiability or explicit
knowledge of the problem structure. As a result, these algorithms are
very robust to time-varying behavior, even though they may exhibit low
speed of convergence. EC covers many important families of stochastic
algorithms, including evolutionary strategies (ES), proposed by
Rechenberg [38] and Schwefel [39], evolutionary programming (EP),
introduced by Fogel [40-41], and genetic algorithms (GAs), based on the
work of Fraser [42], Bremermann [43], Reed et al. [44], and Holland
[45-47], which contain as a subset genetic programming (GP), introduced
by Koza [48]. The history of EC is too complex to be completely
summarized in a few paragraphs. It could be traced back to Friedberg
[49], who studied the evolution of a learning machine capable of
computing a given input-output function; Fraser [42] and Bremermann
[43], who investigated some concepts of genetic algorithms using a
binary encoding of the genotype; Barricelli [50], who performed some
numerical simulation of evolutionary processes; and Reed et al. [44],
who explored similar concepts in a simplified poker game
simulation. The interested reader is
referred to [51] for a comprehensive overview of evolutionary computing
and to [52] for an encyclopedic treatment of the same subject. A
collection of selected papers illustrating the history of EC can be
found in [53]. As noted by Fogel [51], ES, EP, and GAs share many common
traits: “…Each maintains a population of trial solutions, imposes
random changes to those solutions, and incorporates selection to
determine which solutions to maintain in future generations...” Fogel
also notes that “… GAs emphasize models of genetic operators as observed
in nature, such as crossing-over, inversion, and point mutation, and
apply these to abstracted chromosomes…” while ES and EP “… emphasize
mutational transformations that maintain behavioral linkage between each
parent and its offspring.” Finally, we would like to remark that EC
components have increasingly shared their typical traits: ES have added
recombination operators similar to GAs, while GAs have been extended by
the use of real-number-encoded chromosomes, adaptive mutation rates, and
additive mutation operators.
سیستمهای ترکیبی Soft Computing :
ما به کجا می رویم؟
چکیده:
Soft Computing یک روش محاسباتی است که
شامل منطق فازی،محاسبات عصبی ، محاسبات تکمیلی و محاسبات احتمالی می
باشد.بعد از یک نگاه اجمالی به اجزای Soft Computing ،برخی از مهمترین
ترکیبات آنرا مورد بررسی و تجزیه وتحلیل قرار میدهیم.ما بر روی توسعه کنترل
کننده های الگوریتمی هوشمند،همانند استفاده از منطق فازی برای کنترل
پارامترهای محاسبات تکمیلی تاکید میکنیم و در مورد کاربرد الگوریتمهای
تکمیلی برای تنظیم کنترل کننده های فازی صحبت خواهیم کرد.ما بر روی سه
کاربرد از Soft Computing در جهان واقعی تاکید میکنیم که همگی توسط
سیستمهای ترکیبی ایجاد شده اند.
1- نگاه کلی به Soft Computing
Soft Computing (SC) واژه ای است که در
ابتدا توسط زاده برای مشخص کردن سیستمهایی که " از خطای بی دقتی، مبهم بودن
و کمی درست بودن ،برای کنترل درست،کم هزینه و سازگارتر با جهان واقعی
استفاده میکنند."
بطور معمول SC شامل چهار تکنیک می
باشد:دوتای اول آن ،سیستمهای استدلال آماری(PR) و منطق فازی(FL) ،بر پایه
استدلال بر اساس دانش است . دو تای دیگر،محاسبه عصبی (NC) و محاسبه
تکمیلی(EC) ،بر پایه روشهای تحقیق و بهینه سازی بر اساس داده می باشند. با
توجه به اینکه ما به یک توافق در مورد چارچوب SC یا ماهیت این پیوستگی دست
پیدا نکرده ایم، غیره منتظره بودن این روش جدید انکارناپذیر است. این مقاله
نمونه ساده شده ای از این سرفصلهای بسیار گسترده می باشد که می توانید
آنها را در پی نوشت 5 پیدا کنید.
2- اجزا و رده بندی SC
1-2 محاسبه فازی
اصلاح اشتباه و ابهام را می توان در
کارهای گذشته کلیین و لوکازوئیچ ،منطق دانان چند فازی که در اوایل دهه 1930
استفاده از سیستمهای منطقی سه ارزشی(که بعداً بوسیله منطق با ارزش بینهایت
دنبال شد) را برای نشان دادن نامعینی ، مجهول بودن یا سایر ارزشهای
احتمالی بین ارزشهای واقعی بین ارزشهای درست و غلط جبر بول کلاسیک را
پیشنهاد کردند،دنبال نمود.در سال 1937 ،اندیشمند ماکس بلک پیشنهاد کرد که
از یک پروفایل همبستگی برای نشان دادن مفاهیم مبهم استفاده شود. در حالیکه
ابهام به نشانه های گنگ و نا مشخص ناشی از لبه های مرزی تیز مربوط میشد.این
مسئله تا سال 1965 ادامه پیدا کرد،زمانی که زاده یک تئوری کامل از مجموعه
های فازی(که متناظر آن منطق فازی میباشد)را ارائه نمود،که بر اساس آن
ما می توانستیم تصویر کلی که بدرستی تعریف نشده است را نشان داده و
آنرا کنترل نماییم.
بعبارت دقیقتر،منطق فازی را می توان به
صورت یک تابع منطقی از منطق چند ارزشی آلف-1 لوکازوئیچ دانست.اگرچه،در
مفهوم وسیعتر،این تعبیر دقیق تنها یکی از چهار جنبه FL را نشان میدهد. بطور
خاص ،FL دارای یک جنبه منطقی ،که از اجداد منطقی چند ارزشی آن مشتق شده
،یک جنبه فرضی که از نمایش مجموعه ای از مرزهایی که بدرستی تعیین نشده است
نشات گرفته ،یک جنبه ارتباطی ،که برروی نمایش واستفاده از روابط منطقی
متمرکز است و یک جنبه اپیستمیک که در برگیرنده استفاده از FL برای دانش
فازی مبتنی بر سیستمها و بانکهای اطلاعاتی می باشد،است.
یک بررسی جامع از منطق فازی و محاسبه فازی
را می توان در پی نوشت 11 مشاهده کرد.منطق فازی به ما یک زبان همراه با
علم نحو و معانی خاص آنرا میدهد ،که توسط آن ما می توانیم اطلاعات کیفی
راجع به مشکلی که قرار است حل شود را ترجمه می کند. بطور خاص ،FL به این
اجازه را می دهد که از متغیرهای زبان شناسی برای شبیه سازی سیستمهای
دینامیکی استفاده کنیم. اینها متغیرهایی با ارزش فازی هستند که بوسیله یک
لیبل (عبارت ایجاد شده توسط علم نحو)و یک معنی(یک تابع عضویت که توسط یک
دستورالعمل نحوی محلی تعیین شده است) مشخص میشوند.معنی یک کتغیر کلامی می
تواند بصورت یک محدودیت قابل انعطاف برای ارزش آن ،تفسیر شود.این محدویتها
بوسیله عملیات استنتاجی فازی و بر اساس modus-ponens عمومی شده ،گسترش می
یابند.این مکانیسم استدلالی ،همراه با خصوصیات درون یابی آن ،FL را با
توجه به تغییر در پارامترهای سیستم ،اختلالات ،و غیره قدرتمند ساخته است که
یکی از ویژگیهای اصلی FL هم همین توانمند بودن آن است.
2-2 محاسبه احتمالی
بجای بررسی مجدد تاریخچه احتمال ،ما بر
روی توسعه احتمالی (pc)تمرکز کرده وراهی که در محاسبه فازی مورد استفاده
قرار می گیرد را نشان می دهیم .همانگونه که در شکل 1 نشان داده شده است ،می
توانیم محاسبه احتمالی را به دو گروه تقسیم کنیم :سیستم های یک ارزشی
وسیستمهای بین ارزشی .
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