The concept map boils down to following statements—(1) Surface
roughness (Ra ) of turned surfaces depends on
three factors—cutting velocity (vc ), depth of
cut (ap ), and feed rate (f ), as
demonstrated by experimental results; (2) A new variable\(cv=\frac{f^{a}}{\left(\left(a_{p}\right)^{b}\left(v_{c}\right)^{c}\right)}\)defines the relationship between the said three factors; and (3)
Experimental results shown here yield \(R_{a}=0.163+68.36*cv\) so
that a , b , and c equal 1.8, 0.1, 0.4, respectively.
Statement (3) is a piece of relation-of-ideas-assisted inductive
knowledge because the expression for Ra is
established based on a relation of ideas (cv ), and it is valid
only for the given dataset. The other two statements do not qualify as
relation-of-ideas-assisted inductive knowledge. Statement (2), in
particular, is a piece of relation-of-ideas-based knowledge, which
defines a new variable (cv ) relating existing parameters—f , ap , andvc —found in the provenance. Statement (1), on
the other hand, is a piece of informal-induction-based knowledge evolved
from the dataset described in Figure 4(a ) without the need for
any formal computation. This example also demonstrates that different
categories of knowledge co-exist when a meaningful representation of
knowledge is performed.
In a general sense, when a relatively complex machine-learning approach
is adopted to understand the structure underlying a dataset or
observation, complex-induction-based knowledge evolves. In other words,
knowledge acquired by machine learning can roughly be considered
complex-induction-based knowledge. Therefore, when
computational-intelligence techniques are applied to a set of
data/observations, the extracted knowledge can be categorized as
complex-induction-based knowledge. Examples of such techniques include
probabilistic reasoning, stochastic simulation, artificial neural
network, genetic algorithm, fuzzy or multi-valued logic, rough sets,
simulated annealing, deep learning, DNA computing,
multi-criteria/objective decision-making/optimization, decision-tree
induction (ID3, C5.0), and hidden Markov modeling (Quinlan, 1979;
Hayes-Rotb et al., 1983; Quinlan, 1986; Nagao, 1990; Heckerman et al.,
1995; Studer et al., 1998; Zadeh, 2002; Rathman et al., 2017; Ullah and
Harib, 2008; Ullah et al., 2014; Ullah, 2019; Ghosh et al., 2019). For
example, consider the case described in Figure 5. Figure 5(a )
schematically illustrates two fuzzy numbers—A andB —induced from cutting-torque time-series data recorded under
two sets of cutting conditions referred to as case-1 and case-2.
Numerous methods can be used to induce a fuzzy number from a given set
of time-series numerical data (Masson and Denœux, 2006; Ullah and
Shamsuzzaman, 2013). Such an induction is a complex process requiring
all types and categories of knowledge. Thus, if fuzzy numbers in Figure
5(a ) are considered knowledge provenance, some pieces of
knowledge represented by the concept map in Figure 5(b ) qualify
as complex-induction-based knowledge. The concept map in Figure
5(b ) boils down to following statements—(1) Cutting torque of
end-milling operation in case-1 is denoted as A ; (2) Cutting
torque of end-milling operation in case-2 is denoted by B ; (3)A is a triangular fuzzy number; (4) B is a triangular
fuzzy number; (5) Case-2 is more effective at reducing cutting torque
compared to case-1; and (6) Cutting torques A and B are
stored “here.” The first two statements represent pieces of
complex-induction-based knowledge, since a complex
computational-intelligence-based procedure underlies the induction ofA and B . Statements (3) and (4) qualify as pieces of
definitional knowledge, whereas statement (5) represents
informal-induction-based knowledge that evolves from visual inspection
of relative positions of A and B . The last statement is a
piece of information (not knowledge) that directs a user to the
provenance—i.e., data sources relevant to Figure 5(a ). This
example demonstrates that different types and categories of knowledge
constitute a concept map, and some portion of which need not necessarily
be a piece of knowledge.