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.