# Overview of Cognition Modeling

*Cognitive modeling* is a discipline of computer science that involves creating computational representations of human cognition to simulate human problem solving and mental task processes (Badler, Phillips, & Zeltzer, 1993; Funge, Tu, & Terzopoulos, 1999). The products of cognitive modeling are cognitive models, which can then be used in a variety of ways, including decision-aids to support decision-making tasks (Dhukaram & Baber, 2016; Todd & Benbasat, 1994; Vitoriano, Montero de Juan, & Ruan, 2013).

There is a broad range of cognitive-modeling approaches (see Busemeyer & Diederich, 2010) and a complete overview is outside the scope of this chapter. Instead, this chapter will briefly discuss similar characteristics shared by decisionmaking models. (It is important to note that this overview is not a prescription, but rather a description of certain core characteristics of decision-making models). Each model represents human decision making by dividing the decision-making process into the following five primary subprocesses defined below:

- 1.
*Recognition*involves receiving new information from the input space that can come in various forms, including structured reports, events, or unstructured information. - 2.
*Situation assessment*involves an understanding of an identification/ diagnosis of the current situation and how it fits within the context. - 3.
*Situational analysis*is an analysis routine that involves a reasoning mechanism that compares the current situation to what is already known. It also contains a formulation of a set of goals that are needed to address the current situation. - 4.
*Planning/evaluation*is a cognitive process that transforms goals into a plan by decomposing the goals into tasks. - 5.
*Decision/act*that performs a specific activity that impacts the output space.**Fuzzy Cognitive Maps**

*FCM* are a kind of cognitive model that uses fuzzy casual graphs to model the relationship between inputs and outputs of a given system. Introduced by Bart Kosko in 1986, FCMs combine fuzzy logic (introduced by Lotfi A. Zadeh in 1965) and cognitive mapping (introduced by Robert Axelrod in 1976). Fuzzy logic is based on fuzzy set theory that extends classical (or Boolean) logic, where values may only be 0 (false) or 1 (true), to represent the notion of partial values, where values may be any real number between -1 and 1 (defined as partial truths).^{[1]}

Cognitive mapping is based on graph theory and was designed to represent social scientific knowledge, where a cognitive map represents a mental landscape of a system (Jacobs & Schenk, 2003; Kitchin, 1994; O’Keefe & Nadel, 1978). In practice, cognitive maps are graphical tools that allow people to organize and structure knowledge (Goldstein, 2010; Gray, Gray, Cox, & Henly-Shepard, 2013; Knight, 2002; Kosko, 1986; Manns & Eichernbaum, 2009; to name a few). Cognitive maps represent concepts, such as ideas and information, as geometric shapes, typically boxes or circles that connect to other concepts with labeled arrows. The labeled arrows denote the relationship between concepts and can be articulated in linking phrases, such as *causes*, *requires*, or *contributes to*.

A FCM is a signed fuzzy-directed graph that consists of nodes that represent elements (e.g., concepts and events.) of a system. Each node is connected to other nodes by a directed line (i.e., line with an arrow) that indicates the relationship of the nodes. The direction of the arrow denotes which node influences or impacts other nodes, where the concept and where the arrow is flowing from, impacts or influences the node where the arrow is flowing toward. Each directed line is labeled with a fuzzy value (weight value) to indicate the strength of the causal conditions between nodes.

Computationally, a node has a value of 0 when the node is inactive (or the state is *false* if the node is an input node) and has a value of 1 when the node is active (or the state is *true* if the node is an input node). A threshold (or squashing) function is used to activate all noninput nodes. In practice, many different squashing functions can be used and the FCMs presented in this chapter used a binary function that was suggested by Kosko (1986), Dickerson & Kosko (1993), and Taber (1991). With the binary function, all noninput nodes become inactive and can only become active when the sum of all connected nodes multiplied by their corresponding weight value is greater than or equal to 1. Formally, the equation is represented in the Equation 10.1. Formula to compute activation value for a single FCM concept is given in Equation 10.1 as

where:

*c* is a noninput concept

*a _{k}* represents the activation value for node

*k*(that is connected to c)

*w _{k}* represents the weight value between

*c*and

*k*

Consider the FCM in Figure 10.1 below that models how a student can receive an A in a class. For this FCM, there are five input concepts: *do homework, attend class, meet with instructor, read textbook,* and *study for tests.* These input nodes are factors

**FIGURE 10.1 Sample FCM.**

to the output concept, *receive A in class.* Each input concept has a weight that defines the strength of influences on the output concept. For example, concepts *do homework, attend class,* and *study for tests* each influence the output by 0.30.

For *receive A in class* to be true, the sum of all input nodes multiplied by their corresponding weight must be greater than or equal to 1. For this to occur, A, B, D, and E must be active. In other words, for *receive A in class* to be true, *do homework*, *attend class*, *read textbook*, and *study for tests* must all be true. No one concept has a strong enough value to influence the output without the help of others and the concept, *meet with instructor* does not have a weight value to influence the output at all.^{[2]}

FCMs represent a soft AI approach to modeling systems. Hard AI approaches, such as neural networks, Bayesian networks, and so on, use symbolic processing to represent knowledge (Jones, 2006; Kosko, 1993). Kosko (1986) has argued that symbolic processing is limited during the *recognition* process when uncertainty exists (due to ambiguous, unknown, or uncertain information). The reason for this is that symbolic processing requires knowledge to be exact and has a hard time representing knowledge with inexact states. Conversely, the fuzzy-graphical structures of FCMs offer the capability to represent uncertainty by representing knowledge with hazy degrees of states.

As a cognitive model, FCMs model the cause-and-effect relationships that define a complex system. Unique to FCMs is their ability to represent attributes of the decision-making process as qualitative states, rather than numerical values, which is more aligned with how humans make decisions. For example, a person may turn on an air conditioner when the temperature is hot and not know the exact numerical temperature value and for team decision making, humans typically rely on qualitative states rather than numerical values. Furthermore, by using qualitative states, FCMs can model emergent and nonlinear qualities of a complex system. Thus, this transformational grammar that translates numerical values into qualitative states is a significant characteristic used by FCMs and has been highlighted by several researchers (Perusich & McNeese, 1998).

It has been a popular misconception to confuse fuzzy logic with probability. The distinction between fuzzy logic and probability involves how each refers to uncertainty. Fuzzy logic is specifically designed to deal with imprecision of facts (fuzzy logic statements), whereas probability deals with chances of an event occurring (but still considering the result to be precise). In other words, fuzzy logical statements represent membership in vaguely defined sets, whereas probabilities represent the likelihood of some event or condition. To illustrate the difference, consider the following scenario: Bob is in a house with two adjacent rooms: the kitchen and the dining room. In probabilistic terms, Bob is either in the kitchen or not in the kitchen (for this specific scenario, there is a 50% chance that he is in the kitchen). However, fuzzy logic statements will not refer to his chances of being in the kitchen; instead, it will convey the degree of Bob being in the kitchen. This becomes especially important when Bob is in the doorway that is between the two rooms where he would be considered both *partially in the dining room* and *partially in the kitchen*.