There are many methodologies to choose from when it comes to modelling and simulation for decision support, of which are covered under the fields of Artificial Intelligence (AI), Computational Intelligence (CI) and Soft Computing (SC). Soft computing is an association of computing methodologies that includes as its principal members Fuzzy Logic, Neuro-Computing, Evolutionary Computing and Probabilistic Neuro-Computing, such as; Bayesian Networks, Neural Networks, Fuzzy Logic, Fuzzy Set Theory, Evolutionary Algorithms, et cetera (146-154), as described in Table 4.
A well-researched field, they are a good match for real-world applications that are characterised by imprecise, uncertain data, and incomplete domain knowledge.
Table 4 - Computational Intelligence Methodologies
Method Name Category Approach Mechanism
Bayesian Network Probabilistic Computing
Approximate Reasoning Conditioning
Dempster-Shafer Theory Probabilistic Computing
Approximate Conditioning
Multi-Valued Algebra Multi-Valued Logic and Fuzzy Computing
Approximate Rule of Inference
51 Fuzzy Logic Multi-Valued
Logic and Fuzzy Computing
Approximate Rule of Inference
Feedforward Neural Network, Recurrent Neural Network, etc.
Neural Computing Search / Optimization Local Search
Genetic Algorithm, Particle Swarm, etc.
Evolutionary Computing
Search / Optimization Global Search
Petri Nets, Bayesian Networks and Neural Networks are all well suited to models constructed with little knowledge of existing processes, or where classification and learning are required to describe the data. Alternatively, Fuzzy Logic is better suited to First-order logic situations, which allow the truth of a statement to be represented as a value between 0 and 1.
For the purposes of this study, two general approaches could be taken depending on the overall goal. If the goal is to develop a PBC process, then arguably learning, classification and probabilistic methods would be effective and therefore Petri Nets, Bayesian Networks and Neural Networks would be suitable methodologies to employ. If the goal is to simulate an existing known process, such as the PBC Framework, where there may be more to the logic than True or False, then Fuzzy Logic is the more suitable.
The proposed concept in this study does not require a learning process, and considering that the design of the PBC Framework relies on a variation in the range of specific parameters with known limitations in the scoring methodology, Fuzzy Logic appears to be an appropriate mechanism through which to generate a simulation of a performance-based contract performance.
52 2.12.1
Fuzzy Logic
Introduced with the 1965 theory by Lofti A. Zadeh, Fuzzy Logic has been applied to many fields, from control theory to artificial intelligence. One point of view, Fuzzy Logic is simply a logical system, however in much broader sense, Fuzzy Logic is much more than a logical system, as Zadeh (2008) suggests, Fuzzy Logic has four principal facets (155):
1. The fuzzy set theoretic facet, 2. The logical facet,
3. The epistemic facet, 4. The relational facet.
Fuzzy set theoretic facet; is focused on fuzzy sets, that is, on classes whose boundaries are not sharp, e.g., the class of tall mountains. Logical facet is Fuzzy Logic in its narrow sense. It may be viewed as a generalisation of multivalued logic, similar to classical logic, the truth values are allowed to be fuzzy sets. The epistemic facet is concerned with knowledge representation, semantics of natural languages and information analysis. An important branch of this facet is the use of possibility theory. The relational facet, is focused on fuzzy relations and more generally, on fuzzy dependencies. In the relational facet, a granulated function is described as a collection of fuzzy if-then rules of the form: if X is A then Y is B, where A and B are fuzzy sets carrying linguistic labels like small, medium, and large. (155)
Fuzzy Logic is a form logic that takes on varying values, and it is designed to work with approximate reasoning instead of fixed and exact. In comparison to the more traditional use of binary sets, where variables may take either true or false values, the variables used in fuzzy logic may have a truth value that ranges in degree between 0 and 1. Fuzzy logic has been extended to handle the concept of partial truth, where the truth-value may range between completely true and completely false. Additionally, when linguistic variables are used, these degrees may be managed by specific functions.
Fuzzy Logic, like probability theory, is a different way of expressing uncertainty. Although, not a direct replacement from probability theory, Zadeh (1988) argues that Fuzzy Logic is
53 different in character, being that a fuzzified probability to fuzzy probability can be generalized and to what is called possibility theory. (156) Additionally, Zadeh (1973) states that fuzzy logic is one of many different proposed extensions to probabilistic logics, and is intended to deal with issues of uncertainty in classical logic, the inapplicability of probability theory in many domains, and the paradoxes of Dempster-Shafter theory. (157)
Mukaidono (2002) concluded, “It is a big task to exactly define, formalize and model complicated systems”, and Jarrett (2011) states that it is at this task in which Fuzzy Logic excels. (158, 159) Additionally Jarrett (2011) claims that Fuzzy Logic has often proven to overtake classical mathematical and statistical modelling techniques for many applications involving the modelling of real world data. Furthermore, highlighting wide acceptance within the field of systems control, as one example (159), the applications of which range from the speed control of a small electric motor, to the control of an entire subway system.
Zadeh (2008) suggests that Fuzzy Logic can add to existing theories, through the capability to operate on information described in natural language or on perception-based information.
Additionally, that the issue of natural language is likely to grow in visibility and importance, in fields such as economics, law, medicine, search, question-answering and, probability theory and decision analysis. (155)
Already a well-researched field, some of the benefits to Fuzzy Logic is that it can be built on top of the experience of experts, which is in direct contrast to Neural Networks. Building a Neural Network requires data training, which may, depending on the quality of the data, create impenetrable models. Alternatively, Fuzzy Logic lets you rely on the experience of people who already understand your system. (157, 160-163)
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