Since the conception of fuzzy logic, there have been many doubts about its usability. People have been raising questions like:
- Is there a need for fuzzy logic?
- Doesn’t fuzzy logic contradict classical logic?
- Isn’t fuzzy logic inconsistent?
In this section, we’ll focus on the question of usability and the need for fuzzy logic.
Defining Fuzzy Logic
Fuzzy logic is a logic of imprecision and approximate reasoning. Put another way, fuzzy logic helps you provide reasoning for vague concepts.
Fuzzy logic is not a new idea; it is been with us for a very long time. In spite of this, the utility of fuzzy logic has always been questioned. Its usability is mostly restricted to linguistic variables and the associated machinery of fuzzy if-then rules. But, in fact, there are many other areas where fuzzy logic can potentially help us.
Below are some of the use cases where fuzzy logic is currently being used and could be of great importance.
Fuzzy Logic Use Cases
Linguistic variables and fuzzy if-then rules – A linguistic variable is a variable whose value is a word in a natural language. For example, “temperature” is a linguistic variable; it can take values like “very hot”, “hot”, “moderate”, etc. Fuzzy if-then rules are simple conditions that associate values to a linguistic variable. The combination of a linguistic variable and fuzzy if-then logic is continuing to play an important role in control system and consumer product design. This is one of the areas where fuzzy logic is widely used and accepted.
FL generalization – Fuzzy logic has significantly higher generality than bivalent logic. Bivalent logic means that the system has exactly two values, e.g. true and false. The problem with bivalent logic is that human cognition has no clear separation between the classes/output, e.g. there is no clear boundary defining hot and moderate weather – they overlap. This problem can be resolved by using fuzzy logic to generalize bivalent logic. The generalization of bivalent logic helps us to construct a better model of reality.
Natural Language (NL) Computation, Computing with Words (CW)- There is a plethora of information available to us in the form of natural language, but the problem with natural language is that it is imprecise. Since bivalent logic is inflexible and unable to handle imprecision, fuzzy logic provides a much more reliable way to process this information.
Possibility theory – Possibility theory, a subdivision of fuzzy logic, is an uncertainty theory devoted to the modeling of incomplete information. Possibility theory provides the basic framework for preference modeling. In the past, this theory has not been used very significantly. However – based on its connection to symbolic artificial intelligence, decision theory, and imprecise statistics – it will likely be of great importance in the near future.
Fuzzy logic as modelling language – Machine Learning algorithms are widely used for information extraction and inference; when used in combination with fuzzy logic, they provide much more flexible results. Clustering and classification are the two major use cases where fuzzy-based machine learning algorithms are already providing good results.
Fuzzy clustering algorithms – In fuzzy-based clustering (also known as soft clustering) each data point or object can belong to more than one cluster (instead of belonging to one cluster, as in the classical clustering algorithm). There are already many fuzzy clustering algorithms available, i.e. fuzzy c-means clustering, possibilistic c-means clustering, etc
Fuzzy classification – In fuzzy classification, a supervised classification algorithm is used in conjunction with fuzzy logic to produce much more reliable output. Neuro-fuzzy models are an example of this approach, which has been applied in fields such as disease prediction, risk analysis, etc.
As mentioned above, there are several fuzzy logic implementations that cater to different use cases in solving analog and digital problems. This is owing to fuzzy logic’s ability to approximate non-linear ambiguous behavior into numbers that make logical sense. More complex adaptations of fuzzy logic are powerful enough to see their usage in modern applications.
In other words, there is a need for fuzzy logic.
Technical articles are published from the Absolutdata Labs group, and hail from The Absolutdata Data Science Center of Excellence. These articles also appear in BrainWave, Absolutdata’s quarterly data science digest.