Difference between Fuzzy Set and Crisp SetFuzzy set and Crisp set are two different set theories. The crisp set utilizes the bivalued logic. In contrast, the fuzzy set utilizes the infinitevalued logic. Crisp sets have elements with binary membership, whereas fuzzy sets have components with degrees of membership. In this article, you will learn about the difference between Fuzzy and Crisp sets. But before discussing the differences, you must know about the Fuzzy set and Crisp set with their advantages and disadvantages. What is Fuzzy Set?A fuzzy set is a collection of components with varying degrees of membership in the set. The term "fuzzy" relates to ambiguity; that is, the transition between different degrees of membership means that the boundaries of the fuzzy sets are uncertain. As a result, the membership of the universe's items in the set is compared to a function for detecting uncertainty and ambiguity. The fuzzy set theory was originally proposed by computer scientist Lotfi A. Zadeh in the year of 1965. After that, various theoretical development in a related topic occurred. In the past, dual logicbased crisp sets were used in formal reasoning and computers to represent solutions in one of two forms, like "true" or "false" and "yes" or "no". Fuzzy LogicFuzzy logic incorporates approximate human reasoning capabilities to be used in knowledgebased systems. The fuzzy logic theory gives a mathematical way of apprehending ambiguities in the human cognitive process, such as thinking and reasoning, and it may also deal with the issue of lexical imprecision and uncertainty. Advantages and Disadvantages of Fuzzy SetThere are various advantages and disadvantages of the Fuzzy Set. Some main advantages and disadvantages of the Fuzzy Set are as follows: Advantages
Disadvantages
What is Crisp Set?The crisp set is a group of objects (say U) that have the similar countability and finiteness qualities. A crisp set 'A' is a collection of items over the universal set U, where a random element can or cannot be a part of A. It means that there are only two chances: either the element belongs to set A or does not belong to set A. It is capable of performing operations such as union, intersection, complement, and difference. The crisp set displays various features, including idempotency, commutativity, transitivity, distributivity, associativity, identity, and involution. However, fuzzy sets also share the same functionalities. Crisp LogicThe standard method of knowledge representation doesn't offer a suitable means to interpret ambiguous and noncategorical data. Since its operations are based on classical probability theory and firstorder logic, in another sense, it is unable to portray human intelligence. Features of Crisp SetThere are various features of the Crisp Set. Some main features of Crisp Set are as follows:
Key Differences between Fuzzy Set and Crisp SetThere are various key differences between Fuzzy Set and Crisp Set. Some main differences between Fuzzy Set and Crisp Set are as follows:
Headtohead comparison between Fuzzy Set and Crisp SetHere, you will learn the headtohead comparisons between Fuzzy Set and Crisp Set. The main differences between Fuzzy Set and Crisp Set are as follows:
ConclusionThe fuzzy set theory is designed to bring vagueness and imprecision to attempt to replicate the human brain in AI. Its importance in the field of expert systems is growing by the day. On the other hand, the Crisp set theory was particularly useful as the starting notion for modelling digital and expert systems based on binary logic.
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