What is bipolar fuzzy graph?
A bipolar fuzzy graph structure is a generalization of a bipolar fuzzy graph. In this paper, we present several different types of operations, including composition, Cartesian product, strong product, cross product, and lexicographic product on bipolar fuzzy graph structures.
What is fuzzy graph with example?
Definition 2.1. 1 A fuzzy graph G = (V, σ, µ) is a triple consisting of a nonempty set V together with a pair of functions σ : V → [0, 1] and µ : E → [0, 1] such that for all x, y ∈ V, µ(xy) ≤ σ(x) ∧ σ(y). The fuzzy set σ is called the fuzzy vertex set of G and µ the fuzzy edge set of G.
What is intuitionistic fuzzy graph?
The structure of an Intuitionistic Fuzzy Graph (IFG) depends mainly on its arcs, as in crisp graphs. In an IFG, the arcs are classified into α-strong, β-strong and δ-weak, based on its strength. These arcs are used to study the structure of complete IFG and constant IFG. Their properties have also been studied.
What is fuzzy graph structures?
A fuzzy graph structure is an extension of a fuzzy graph. In this research paper, we present certain notions, including semi strong min-product of fuzzy graph structures, regular fuzzy graph structures, strong and complete fuzzy graph structures.
What is the meaning of fuzzy in mathematics?
Fuzzy mathematics is the branch of mathematics including fuzzy set theory and fuzzy logic that deals with partial inclusion of elements in a set on a spectrum, as opposed to simple binary “yes” or “no” (0 or 1) inclusion.
Who introduced fuzzy graph?
In 1973, Kaufmann defined fuzzy graphs for the first time. Then Azriel Rosenfeld developed the theory of fuzzy graphs in 1975. Here we have presented the contributions of several authors towards the field of this fast growing fuzzy graph theory. 1991 Mathematics Subject Classification.
Why is fuzzy mathematics useful?
The benefit of fuzzy logic is that a new analysis, or a change in the rules or the criteria is not required, which saves time and effort. In fuzzy systems, values are indicated by a number (called a truth value) in the range from 0 to 1, where 0.0 represents absolute falseness and 1.0 represents absolute truth.
What is Mathematics fuzzy logic?
Fuzzy logic is an extension or a superset of the Boolean logic – aimed at maintaining the concept of the “partial truth,” i.e. expression values ranging from “completely truthful” to “completely untruthful” (from 0 to 1).
What are the applications of fuzzy sets?
Applications of Fuzzy Sets and their Extensions in Engineering
- IoT/cloud services ranking models based on FSTEs.
- Additive manufacturing process selection based on FSTEs.
- Medical decision making based on FSTEs.
- Controller network based on FSTEs.
- Transport systems based on FSTEs.
- Failure mode and effect analysis based on FSTEs.
Who invented fuzzy mathematics?
Lotfi A. Zadeh
| Lotfi A. Zadeh | |
|---|---|
| Born | Lotfi Aliaskerzadeh4 February 1921 Baku, Azerbaijan SSR |
| Died | 6 September 2017 (aged 96) Berkeley, California, US |
| Alma mater | University of Tehran Massachusetts Institute of Technology Columbia University |
| Known for | Founder of fuzzy mathematics, fuzzy set theory, and fuzzy logic, Z numbers, Z-transform |
What are some application areas of fuzzy logic?
Fuzzy Logic – Applications
- Altitude control of spacecraft.
- Satellite altitude control.
- Flow and mixture regulation in aircraft deicing vehicles.
What is the main concept or purpose of fuzzy analysis?
A fuzzy concept is a kind of concept of which the boundaries of application can vary considerably according to context or conditions, instead of being fixed once and for all. This means the concept is vague in some way, lacking a fixed, precise meaning, without however being unclear or meaningless altogether.
What is fuzzy math used for?
Fuzzy math is a catch phrase used often by American politicians to describe numbers, particularly in regard to government spending, that they claim do not add up correctly. It is frequently used by politicians who are dismissing another politician’s numbers as doubtful or otherwise inaccurate.
Who is the father of fuzzy logic?
Bipolar fuzzy graphs By a bipolar fuzzy graph of a graph we mean a pair , where is a bipolar fuzzy set on V and is a bipolar fuzzy relation on E such that for all . Throughout this paper, is a crisp graph, and G is a bipolar fuzzy graph.
How is fuzzy graph theory used in Computer Science?
Fuzzy graph theory is highly utilized in computer science applications. Especially in research areas of computer science including database theory, data mining, neural networks, expert systems, cluster analysis, control theory, and image capturing.
What is bipolar fuzzy set theory?
A bipolar fuzzy set is an extension of Zadeh’s fuzzy set theory whose membership degree range is [−1, 1].