Abstract:
In this paper, the notion of a Quasi complete strong fuzzy graph (QCSFG) is introduced. It is proved that, A fuzzy graph G(V,, ) with at least three vertices is a Quasi complete strong fuzzy graph if and only if any two vertices m and n of G with membership grade σ(m) and σ(n) lie on the same triangle with µ((mn) ̅) = minimum of σ(m) and σ(n) or they lie on different triangles having common vertex s with µ((ms) ̅) = min {σ(m), σ(s)} and µ((sn) ̅) = min {σ(s), σ(n)}. It is also observed that, G:(V, σ, µ) is a Quasi complete strong fuzzy graph with edge disjoint union of triangles, then all the triangles have a common vertex w with σ(w) as membership grade and µ((wv_i ) ̅) = min { σ(w), σ(vi) / vi is neighbor of w}.
Key
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Quasi Complete Fuzzy Graphs: In this section we introduced a definition of distance of Quasi complete strong fuzzy graph.
3.1 Definition: A fuzzy graph G(V,, ) is a Quasi complete strong fuzzy graph iff it is simple and for any two vertices ‘m, n’ there is a vertex ‘s’ of G(V,, ) such that ‘s’ is adjacent to both ‘m’ and ‘n’ in G and µ is a fuzzy relation on σ such that µ((mn) ̅) = σ(m) ∧ σ(n), µ((sv_i ) ̅) = σ(s) ∧ σ (vi), vi, vertex adjacent to
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If µ((mn) ̅) =1 for all the edges in G, then Quasi complete strong fuzzy graph is a semi complete graph. 2. A fuzzy graph with vertex set V= {m1, m2} and edge set E = { (m_1 m_2 ) ̅ } with as fuzzy set on V and fuzzy set on E defined as ((m_1 m_2 ) ̅) = ( m1) ∧ σ(m2) for all m1, m2 V is a complete fuzzy graph but not a quasi complete strong fuzzy graph. 3. A fuzzy graph with vertex set V= {v} with edge set E = , fuzzy set on V is trivially a quasi complete strong fuzzy graph and also complete.
Throughout this paper we take non-trivial fuzzy graphs with at least three vertices and its membership grade greater than zero.
3.3 Example : Fuzzy graph G:(V, σ, µ) with vertex set V = {V1, V2, V3, V4, V5} and edge set {(v_(1 ) v_2 ) ̅ , (v_(2 ) v_3 ) ̅, (v_(3 ) v_4 ) ̅ (v_(4 ) v_5 ) ̅ (v_(2 ) v_4 ) ̅ (v_(2 ) v_5 ) ̅ } with membership grades σ(v1) = 0.8, σ(v2) = 0.9, σ(v3) = 0.9, σ(v4) = 0.8, σ(v5) = 0.9, and µ((v_(1 ) v_2 ) ̅) = 0.8, µ((v_(1 ) v_5 ) ̅) = 0.8 µ((v_(2 ) v_3 ) ̅) = 0.9, µ((v_(3 ) v_4 ) ̅) = 0.8, µ((v_(4 ) v_5 ) ̅) = 0.8, µ((v_(2 ) v_4 ) ̅) = 0.8, µ((v_(2 ) v_5 ) ̅) = 0.9} is a quasi complete strong fuzzy
Mill, J. S. (2000). System of Logic Ratiocinative and Inductive. London: Longmans, Green, and Co.
This final week I learned a little bit more about NP-Completeness and also looked into impossible problems like the halting problem. For the discussion post, I needed to explain what the halting problem is and what benefits it provides in the analysis of algorithms. Additionally, I began preparing for the end of the course by completing the course evaluation, studying my notes, and reviewing each unit’s learning guides and quizzes.
Harris, John M., Jeffry L. Hirst, and Michael J. Mossinghoff. Combinatorics and Graph Theory. New York: Springer, 2008.
- Trait like model represents one factor, meaning that each relationship will display the same attachment
graphs under various circumstances. In more speci c terms, Ramsey Theory asks how many vertices a graph
...gic is based on uncertainties in traditional logic there is no place for uncertainties. Some technologic areas that fuzzy logic is used can be ordered like that:
This essay will consist in an exposition and criticism of the Verification Principle, as expounded by A.J. Ayer in his book Language, Truth and Logic. Ayer, wrote this book in 1936, but also wrote a new introduction to the second edition ten years later. The latter amounted to a revision of his earlier theses on the principle.It is to both accounts that this essay shall be referring.
McCarthy, J. & Hayes, P. (1969). Some philosophical problems from the stand point of artificial intelligence. In B. Metltzer & D. Michie (Eds.), Machine Intelligence Vol. 4, (pp. 463-502). Edinburgh, U.K.: Edinburgh University Press.
... a certain degree, because of some of the instances I mentioned in this paper.
Let us now see the quality of individual the population over the time. As shown below at the starting point of the algorithm individuals are of less quality. However as the time goes by population’s individuals are getting of higher quality and reaching the pick of global and local optima. The image below illustrate these stages of the algorithm.
There are two histograms, showing information on GPA, and showing information on final grade. Histograms are commonly used with interval or ratio level data (Corty, 2007). The data in the GPA is distributed and slightly skewed to the right, which means it has a positive skew and has a peaked distribution. The final histogram also has a leptokurtic frequency distribution, but is skewed to the left meaning this has a negative skew.
ABSTRACT: A Dedekind algebra is an ordered pair (B, h) where B is a non-empty set and h is a "similarity transformation" on B. Among the Dedekind algebras is the sequence of positive integers. Each Dedekind algebra can be decomposed into a family of disjointed, countable subalgebras which are called the configurations of the algebra. There are many isomorphic types of configurations. Each Dedekind algebra is associated with a cardinal value function called the confirmation signature which counts the number of configurations in each isomorphism type occurring in the decomposition of the algebra. Two Dedekind algebras are isomorphic if their configuration signatures are identical. I introduce conditions on configuration signatures that are sufficient for characterizing Dedekind algebras uniquely up to isomorphisms in second order logic. I show Dedekind's characterization of the sequence of positive integers to be a consequence of these more general results, and use configuration signatures to delineate homogeneous, universal and homogeneous-universal Dedekind algebras. These delineations establish various results about these classes of Dedekind algebras including existence and uniqueness.
The Logical Hylomorphism is based on a logic which is formal description of a traditional account of what is distinguishing features about logic. The very distinction between the formal and material aspect of all the arguments has been
Then classification is performed on the basis of similarity score of a class with respect to a neighbor.
can be highly predictable a given adjacency pair may be regarded as redundant and omitted by