An approach to develop new measures of fuzzy directed divergence is proposed here. A new measure of fuzzy directed divergence is proposed, and some mathematical properties of this measure are proved. The application of fuzzy directed divergence in image segmentation is explained. The proposed technique minimizes the fuzzy divergence or the separation between the actual and ideal thresholded image.

We introduce a partial order structure on the set of interval orders of a given size, and prove that such a structure is in fact a lattice. We also provide a way to compute meet and join inside this lattice. Finally, we show that, if we restrict to series parallel interval order, what we obtain is the classical Tamari poset.

Over the past 15 years, Ramsey theoretic techniques and concepts have been applied with great success to partially ordered sets. In the last year alone, four new applications of Ramsey theory to posets have produced solutions to some challenging combinatorial problems. First, Kierstead and Trotter showed that dimension for interval orders can be characterized by a single ramsey trail by proving...

We show that a minimal triangulation of the associahedron (Stasheff polytope) of dimension n is made of (n+ 1)n−1 simplices. We construct a natural bijection with the set of parking functions from a new interpretation of parking functions in terms of shuffles. Introduction The Stasheff polytope, also known as the associahedron, is a polytope which comes naturally with a poset structure on the s...

A new domination parameter in a fuzzy digraph is proposed to espouse contribution the domain of graph and directed graph. Let GD*=V,A be simple graph, where V finite nonempty set A=x,y:x,y∈V,x≠y. GD=σD,μD pair two functions σD:V→0,1 μD:A→0,1, such that μDx,y≤σDx∧σDy, x,y∈V. An edge μDx,y called an effective if μDx,y=σDx∧σDy. The vertex σDx dominates σDy GD edge. S⊆V, u∈V\S, v∈S. subset σDS⊆σD d...

Abstract It is proved that for every positive integer n , the number of non-Tukey-equivalent directed sets cardinality $\leq \aleph _n$ at least $c_{n+2}$ $(n+2)$ -Catalan number. Moreover, class $\mathcal D_{\aleph _n}$ contains an isomorphic copy poset Dyck -paths. Furthermore, we give a complete description whether two successive elements in contain another set between or not.

nets, useful topological tools, used to generalize certainconcepts that may only be general enough in the context of metricspaces. in this work we introduce this concept in an $s$-poset, aposet with an action of a posemigroup $s$ on it whichis a very useful structure in computer sciences and interestingfor mathematicians, and give the the concept of $s$-net. using $s$-nets and itsconvergency we...

We use a variety of combinatorial techniques to prove several theorems concerning fractional dimension of partially ordered sets. In particular, we settle a conjecture of Brightwell and Scheinerman by showing that the fractional dimension of a poset is never more than the maximum degree plus one. Furthermore, when the maximum degree k is at least two, we show that equality holds if and only if ...

A sectionally pseudocomplemented poset P is one which has the top element and in which every principal order filter is a pseudocomplemented poset. The sectional pseudocomplements give rise to an implication-like operation on P which coincides with the relative pseudocomplementation if P is relatively psudocomplemented. We characterise this operation and study some elementary properties of upper...

Finite smooth digraphs, that is, finite directed graphs without sources and sinks, can be partially ordered via pp-constructability. We give a complete description of this poset and, in particular, we prove it is distributive lattice. Moreover, show order to separate two digraphs our suffices the polymorphism clone one satisfies prime cyclic loop condition not satisfied by other. Furthermore, c...