‎In this paper we prove that a simplicial complex is determined‎ ‎uniquely up to isomorphism by its barycentric subdivision as well as‎ ‎its comparability graph‎. ‎We also put together several algebraic‎, ‎combinatorial and topological invariants of simplicial complexes‎.

A comparability graph is a graph whose edges can be oriented transitively. Given a comparability graph G = (V, E) and an arbitrary edge ê ∈ E we explore the question whether the graph G − ê, obtained by removing the undirected edge ê, is a comparability graph as well. We define a new substructure of implication classes and present a complete mathematical characterization of all those edges.

In the paper aspect of comparability alternatives in decision making problem by imprecise or incomplete information isexamined. In particular, new definitions of transitivity based on the measure of the intensity preference between pairsof alternatives in epistemic and ontic case is presented and its application to solve decision making problem is proposed.

Given a class of graphs G, a graphG is a probe graph of G if its vertices can be partitioned into a set of probes and an independent set of nonprobes such that G can be embedded into a graph of G by adding edges between certain nonprobes. If the partition of the vertices is part of the input, we call G a partitioned probe graph of G. In this paper we show that there exists a polynomial-time alg...

Comparability graphs are graphs which have transitive orientations. The dimension of a poset is the least number of linear orders whose intersection gives this poset. The dimension dim(X) of a comparability graph X is the dimension of any transitive orientation of X, and by k-DIM we denote the class of comparability graphs X with dim(X) ≤ k. It is known that the complements of comparability gra...

Similarity and comparability are complementary notions that are easy to confuse and difficult to tease apart. Semantic similarity makes comparison meaningful, while comparison is often the pragmatic means through which similarity is perceived and constructed. To date, WordNet has found wide application as a basis for modeling and measuring semantic similarity, but is lacking as a basis for well...

Psychological theories of subjective probability judgments assume that accumulated evidence (support) mediates the relation between the description of a to-be-judged event (hypothesis) and the judgment. To scale a probability from the support for a hypothesis, these psychological theories make a strong independence assumption. This assumption is stated in the form of the product rule, in which ...

The realization that numerous factors contribute to how individuals make judgements and respond within interview based surveys is not new (Jobe & Mingay 1989; Kahneman, Slovic & Tversky 1982). Over the past 50 years or so, investigations in the area of " respondent bias " have documented various sources of error, i.e., factors that may contribute to the difference between what is truth, what is...

A function diagram (f-diagram) D consists of the family of curves {i, . . . , ii} obtained from n continuous functions fi : [O, 1] -B R (1 G i d n). We call the intersection graph of D a function graph (f-graph). It is shown that a graph G is an f-graph if and only if its complement 0 is a comparability graph. An f-diagram generalizes the notion cf a permutation diagram where the fi are linear ...