let $g$ be a simple graph of order $n$‎. ‎we consider the‎ ‎independence polynomial and the domination polynomial of a graph‎ ‎$g$‎. ‎the value of a graph polynomial at a specific point can give‎ ‎sometimes a very surprising information about the structure of the‎ ‎graph‎. ‎in this paper we investigate independence and domination‎ ‎polynomial at $-1$ and $1$‎.

In this paper, we introduce the genetic design of independent input rule-based fuzzy neural networks. The premise part of the rules of the proposed networks is realized by partitioning of the independent input space using hard-c means clustering. The independently partitioned spaces express the fuzzy rules for respective inputs. The consequence part of the rules is represented by polynomial fun...

The Disjunctive Fuzzy Temporal Constraint Network model allows to express complex qualitative and quantitative temporal constraints, but its complexity is exponential. There are several subsets of these networks that can be solved in polynomial time. Another subset can be reduced to equivalent networks with a tree structure. In order to study the usefulness of these approaches, an evaluation ha...

Stability analysis of fuzzy control systems using polynomial methods is proposed. First, a new approach is introduced to search for poles of a T-S fuzzy system in any mixed weighting case. Next, through the technique of the pole placement, a controller can be designed to achieve the desired response. Then, using the following methods, such as the Kharitonov polynomials, Edge Theorem, Routh stab...

This paper considers a generalized fuzzy random version of bottleneck spanning tree problem in which edge costs are fuzzy random variables. The problem is to find an optimal spanning tree under chance constraint with respect to possibility measure of bottleneck (maximum cost) edge of spanning tree. The problem is first transformed into a deterministic equivalent problem. Then its subproblem is ...

In this paper we deal with the problem of studying some mathematical aspects regarding the polytope of fuzzy measures when the referential set is finite. More concretely, we study whether two extreme points are adjacent; for general polytopes, this is a NP-hard problem. However, for the case of fuzzy measures, we give a necessary and sufficient condition for two extreme points to be adjacent. T...

A lot of problems involve unknown data relations, which can define a derivative based model of dependent variables generalization. Standard softcomputing methods (as artificial neural networks or fuzzy rules) apply usual absolute interval values of input variables. The new proposed differential polynomial neural network makes use of relative data, which can better describe the character regardi...

we find an explicit expression of the tutte polynomial of an $n$-fan. we also find a formula of the tutte polynomial of an $n$-wheel in terms of the tutte polynomial of $n$-fans. finally, we give an alternative expression of the tutte polynomial of an $n$-wheel and then prove the explicit formula for the tutte polynomial of an $n$-wheel.

In this paper the notion of minimality is extended to relative semi-dynamical systems. We consider transitivity from the point of view of an observer which is a fuzzy set. Relative topological entropy of a relative semi-dynamical system as an invariant object of relative conjugate relations is studied. Finally illustrated example in polynomial functions is given to explain the idea of the paper.

Fuzzy circular interval graphs are a generalization of proper circular arc graphs and have been recently introduced by Chudnovsky and Seymour as a fundamental subclass of claw-free graphs. In this paper, we provide a polynomial-time algorithm for recognizing such graphs, and more importantly for building a suitable representation.