In this paper optimal control problem of fuzzy linear time invariant systems is considered. Determining of system optimal input with minimizing quadratic integral criterion by using Pontryagin Minimum Principle will make the Fuzzy Partial Differential Equations [FPDEs] system solve the problem. The quality of obtaining system optimal input by solving the FPDEs system has been studied based on n...

The theory of fuzzy sets with reference to subnormality needs to be properly explained. We shall in this article put forward the actual mathematical explanation of subnormal partial presence of an element in a set, better known as subnormal fuzziness. We shall first show that every law of subnormal fuzziness can be expressed in terms of two Lebesgue-Stieltjes measures. Thereafter we would defin...

The extended answer set semantics for simple logic programs, i.e. programs with only classical negation, allows for the defeat of rules to resolve contradictions. In addition, a partial order relation on the program’s rules can be used to deduce a preference relation on its extended answer sets. In this paper, we propose a “quantitative” preference relation that associates a weight with each ru...

Pedigrees are directed acyclic graphs that represent ancestral relationships between individuals in a population. Based on a schematic recombination process, we describe two simple Markov models for sequences evolving on pedigrees--Model R (recombinations without mutations) and Model RM (recombinations with mutations). For these models, we ask an identifiability question: is it possible to cons...

Let G be a subgraph-closed graph class with bounded maximum degree. We show that if G has balanced separators whose size is smaller than linear by a polynomial factor, then G has subexponential expansion. This gives a partial converse to a result of Nešetřil and Ossona de Mendez. As an intermediate step, the proof uses a new kind of graph decompositions. The concept of graph classes with bounde...

In this paper, we introduce the concept of generalised inverse (ginverse) for intuitionistic fuzzy matrices (IFMs). We define minus partial ordering and studied several properties of it. Here we have shown that the minus partial ordering is a partial ordering for IFMs.

When a small pattern graph does not occur inside a larger target graph, we can ask how to find “as much of the pattern as possible” inside the target graph. In general, this is known as the maximum common subgraph problem, which is much more computationally challenging in practice than subgraph isomorphism. We introduce a restricted alternative, where we ask if all but k vertices from the patte...