It is well known that, in forward inference in fuzzy logic, the generalized modus ponens is guaranteed by a functional inequality called the law of T-conditionality. In this paper, the T-conditionality for T-power based implications is deeply studied and the concise necessary and sufficient conditions for a power based implication IT being T-conditional are obtained. Moreover, the sufficient conditions under which a power based implication IT is T∗-conditional are discussed, this discussions give an ideas to construct a t-norm T∗ such that the power based implication IT is T∗-conditional.
In a crystalline algorithm, a tangential velocity is used implicitly. In this short note, it is specified for the case of evolving plane curves, and is characterized by using the intrinsic heat equation.
It is well-known that the topological boundary of the spectrum of an operator is contained in the approximate point spectrum. We show that the one-sided version of this result is not true. This gives also a negative answer to a problem of Schmoeger.
Motivated by the conjectures in [11], we introduce the maximal chains of a cycle permutation graph, and we use the properties of maximal chains to establish the upper bounds for the toughness of cycle permutation graphs. Our results confirm two conjectures in [11].