• 충청수학회지
• /
• 제20권3호
• /
• pp.279-286
• /
• 2007

Using t-norm T and s-norm S, we introduce the notion of intuitionistic (T, S)-normed fuzzy subalgebra in BCK/BCI-algebra, and some related properties are investigated.

• 한국데이터정보과학회:학술대회논문집
• /
• 한국데이터정보과학회 2006년도 추계 학술발표회 논문집
• /
• pp.81-95
• /
• 2006

The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. A t-norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation if this arithmetic operation is closed for this class. It is important to know which t-norms are consistent with a particular type of fuzzy intervals. Recently Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. A result proved by Mesiar on a strict t-norm based shape preserving additions of LR-fuzzy intervals with unbounded support is recalled. As applications, we define a broader class of bell-shaped fuzzy intervals. Then we study t-norms which are consistent with these particular types of fuzzy intervals. Dombi and Gyorbiro's results are special cases of the results described in this paper.

• 한국지능시스템학회논문지
• /
• 제17권6호
• /
• pp.804-806
• /
• 2007

The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. Recently, Hong [Fuzzy Sets and Systems 158(2007) 739-746] defined a broader class of bell-shaped fuzzy intervals. Then he study t-norms which are consistent with these particular types of fuzzy intervals as applications of a result proved by Mesiar on a strict f-norm based shape preserving additions of LR-fuzzy intervals with unbounded support. In this note, we give a direct proof of the main results of Hong.

• East Asian mathematical journal
• /
• 제22권1호
• /
• pp.93-109
• /
• 2006

The concept of intuitionistic fuzzy set was first introduced by Atanassov in 1986. In this paper, we define the intuitionistic(S,T)-fuzzy left h-ideals of a hemiring by using an s-norm S and a t-norm T and study their properties. In particular, some results of fuzzy left h-ideals in hemirings recently obtained by Jun, $\"{O}zt\"{u}rk$, Song, and others are extended and generalized to intuitionistic (S,T)-fuzzy ideals over hemirings.

• 대한수학회보
• /
• 제39권2호
• /
• pp.277-282
• /
• 2002

We Show that When ($M,\;\omega$) is a closed, simply connected, symplectic manifold for all $\gamma\;\in\;\pi_1(Ham(M),\;id)$ the following inequality holds: $\parallel\gamma\parallel\;{\geq}\;sup_{\={x}}\;|A(\={x})|,\;where\;\parallel\gamma\parallel$ is the coarse Hofer's norm, $\={x}$ run over all extensions to $D^2$ of an orbit $x(t)\;=\;{\varphi}_t(z)$ of a fixed point $z\;\in\;M,\;A(\={x})$ the symplectic action of $\={x}$, and the Hamiltonian diffeomorphisms {${\varphi}_t$} of M represent $\gamma$.

• Korean Journal of Mathematics
• /
• 제16권2호
• /
• pp.215-231
• /
• 2008

Let E be a uniformly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm, C a nonempty closed convex subset of E, and $T:C{\rightarrow}{\mathcal{K}}(E)$ a multivalued nonself-mapping such that $P_T$ is nonexpansive, where $P_T(x)=\{u_x{\in}Tx:{\parallel}x-u_x{\parallel}=d(x,Tx)\}$. For $f:C{\rightarrow}C$ a contraction and $t{\in}(0,1)$, let $x_t$ be a fixed point of a contraction $S_t:C{\rightarrow}{\mathcal{K}}(E)$, defined by $S_tx:=tP_T(x)+(1-t)f(x)$, $x{\in}C$. It is proved that if C is a nonexpansive retract of E and $\{x_t\}$ is bounded, then the strong ${\lim}_{t{\rightarrow}1}x_t$ exists and belongs to the fixed point set of T. Moreover, we study the strong convergence of $\{x_t\}$ with the weak inwardness condition on T in a reflexive Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm. Our results provide a partial answer to Jung's question.

• 대한수학회논문집
• /
• 제9권3호
• /
• pp.731-737
• /
• 1994

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measures on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$- algebras of F. If $r > 0$, let $J = [-r, 0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert_C = sup_{s \in J} $\mid$\gamma(x)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E and F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$ with the norm $\Vert T \Vert = sup {$\mid$T(x)$\mid$_F : x \in E, $\mid$x$\mid$_E \leq 1}$.

• 논리연구
• /
• 제9권2호
• /
• pp.1-30
• /
• 2006

This paper investigates algebraic semantics for some weak Boolean (wB) logics, which may be regarded as left-continuous t-norm based logics (or monoidal t-norm based logics (MTLs)). We investigate as infinite-valued logics each of wB-LC and wB-sKD, and each corresponding first order extension $wB-LC\forall$ and $wB-sKD\forall$. We give algebraic completeness for each of them.

• 대한수학회논문집
• /
• 제39권3호
• /
• pp.693-715
• /
• 2024

Let n ∈ ℕ, n ≥ 2. An element (x₁, . . . , x_n) ∈ Eⁿ is called a norming point of T ∈ 𝓛(ⁿE) if ||x₁|| = ··· = ||x_n|| = 1 and |T(x₁, . . . , x_n)| = ||T||, where 𝓛(ⁿE) denotes the space of all continuous n-linear forms on E. For T ∈ 𝓛(ⁿE), we define Norm(T) = {(x₁, . . . , x_n) ∈ Eⁿ : (x₁, . . . , x_n) is a norming point of T}. Norm(T) is called the norming set of T. Let $0{\leq}{\theta}{\leq}{\frac{{\pi}}{4}}$ and ${\ell}^2_{{\infty},{\theta}}={\mathbb{R}}^2$ with the rotated supremum norm $${\parallel}(x,y){\parallel}_{({\infty},{\theta})}={\max}\{{\mid}x\;cos\;{\theta}+y\;sin\;{\theta}{\mid},\;{\mid}x\;sin\;{\theta}-y\;cos\;{\theta}|\}$$. In this paper, we characterize the norming set of T ∈ 𝓛(ⁿℓ²_(∞,θ)). Using this result, we completely describe the norming set of T ∈ 𝓛_s(ⁿℓ²_(∞,θ)) for n = 3, 4, 5, where 𝓛_s(ⁿℓ²_(∞,θ)) denotes the space of all continuous symmetric n-linear forms on ℓ²_(∞,θ). We generalizes the results from [9] for n = 3 and ${\theta}={\frac{{\pi}}{4}}$.

• 대한수학회지
• /
• 제56권1호
• /
• pp.149-167
• /
• 2019

In this work, we study the existence, uniqueness and stability in the ${\alpha}$-norm of solutions for some stochastic partial functional integrodifferential equations. We suppose that the linear part has an analytic resolvent operator in the sense given in Grimmer [8] and the nonlinear part satisfies a $H{\ddot{o}}lder$ type condition with respect to the ${\alpha}$-norm associated to the linear part. Firstly, we study the existence of the mild solutions. Secondly, we study the exponential stability in pth moment (p > 2). Our results are illustrated by an example. This work extends many previous results on stochastic partial functional differential equations.