• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제7권1호
• /
• pp.66-70
• /
• 2007

Note that Choquet integral is a generalized concept of Lebesgue integral, because two definitions of Choquet integral and Lebesgue integral are equal if a fuzzy measure is a classical measure. In this paper, we consider interval-valued Choquet integrals with respect to fuzzy measures(see [4,5,6,7]). Using these Choquet integrals, we define a mappings on the classes of Choquet integrable functions and give an example of a mapping defined by interval-valued Choquet integrals. And we will investigate some relations between m-convex mappings ${\phi}$ on the class of Choquet integrable functions and m-convex mappings $T_{\phi}$, defined by the class of closed set-valued Choquet integrals with respect to fuzzy measures.

• 대한수학회지
• /
• 제52권1호
• /
• pp.177-190
• /
• 2015

Let X be a completely regular Hausdorff space, and E and F be Banach spaces. Let $C_{rc}(X,E)$ be the Banach space of all continuous functions $f:X{\rightarrow}E$ such that f(X) is a relatively compact set in E. We establish an integral representation theorem for bounded linear operators $T:C_{rc}(X,E){\rightarrow}F$. We characterize continuous operators from $C_{rc}(X,E)$, provided with the strict topologies ${\beta}_z(X,E)$ ($z={\sigma},{\tau}$) to F, in terms of their representing operator-valued measures.

• 대한수학회논문집
• /
• 제25권1호
• /
• pp.139-147
• /
• 2010

A generalized nondifferentiable fractional optimization problem (GFP), which consists of a maximum objective function defined by finite fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions, is considered. Recently, Kim et al. [Journal of Optimization Theory and Applications 129 (2006), no. 1, 131-146] proved optimality theorems and duality theorems for a nondifferentiable multiobjective fractional programming problem (MFP), which consists of a vector-valued function whose components are fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions. In fact if $\overline{x}$ is a solution of (GFP), then $\overline{x}$ is a weakly efficient solution of (MFP), but the converse may not be true. So, it seems to be not trivial that we apply the approach of Kim et al. to (GFP). However, modifying their approach, we obtain optimality conditions and duality results for (GFP).

• 충청수학회지
• /
• 제23권1호
• /
• pp.37-48
• /
• 2010

In this paper we use a generalized Brownian motion process to defined an analytic operator-valued generalized Feynman integral. We then obtain explicit formulas for the analytic operatorvalued generalized Feynman integrals for functionals of the form $$F(x)=f\({\int}^T_0{\alpha}_1(t)dx(t),{\cdots},{\int}_0^T{\alpha}_n(t)dx(t)\)$$, where x is a continuous function on [0, T] and {${\alpha}_1,{\cdots},{\alpha}_n$} is an orthonormal set of functions from ($L^2_{a,b}[0,T]$, ${\parallel}{\cdot}{\parallel}_{a,b}$).

• 한국지능시스템학회논문지
• /
• 제12권4호
• /
• pp.323-326
• /
• 2002

이 논문에서 구간 수의 값을 갖는 함수들의 쇼케이적분을 생각하고자 한다. 이러한 구간 수의 값을 갖는 함수들의 성질들을 조사하여 오토연속인 퍼지측도에 관련된 쇼케이적분에 대한 수렴성 정리를 증명한다.

• 한국지능시스템학회:학술대회논문집
• /
• 한국퍼지및지능시스템학회 1993년도 Fifth International Fuzzy Systems Association World Congress 93
• /
• pp.1281-1284
• /
• 1993

By the exponential representation form (EF) for fuzzy logic, any fuzzy value a (in fuzzy valued logic or fuzzy linguistic valued logic) can be represented as Bc, where B is called the truth base and C the confidence exponent. This paper will propose the basic concepts of this form and discuss its interesting properties. By using a different truth base, the exponential form can be used to represent the positive and the negative logic in fuzzy valued logic as well as in fuzzy linguistic valued logic. Some Simple application examples of EF for approximate reasoning are also illustrated in this paper.

• 대한수학회지
• /
• 제33권1호
• /
• pp.155-167
• /
• 1996

Let X be a compact Hausdorff space, C(X) denote the set of all continuous real valued functions on X and $\ell \in N$ be any natural number.

• 융합신호처리학회논문지
• /
• 제6권3호
• /
• pp.134-142
• /
• 2005

전류모드 CMOS 회로기반 다치 논리 회로가 최근에 구현되고 있다. 본 논문에서는 4-치 Unary 다치 논리 함수를 전류모드 CMOS 논리 회로를 사용하여 합성하였다. 전류모드 CMOS(CMCL)회로의 덧셈은 각 전류 값들이 회로비용 없이 수행될 수 있고 또한 부의 논리 값은 전류흐름을 반대로 함으로써 쉽게 구현이 가능 하다. 이러한 CMCL 회로 설계과정은 논리적으로 조합된 기본 소자들을 사용하였다. 제안된 알고리듬을 적용한 결과 트랜지스터의 숫자를 고려하는 기존의 기법보다 더욱 적은 비용으로 구현할 수 있었다. 또한 비용-테이블 기법의 대안으로써 Unary 함수에 대해서 범용 UUPC(Universal Unary Programmable Circuit) 소자를 제안하였다.

• 대한수학회보
• /
• 제37권4호
• /
• pp.743-753
• /
• 2000

In the space $C_1(X)$ of real-valued continuous functions with $L_1-norm$, every bounded set has a relative Chebyshev center in a finite-dimensional subspace S. Moreover, the set function $F\rightarrowZ_S(F)$ corresponding to F the set of its relative Chebyshev centers, in continuous on the space B[$C_1(X)$(X)] of nonempty bounded subsets of $C_1(X)$ (X) with the Hausdorff metric. In particular, every bounded set has a relative Chebyshev center in the closed convex set S(F) of S and the set function $F\rightarrowZ_S(F)$(F) is continuous on B[$C_1(X)$ (X)] with a condition that the sets S(.) are equal.

• 대한수학회논문집
• /
• 제29권4호
• /
• pp.527-538
• /
• 2014

Let K be a compact Hausdorff space, $\mathfrak{A}$ a commutative complex Banach algebra with identity and $\mathfrak{C}(\mathfrak{A})$ the set of characters of $\mathfrak{A}$. In this note, we study the class of functions $f:K{\rightarrow}\mathfrak{A}$ such that ${\Omega}_{\mathfrak{A}}{\circ}f$ is continuous, where ${\Omega}_{\mathfrak{A}}$ denotes the Gelfand representation of $\mathfrak{A}$. The inclusion relations between this class, the class of continuous functions, the class of bounded functions and the class of weakly continuous functions relative to the weak topology ${\sigma}(\mathfrak{A},\mathfrak{C}(\mathfrak{A}))$, are discussed. We also provide some results on its completeness under the norm defined by ${\mid}{\parallel}f{\parallel}{\mid}={\parallel}{\Omega}_{\mathfrak{A}}{\circ}f{\parallel}_{\infty}$.