We demonstrate the versatility of tangle-tree duality theorem for abstract separation systems by using it to prove tree-of-tangles theorems. This approach allows us strengthen some existing theorems bounding node degrees in them. also present a slight strengthening and simplified proof theorem, which derive tangles different orders.

In this note we extend duality theorems for crossed products obtained by M. Koppinen and C. Chen from the case of a base field or a Dedekind domain to the case of an arbitrary noetherian commutative ground ring under fairly weak conditions. In particular we extend an improved version of the celebrated Blattner-Montgomery duality theorem to the case of arbitrary noetherian ground rings.

In this paper, we point out some deficiencies in a recent paper (Lee and Kim in J. Nonlinear Convex Anal. 13:599–614, 2012), and we establish strong duality and converse duality theorems for two types of nondifferentiable higher-order symmetric duals multiobjective programming involving cones.

This text is a further elaboration of the previous research report [5]. Graded properties of binary and unary connectives valued in MTL4-algebras are studied in the framework of Fuzzy Class Theory (or higher-order fuzzy logic) FCT, which serves as a tool for easy derivation of graded theorems. The properties studied include graded monotonicity, a generalized Lipschitz property, commutativity, a...

in the present paper, we introduce and study a fuzzy vector equilibrium problem and prove some existence results with and without convexity assumptions by using some particular forms of results of textit{kim} and textit{lee} [w.k. kim and k.h. lee, generalized fuzzy games and fuzzy equilibria, fuzzy sets and systems, 122 (2001), 293-301] and textit{tarafdar} [e. tarafdar, fixed point theorems i...

We prove a general width duality theorem for combinatorial structures with well-defined notions of cohesion and separation. These might be graphs and matroids, but can be much more general or quite di↵erent. The theorem asserts a duality between the existence of high cohesiveness somewhere local and a global overall tree structure. We describe cohesive substructures in a unified way in the form...

Convexity assumptions for fractional programming of variational type are relaxed to generalized invexity. The sufficient optimality conditions are employed to construct a mixed dual programming problem. It will involve the Wolfe type dual and Mond-Weir type dual as its special situations. Several duality theorems concerning weak, strong, and strict converse duality under the framework in mixed ...

The concept of symmetric duality for multiobjective fractional problems has been extended to the class of multiobjective variational problems. Weak, strong and converse duality theorems are proved under generalized invexity assumptions. A close relationship between these problems and multiobjective fractional symmetric dual problems is also presented. 2005 Elsevier Inc. All rights reserved.

let $s$ be an ordered semigroup. a fuzzy subset of $s$ is anarbitrary mapping   from $s$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. in this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $s$ is introduced.regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.finally, two m...

The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by  Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which th...