A duality between LM-fuzzy possibility computations and their logical semantics

Domain semantics of possibility computations

A generalization of the Chen-Wu duality into quantale-valued setting

With the unit interval [0,1] as the truth value table, Chen and Wupresented the concept of  possibility computation over dcpos.Indeed, every possibility computation can be considered as a[0,1]-valued Scott open set on a dcpo. The aim of this paper is tostudy Chen-Wu's duality on quantale-valued setting. For clarity,with a commutative unital quantale $L$ as the truth value table, weintroduce a c...

Duality in fuzzy linear programming with possibility and necessity relations

A class of fuzzy linear programming (FLP) problems with fuzzy coefficients based on fuzzy relations is introduced, the concepts of feasible and (α, β)-maximal and minimal solutions are defined. The class of crisp (classical) LP problems can be embedded into the class of FLP ones. Moreover, for FLP problems a new concept of duality is introduced and the weak and strong duality theorems are deriv...

Fuzzy Logical Algebras and Their Applications

1Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China 2Department of Mathematics, Yazd University, P.O. Box 89195-741, Yazd, Iran 3Institute of Mathematics and Computer Science, Wroclaw University of Technology, 50-370 Wroclaw, Poland 4Department of Mathematics Education, Gyeongsang National University, Jinju 660-701, Republic of Korea 5Department of Mathema...

A duality between fuzzy domains and strongly completely distributive $L$-ordered sets

The aim of this paper is to establish a fuzzy version of the dualitybetween domains and completely distributive lattices. All values aretaken in a fixed frame $L$. A definition of (strongly) completelydistributive $L$-ordered sets is introduced. The main result inthis paper is that the category of fuzzy domains is dually equivalentto the category of strongly completely distributive $L$-ordereds...

A Note on Logical Relations Between Semantics and Syntax

This note gives a new proof of the ‘operational extensionality’ property of Abramsky’s lazy lambda calculus—namely the coincidence of contextual equivalence with a co-inductively defined notion of ‘applicative bisimilarity’. This purely syntactic result is here proved using a logical relation (due to Plotkin) between the syntax and its denotational semantics. The proof exploits a mixed inductiv...