000002853 001__ 2853
000002853 005__ 20141118153417.0
000002853 04107 $$acze
000002853 046__ $$k2008-12-04
000002853 100__ $$aMorsi, N.
000002853 24500 $$aApplications of Tied Implications to Approximate Reasoning and Fuzzy Control

000002853 24630 $$n1.$$p70 Years of FCE STU - Proceedings of the International Scientific Conference
000002853 260__ $$bSlovak University of Technology in Bratislava, Faculty of Civil Engineering, 2008 
000002853 506__ $$arestricted
000002853 520__ $$2eng$$aThe logic of tied implications deals with implications ⇒: P × L → L (on two lattices (P, ≤P , 1P ) and (L, ≤L )), tied by an integral commutative ordered monoid operation ⊗ on P , in the sense of the following identity: ((x ⊗ y) ⇒ c) = (x ⇒ (y ⇒ c)) . We demonstrate the usefulness of tied implications through some applications. We use the connectives of a tied algebra to interpret Generalized Modus Ponens (GMP) inference schemata, in the vein of both the Compositional Rule of Inference (CRI) of Zadeh, and the Consequent Dilation Rule (CDR), due to Magrez and Smets and developed by Morsi and Fahmy. We show that a multiple-rule, generalized modus ponens inference scheme is equivalent, as far as CRI or CDR are concerned, to a scheme that satisfies the "basic requirement for fuzzy reasoning", proposed by Fukami, Lehmke, Perfilieva, Tian and Turksen. We end by investigating the principles of fuzzy control in general with interpretations based on a particular case of CRI, called Generalized Conjunctive Rule (GCR), due to Hájek. We show that the basic requirement for fuzzy reasoning is satisfied by GCR in all single rule inference schemata, using the connectives of a tied algebra, and we indicate a special type of multiple-rule schemata in which this requirement is satisfied.

000002853 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000002853 653__ $$aFuzzy logic; Generalized modus ponens; Fuzzy control; Nonclassical logics; Tied implication; Prelinearity

000002853 7112_ $$aInternational Scientific Conference 70 Years of FCE STU$$cBratislava (SK)$$d2008-12-04 / 2008-12-05$$gHMC13
000002853 720__ $$aMorsi, N.$$iEl-Zekey, M.
000002853 8560_ $$ffischerc@itam.cas.cz
000002853 8564_ $$s256427$$uhttps://invenio.itam.cas.cz/record/2853/files/05_A_Morsi_El-Zekey.pdf$$y
             Original version of the author's contribution as presented on CD, .
            
000002853 962__ $$r2540
000002853 980__ $$aPAPER