Neutrality and Many-Valued Logics

In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert's style, sequent, and hypersequent. We present a general way that allows to construct systematically analytic calculi for a large family of non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and p-adic valued logics characterized by a special format of semantics with an appropriate rejection of Archimedes' axiom. These logics are built as different extensions of standard many-valued logics (namely, Lukasiewicz's, Goedel's, Product, and Post's logics). The informal sense of Archimedes' axiom is that anything can be measured by a ruler. Also logical multiple-validity without Archimedes' axiom consists in that the set of truth values is infinite and it is not well-founded and well-ordered. On the base of non-Archimedean valued logics, we construct non-Archimedean valued interval neutrosophic logic INL by which we can describe neutrality phenomena.Comment: 119 page

Fuzzy uncertainty modelling for project planning; application to helicopter maintenance

Maintenance is an activity of growing interest specially for critical systems. Particularly, aircraft maintenance costs are becoming an important issue in the aeronautical industry. Managing an aircraft maintenance center is a complex activity. One of the difficulties comes from the numerous uncertainties that affect the activity and disturb the plans at short and medium term. Based on a helicopter maintenance planning and scheduling problem, we study in this paper the integration of uncertainties into tactical and operational multiresource, multi-project planning (respectively Rough Cut Capacity Planning and Resource Constraint Project Scheduling Problem). Our main contributions are in modelling the periodic workload on tactical level considering uncertainties in macro-tasks work contents, and modelling the continuous workload on operational level considering uncertainties in tasks durations. We model uncertainties by a fuzzy/possibilistic approach instead of a stochastic approach since very limited data are available. We refer to the problems as the Fuzzy RoughCut Capacity Problem (FRCCP) and the Fuzzy Resource Constraint Project Scheduling Problem (RCPSP).We apply our models to helicopter maintenance activity within the frame of the Helimaintenance project, an industrial project approved by the French Aerospace Valley cluster which aims at building a center for civil helicopter maintenance