Interval-valued fuzzy soft sets Intuitionistic fuzzy soft sets Interval-valued intuitionistic fuzzy soft sets a b s t r a c t Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. However, it has been pointed out that classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. In this paper, the notion of the interval-valued intuitionistic fuzzy soft set theory is proposed. Our interval-valued intuitionistic fuzzy soft set theory is a combination of an interval-valued intuitionistic fuzzy set theory and a soft set theory. In other words, our interval-valued intuitionistic fuzzy soft set theory is an interval-valued fuzzy extension of the intuitionistic fuzzy soft set theory or an intuitionistic fuzzy extension of the interval-valued fuzzy soft set theory. The complement, ''and'', ''or'', union, intersection, necessity and possibility operations are defined on the interval-valued intuitionistic fuzzy soft sets. The basic properties of the interval-valued intuitionistic fuzzy soft sets are also presented and discussed.

Kinematic significance and time scales of geodynamic processes forming the Altai OrogenicBelt are addressed through structural and petrological analysis combined with zircon and monazite geochronology. The study area is composed of orogenic lower crust represented by a Devonian migmatite-magmatite complex and orogenic middle and upper crust formed by an amphibolite-facies Ordovician sedimentary sequence and a weakly to unmetamorphosed Devonian volcano-sedimentary cover, respectively. The orogenic lower and middle crust were first affected by moderate thickening, which formed subhorizontal Barrovian metamorphic schistosity. This fabric was reworked by deep crustal melting and intrusion of granite sheets during horizontal extension at 400-380 Ma. Soon after, this horizontal fabric was affected by NW-SE shortening generating crustal-scale upright folding associated with subvertical flow of still partially molten orogenic lower crust. During this event, the orogenic lower and middle crust were tightly juxtaposed with upper crustal sedimentary rocks. The last event was related with a NE-SW oriented convergence resulting in large-scale folding and megafold interference pattern in the Permian at 280-273 Ma. Combined with existing regional data, our results allow proposing a Devonian tectonic switching from compression to extension and back to compression, as a response to variations of subduction dynamics between slab advance and retreat in a Pacific-type suprasubduction system. The Permian folding was associated with the progressive northward exhumation of thermally softened crust. This tectonic evolution is in response to the indentation of the rigid Junggar arc domain into the weak Altai wedge.