Transitive Closure of Interval-valued Relations

This paper introduces some concepts of intervalvalued fuzzy relations and some of their properties: reflexivity, symmetry, T-transitivity, composition and locally reflexivity. It is also introduced the concept of T-transitive closure for an interval-valued fuzzy relation. An algorithm to compute the T-transitive closure of finite interval-valued relations, some properties and some examples are given.Peer ReviewedPostprint (published version

Interval valued intuitionistic (S,T)(S,T)-fuzzy HvH_v-submodules

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K.Atanassov, the notion of interval valued intuitionistic fuzzy $H_v$-submodules of an $H_v$-module with respect to $t$-norm $T$ and $s$-norm $S$ is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated.In particular, the connections between interval valued intuitionistic $(S,T)$-fuzzy $H_v$-submodules and interval valued intuitionistic $(S,T)$-fuzzy submodules are discussed

Consensus theories: an oriented survey

This article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly – but not exclusively – concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de Mathématique Sociale (CAMS).Consensus theories ; Arrowian results ; aggregation rules ; metric consensus rules ; median ; tournament solutions ; restricted domains ; lower valuations ; median semilattice ; complexity

On IVF Approximating Spaces

We introduce the concept of IVF approximating spaces and obtain decision conditions that every IVF topological space is an IVF approximating space