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Preference modelling based on Atanassov's intuitionistic fuzzy sets are gaining increasing relevance in the field of group decision making as they provide experts with a flexible and simple tool to express their preferences on a set of alternative options, while allowing, at the same time, to accommodate experts' preference uncertainty, which is inherent to all decision making processes. A key issue...
Formal Concept Analysis (FCA) and its fuzzy extension have been widely used to arrange data into a lattice that is an effective data structure useful to address several aims, such as: data mining, ontology learning and merging, and so on. In literature it is possible to distinguish two main approaches to address fuzzy FCA implementation: the one-sided threshold and the fuzzy closure one. This work...
In many applications domains, time modeling has a fundamental role. Allen temporal relations are one of the most used and known formalisms for modeling and handling temporal data. However, classical Allen relations deal only with crisp time information, but time is often subjective and fuzzy. This paper discusses a disjunctive view of temporal relations between fuzzy time intervals. This approach...
In this paper, we investigate the multiple attribute group decision making (MAGDM) problems based on grey system theory and utility theory to accommodate situations where attribute values take the form of interval type-2 fuzzy sets (IT2FSs). Motivated by the idea of grey incidence analysis theory, we propose two new grey incidence degrees for aggregating the uncertain information and further extend...
Recently α-cut irreducible and δ1δ2-multi-adjoint concept lattices have been introduced as two different methodologies focus on reducing the size of a given fuzzy concept lattice. The philosophy of both methodologies is completely different and so, the obtained lattices too. This paper analyzes the differences and proposes that the best is to combine both methodologies in order to obtain new procedures...
In this paper, by using the concept of gH-differentiability and Kulisch-Miranker order on intervals, we show a differential Gronwall type lemma for inteval-valued functions defined on a real compact interval T.
Previously studied fuzzy bipolar conditions of type ”and if possible” are made of a mandatory condition c and an optional condition w. They allow expressing complex preferences of a conjunctive nature. We define in this paper, a new kind of fuzzy bipolar conditions of the form ”or else” which express complex preferences of a disjunctive nature. We show that the ”or else” form can be used as a negation...
Active sets are introduced in the context of providing a model to underpin mass assignment. It is argued that active sets provide an active definition of a fuzzy set where the agents providing the voting model are active and as such may modify their voting patterns depending on circumstances. We show that the model supports semantic unification and separation and therefore provides a fluid negotiating...
In this paper, we deal with the relational division operation and extend it so that it can handle bipolar fuzzy relations, i.e., relations where each tuple t is attached a pair of grades in the unit interval expressing the extent to which t satisfies a flexible constraint and a flexible wish tied by a consistency condition. The framework considered is that of an extended relational algebra. It is...
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