Fuzzy sets and rough sets are known as uncertainty models. They are proposed to treat different aspects of uncertainty. Therefore, it is natural to combine them to build more powerful mathematical tools for treating problems under uncertainty. In this chapter, we describe the state of the art in the combinations of fuzzy and rough sets dividing into three parts. In the first part, we first desc...

The crecient use of fuzzy systems in complex applications has motivated us to develop a new version of Xfuzzy, the design environment for fuzzy system created at the IMSE (Instituto de Microelectrónica de Sevilla). This new version, Xfuzzy 3.0, offers the advantages of being enterely programmed in Java, and allows designing hierarchical rule bases that can interchange fuzzy or non fuzzy values ...

In the last years, the adoption of adaptive systems has increased in many fields of computer science, such as databases and software engineering. These systems are able to automatically react to events, by collecting information from the external environment and generating new events. However, the collection of data is often hampered by uncertainty and vagueness. The decision making mechanism u...

Linguistic models of vagueness usually record contexts of possible precisifications. A link between such models and fuzzy logic is established by extracting fuzzy sets from context based word meanings and analyzing standard logical connectives in this setting. In a further step Lawry’s voting semantics for fuzzy logics is used to re-interpret standard t-norm based truth functions from the point...

The aim of this short paper is to give a simple look to the historical development of logical connectives for fuzzy sets and fuzzy logic. Concepts that have been (and still are) in the core of extensive theoretical research, like conjunction, disjunction, complement, subsethood and fuzzy conditionals, are considered in an informal way. An extensive list of essential references helps the interes...

To avoid self-contradictions in Fuzzy Set Theory, it is needed to consider only fuzzy sets that are not selfcontradictory and whose complements are also not selfcontradictory. This paper deals with a subset Fnc(E) in [0, 1] , where the above conditions are satisfied. A particular Fuzzy Set Theory is defined in Fnc(E) with adequate logical connectives. Finally, which classical properties hold in...

The main goal of this paper is to apply the method of extension of fuzzy connectives proposed in our previous work for fuzzy implications valued on a bounded lattice. Also we discuss about which properties of implications are preserved by this method and we prove some results involving extension and automorphisms. Finally, we investigate the behavior of the extensions of two special classes of ...

Fuzzy answer set programming (FASP) combines two declarative frameworks, answer set programming and fuzzy logic, in order to model reasoning by default over imprecise information. Several connectives are available to combine different expressions; in particular the Gödel and Lukasiewicz fuzzy connectives are usually considered, due to their properties. Although the Gödel conjunction can be easi...