In this contribution, we will extend results relating to representability of a fuzzy function using a crisp function. And additionally, we show for which functions there exist fuzzy function of a specific form. Our notion of fuzzy function has a graded character. More precisely, any fuzzy relation has a property of being a fuzzy function that is expressed by a truth degree. And it consists of t...

Several real-world applications (e.g., scheduling, configuration, ... ) can be formulated as Constraint Satisfaction Problems (CSP). In these cases, a set of variables have to be settled to a value with the requirement that they satisfy a set of constraints. Classical CSPs are defined only by means of crisp (Boolean) constraints. However, as sometimes Boolean constraints are too strict in relat...

This paper takes into account the Wittgenstein’s idea on family resemblances as a particular crisp relation between some fuzzy sets, that is, between some predicates representable from its use. It is shown that all uses of the same predicate actually do have family resemblance, that some pairs of predicates cannot, and a numerical degree of family resemblance is introduced. Keywords— Degree of ...

This paper takes into account the Wittgenstein’s idea of family resemblance as a particular crisp relation between some fuzzy sets, that is, between some representations of predicates use from its use. It is shown that all uses of the same predicate actually do have some kind of family resemblance, that some pairs of predicates cannot, and how the predicates migration between different universe...

Previous single case reports of males with anorexia nervosa from our database focused on the roles of gender and general personal identity conflicts and panic/guilt over the consequences of impulsivity in precipitating out the illness (Davis & Crisp, 1993; Fry & Crisp, 1989; Toms & Crisp, 1972), the growth stunting but reversible effects of early onset (Toms & Crisp, 1972), and a 35-year long f...

We propose a view of vagueness as a semantic property of names and predicates. All entities are crisp, on this semantic view, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being its extension. We provide a new formulation of ...

A fuzzy option prioritization technique is developed to efficiently model uncertain preferences of DMs in strategic conflicts as fuzzy preferences by using the decision makers’ (DMs’) fuzzy truth values of preference statements at feasible states within the framework of the Graph Model for Conflict Resolution. The preference statements of a DM express desirable combinations of options or course...