Minimum and maximum operators are two well-known t-norm and s-norm used frequently in fuzzy systems. In this paper, two different types of fuzzy inequalities are simultaneously studied where the convex combination of minimum and maximum operators is applied as the fuzzy relational composition. Some basic properties and theoretical aspects of the problem are derived and four necessary and suffi...

of the origin in C ' , and vice versa. But clearly, not every convex compact neighbourhood of the origin in C ~' belongs to a lub norm. The principal problem to be considered here is the geometric characterizat ion of those convex bodies in C ~' which are associated with lub norms. The question arises because of the fact tha t m a n y of the properties of vector norms fall quite easily and natu...

In knowledge representation, when we have to use logical connectives, various continuous t-norms and t-conorms are used. In this paper, we show that every continuous t-norm and t-conorm can be approximated, to an arbitrary degree of accuracy, by a strict Archimedean t-norm (t-conorm).

The label semantics linguistic representation framework is introduced as an alternative approach to computing and modelling with words, based on the concept of appropriateness rather than graded truth. A possible worlds interpretation of label semantics is then proposed. In this model it is shown that certain assumptions about the underlying possible worlds can result in appropriateness measure...

The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical hedge algebra. Then, we consider Gödel’s t-norm and t-conorm to define the logical connectives for our logic. Next, we present a resolution inference rule, in ...

In this paper, a new method for merging multiple inconsistent knowledge bases in the framework of possibilistic logic is presented. We divide the fusion process into two steps: one is called the splitting step and the other is called the combination step. Given several inconsistent possibilistic knowledge bases (i.e. the union of these possibilistic bases is inconsistent), we split each of them...