Fuzzy sets are widely used to model vague properties. According to a common understanding, a fuzzy set represents the degrees of similarity of precisely specified objects with the prototypes of the considered vague property. We propose a logic based on this idea, using an entailment relation which was introduced in a work of Dubois, Prade, Esteva, Garcia, and Godo. The logic allows reasoning ab...

This paper attempts to present the new approach to design sufficient number of systematic fuzzy linguistics in matrix form and map the Fuzzy Linguistic Variable Matrix, which contains linguistic terms, into numeric domain using Fuzzy Normal Distribution based on the Parabola-based Membership Function. Existing fuzzy set theory is difficult to design the systematic and sufficient fuzzy linguisti...

Fuzzy set theory is a useful tool to describe situations in which the data are imprecise or vague. Fuzzy sets handle such situation by attributing a degree to which a certain object belongs to a set. The idea of fuzzy norm was initiated by Katsaras in [1984]. Felbin [1992] defined a fuzzy norm on a linear space whose associated fuzzy metric is of Kaleva and Seikkala type [1984]. Cheng and Morde...