Interval approaches for uncertain reasoning

Abstract

Abstract. This paper presents a framework for reasoning using intervals. Two interpretations of intervals are examined, one treats intervals as bounds of a truth evaluation function, and the other treats end points of intervals as two truth evaluation functions. They lead to two different reasoning approaches, one is based on interval computations, and the other is based on interval structures. A number of interval based reasoning methods are reviewed and compared within the proposed framework.

On Interval Soft Sets with Applications

“…For representing qualitative information, Yao 20 proposed the notion of interval set, and the relationship among interval sets, rough sets and fuzzy sets are investigated in 21,22,23,24 . As a generalization of interval set, Zhang et al 25 introduced lattice-valued interval set and discussed its algebra operations.…”

Interval sets and interval-set algebras

“…The notion of interval sets is a new kind of sets, represented by a pair of sets, namely, its lower and upper bounds [42,50,52,53]. Mathematically, interval sets are defined as follows.…”

“…Dai [3,4] discussed connections between rough sets and 3-valued Łukasiewicz algebras based essentially on Iwiński rough sets. Reasoning based on interval sets have been examined by several authors (for example, Yao [43], Yao and Li [50], Yao and Wong [53], Yamauchi and Mukaidono [39], Qi [29], and Qi et al [30]). …”

“…The boundary of a partially known concept is made up objects whose belongingness to the concept are unknown. Interval sets seem to provide a more suitable model for studying partially known concepts [42,50,52,53].…”

Combination of interval set and soft set

“…Interval sets are closely related to, and complementary to, fuzzy sets and rough sets. The relationships among interval sets, rough sets and fuzzy sets were investigated 22,23 . A significant difference between these models lies in the definition and interpretation of their extended set-theoretic operators.…”