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Orthopairs: A Simple and Widely UsedWay to Model Uncertainty

Ciucci D.

Fundamenta Informaticae

2011

Vol. 108, nr 3/4

287-304

The term orthopair is introduced to group under a unique definition different ways used to denote the same concept. Some orthopairmodels dealing with uncertainty are analyzed both from a mathematical and semantical point of view, outlining similarities and differences among them. Finally, lattice operations on orthopairs are studied and a survey on algebraic structures is provided.

Relative Sets and Rough Sets

Mousavi A., Jabedar-Maralani P.

International Journal of Applied Mathematics and Computer Science

2001

Vol. 11, no 3

637-653

In this paper, by defining a pair of classical sets as a relative set, an extension of the classical set algebra which is a counterpart of Belnap's four-valued logic is achieved. Every relative set partitions all objects into four distinct regions corresponding to four truth-values of Belnap's logic. Like truth-values of Belnap's logic, relative sets have two orderings; one is an order of inclusion and the other is an order of knowledge or information. By defining a rough set as a pair of definable sets, an integrated approach to relative sets and rough sets is obtained. With this definition, we are able to define an approximation of a rough set in an approximation space, and so we can obtain sequential approximations of a set, which is a good model of communication among agents.