A Logic-Algebraic Approach to Graded Inclusion

Issue title: Concurrency Specification and Programming (CS&P)

Article type: Research Article

Authors: Gomolińska, Anna

Affiliations: Department of Mathematics, Białystok University, Akademicka 2, 15267 Białystok, Poland. [email protected]

Note: [] Address for correspondence: Department of Mathematics, Białystok University, Akademicka 2, 15267 Białystok, Poland A preliminary version of this article was presented at the Workshop on Concurrency, Specification and Programming (CS&P'2010) held in Helenenau b. Berlin, Germany [9]. Many thanks to the anonymous referees for useful comments and to Marcin Wolski for help with word processing. The author kindly acknowledges the usage of Paul Taylor's TeX macros for drawing commutative diagrams. The research has been supported by grants N N516 368334 and N N516 077837 from Ministry of Science and Higher Education of the Republic of Poland.

Abstract: In this article we continue searching for functions which might be used as measures of inclusion of information granules in information granules. Starting with a 3-valued logic having an adequate logical matrix, we show how to derive a corresponding graded inclusion function. We report on the results of examination of several best known 3-valued logics in this respect. We also give some basic properties of the inclusion functions obtained.

Keywords: rough inclusion, rough approximation, Zadeh fuzzy inclusion, 3-valued logics

DOI: 10.3233/FI-2011-510

Journal: Fundamenta Informaticae, vol. 109, no. 3, pp. 265-279, 2011