Linguistic Semilinear Algebras and Linguistic Semivector Spaces

Download or read book Linguistic Semilinear Algebras and Linguistic Semivector Spaces written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2022-12-15 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic structures on linguistic sets associated with a linguistic variable are introduced. The linguistics with single closed binary operations are only semigroups and monoids. We describe the new notion of linguistic semirings, linguistic semifields, linguistic semivector spaces and linguistic semilinear algebras defined over linguistic semifields. We also define algebraic structures on linguistic subsets of a linguistic set associated with a linguistic variable. We define the notion of linguistic subset semigroups, linguistic subset monoids and their respective substructures. We also define as in case of deals in classical semigroups, linguistic ideals in linguistic semigroups and linguistic monoids. This concept of linguistic ideals is extended to the case of linguistic subset semigroups and linguistic subset monoids. We also define linguistic substructures.