P- ISSN 1991-8941 E-ISSN 2706-6703 Journal of University of Anbar for Pure Science (JUAPS) Open Access 2023,(17), ( 1 ):204– 211 204 Bornological Soft Sets Anwar N. Imran 1 , Lieth A.Majed 2 , Niran Sabah Jasim 3* , Sh.K.Said Husain 4 1,2 Department of Mathematic, College of Science, University of Diyala, Diyala, Iraq 3 Department of Mathematics, College of Education for Pure Science/ Ibn Al-Haitham, University of Baghdad, Baghdad, Iraq 4 Department of Mathematic, Faculty of Science and Institute for Mathematical Research(INSPEM), University Putra Malaysia. Malaysia; ARTICLE INFO ABSTRACT Received: 25 / 05 /2023 Accepted: 01 / 06/ 2023 Available online: 16 / 06 / 2023 DOI: 10.37652/juaps.2023.179056 The concept of bounded set within this set or space is given by many authors. A bornology is defined on soft set to solve the problems of boundedness for the soft set. Also, we construct soft base and soft subbase as a part of fundamental construction for bornological soft sets. Furthermore, It is a natural to study fundamental construction for bornological soft sets, such as soft subspace, product soft bornology and soft bornological isomorphism. Additionally, a family of bornological soft sets can be a partial ordered set by partial ordered relation and we prove that the intersection of bornological soft sets is bornological soft sets but the union of bornological soft sets is not necessary to be bornological soft sets. The left-right translation is soft bornological isomorphism and the product of bornological soft sets are bornological soft sets. Finally, generate soft bornological structure whose elements are soft unbounded sets. Keywords: Soft set, Bounded set, Bornological set, Bounded map, 1-INTRODUCTION Previously, to solve the limitation or bounded problem for any set or space, the concept of bounded set within this set or space are given. An idea emerged since 1977, [1] to form a structure is called bornology  on a set  to solve the problem of limitation for a set X or any space in general way. In other words, if we have set  a collection bornology of subsets of  such that  covers  also,  is stable under hereditary and finite union see [2], [3], [4], [5]. Molodtsov [6] proposed the soft set theory in 1999 as a new mathematical tool for dealing with uncertainty modelling problems. See [7-14]. The main goal of this work is to solve the problems of boundedness for the soft set by constructing new structure that is called bornological soft sets. Also, we constructed new soft bornological structures in different ways. For example, we *Corresponding author at: Department of Mathematics, College of Education for Pure Science/ Ibn Al-Haitham, University of Baghdad, Baghdad, Iraq; ORCID:https://orcid.org/0000-0001-5340-3020 ;Tel:+9647711835959 E-mail address: niraan.s.j@ihcoedu.uobaghdad.edu.iq constructed soft bornology from soft subbase as well as, we give many results and properties on bornological soft sets. It is a natural to study a fundamental construction of this new structure such as subspace of soft bornological, product soft bornology and soft bornological isomorphism. Furthermore, that a family of bornological soft sets can be partial ordered set, every soft power set of a soft set is bornological soft sets, the composition of two soft bounded maps is soft bounded map, the intersection of bornological soft sets is soft bornological set, the left-right translation is soft bornological isomorphism and the product of bornological soft sets is bornological soft sets. Finally, generate soft bornological structure whose elements are soft unbounded sets. 2-PRELIMINARIES The definition and some results about the soft set theory are presented. Definition(2-1) [6]:  denotes a universal set, while E denotes a set of parameters. The pair (, ) is called a soft set under  where consisting of a subset  of  and a mapping :  ⟶ (). Copyright©Authors, 2023, College of Sciences, University of Anbar. This is an open-access article under the CC BY 4.0 license (http://creativecommons.org/licens es/by/4.0/).