Please use this identifier to cite or link to this item: http://prr.hec.gov.pk/jspui/handle/123456789/11536
Title: Intersectional soft set theory applied to ordered semihypergroups
Authors: Farooq, Muhammad
Keywords: Mathematics
Issue Date: 2019
Publisher: Abdul Wali Khan University, Mardan
Abstract: Throughout this thesis, which contains seven chapters, Z will denote an ordered semihypergroup, unless otherwise stated. Chapter one, which is of introductory nature provides basic definitions and reviews some of the background materials which are needed for the subsequent chapters. In chapter two, definition of int-soft subsemihypergroup and int-soft left (resp., right) hyperideals are introduced. Characterizations of different classes (regular, intra-regular, right weakly regular and weakly-regular) ordered semihypergroups in terms of int-soft hyperideals are given. In this respect, discuss the study of semisimple ordered semihypergroups and characterize it in terms of int-soft hyperideals. The notions of convex soft set and critical soft point are also given. Moreover introduce the notions of (𝑀,𝑁)-int-soft hyperideals and their basic properties are discussed in this chapter. In chapter three, give the concept of int-soft interior hyperideals and characterize simple ordered semihypergroups in terms of int-soft interior hyperideals and int-soft hyperideals. Moreover characterize semisimple ordered semihypergroups in terms of int-soft interior hyperideals. Furthermore, introduce the notion of (𝑀,𝑁)-int-soft interior hyperideals of ordered semihypergroups. Finally, introduce the notion of (𝑀,𝑁)-int-soft simple ordered semihypergroups and characterize it in terms of (𝑀,𝑁)-int-soft hyperideals and (𝑀,𝑁)-int-soft interior hyperideals. In chapter four, the notion of int-soft bi-hyperideals is introduced. Moreover give the characterization of (regular, right weakly regular, intra-regular and right weakly regular, intraregular and left weakly regular) ordered semihypergroups in terms of int-soft bi-hyperideals. Furthermore definitions of prime, strongly prime, semiprime, irreducible and strongly irreducible int-soft bi-hyperideals are given. Finally, characterize ordered semihypergroups by the properties of these notions. In chapter five, definition of int-soft generalized bi-hyperideals is given and the related properties are discussed. Furthermore, characterize some classes in terms of int-soft generalized bi-hyperideals. In chapter six, definition of int-soft quasi-hyperideals is given and discuss some basic properties of int-soft quasi-hyperideals. Characterize (weakly regular, intra-regular and left weakly regular) ix ordered semihypergroups in terms of int-soft quasi-hyperideals. Moreover characterize regular, left (resp., right) simple ordered semihypergroups in terms of int-soft quasi-hyperideals. In chapter seven, the notion of int-soft left (resp., right) hyperfilters is introduced. Numerous related properties are investigated. Moreover, define completely prime int-soft hyperideals of ordered semihpergroups. Finally, characterize int-soft hyperfilters in terms of completely prime int-soft hyperideals.
Gov't Doc #: 18620
URI: http://prr.hec.gov.pk/jspui/handle/123456789/11536
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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