A fuzzy subset of a given set S（or a fuzzy set in S）is described as an arbitrary function f:S→[0,1],where[0,1]is the usual closed in-terval of real numbers.This fundamental concept of fuzzy set was first introduced by L.A.Zadeh in 1965[89],which plays a prominent role for solving real life problems involving uncertainties,after this concept researchers/mathematicians engaged to fuzzy set theory and developed many theories like fuzzy set theory,vague set theory,soft ideal theory,intuitionistic fuzzy set theory and rough set theory.These theories have been successfully applied in various fields such as multicriteria decision making（[10],[89]）,fuzzy logic and approximate reasoning[90],pat-tern recognition[63],artificial intelligence,computer science,control engineering,operation research,robotics and many others.In other words the concept of fuzzy set is used to control uncertainty problems in models representing real life phenomenon.This concept is also used in business,medical science and related health sciences.Maiers and Sharif[49],reviewed the literature of fuzzy industrial controllers and provided an index of applications of fuzzy set theory to twelve subjects areas including decision making,economics,engineering and operation research.Several researchers/mathematicians further extended the concepts and results of algebra to the border framework of fuzzy set theory.Rosenfeld in 1971[64],was the first who considered the concept of fuzzy set theory in groups.Kazim and Naseerudin in 1972,defined the concept of an 4g-groupoid[29].Let S be a non-empty set together with a binary operation "o" is called an A-groupoid if it satisfies（x o y）o z =（z o y）o x for all x,x,z∈S Mushtaq et al.（[56],[57],[58]）,further investigated the structure and added some more useful results to AG-groupoids theory.The ideal theory of AG-groupoids was developed by Mushtaq and Khan[59].Recently fuzzy ideals in AG-groupoids are introduced by Khan and Khan[38].The fundamental concept of a soft set was introduced by Molodtsov[44]in 1999,which provides a natural framework for generalizing sev-eral basic notions of algebra.Ali et al.[19],further extended the concept of soft sets and introduced several new algebraic operations on soft sets.Cagman and Enginoglu[11],developed the uni-int decision making method in virtue of soft sets.Feng et al.[30],investigated soft semirings by using the theory of soft sets.Aktas and Cagman[1],defined the notion of soft groups and derived some related prop-erties.This initiated an important research direction concerning al-gebraic properties of soft sets in miscellaneous kinds of algebras such as BCK/BCI-algebras,d-algebras,semirings,rings,Lie algebras and K-algebras.Feng and Li[18],ascertained the relationship among five different types of soft subsets and considered the free soft algebras as-sociated with soft product operations.It has been shown that soft sets have some non classical algebraic properties which are distinct from those of crisp sets and fuzzy sets.Further,Jun discussed the applications of soft sets in ideal theory of BCK/BCI-algebras and in d-algebras respectively.Recently,combining cubic sets and soft sets,Muhiuddin and Al-roqi[55],introduced the notions of（external,in-ternal）cubic soft sets,P-cubic（resp.,R-cubic）soft subsets,R-union（resp.,R-intersection,P-union and P-intersection）of cubic soft sets and the complement of a cubic soft set.They investigated several re-lated properties and applied the notion of cubic soft sets to BCK/BCI-algebras.Murali in[54],presented the concept of belongingness between a fuzzy point and a fuzzy subset under the natural equivalence on a fuzzy subset.The idea of quasi-coincidence between a fuzzy point and a fuzzy set is defined in[62].These two ideas played an important role to generate some different types of fuzzy subgroups.Bhakat and Das（[6],[7]）,used these two ideas and introduced the concept of（α,β）-fuzzy subgroups,where α,β ∈{∈,q ∈ Vq,∈∧q} and ≠∈∧q.The concept of（∈,∈ Vq）-fuzzy subgroups is an important and valuable generalization of Rosenfeld’s fuzzy subgroups.Bhakat further studied these fuzzy subgroups in（[8],[9]）.It is worth mentioning that the concept of（∈,∈ Vgk）-fuzzy subgroups is a useful and important generalization of Rosenfeld’[s fuzzy subgroups.In[12],Davvas defined the notion of（∈,∈ Vq）-fuzzy subnear-rings and ideals of a near-ring.In[22],Jun and Song introduced the concept of（α,β）-fuzzy interior ideals in semigroups.（∈,∈ ∧q）-fuzzy bi-ideals of a semigroup is studied by Kazanci and Yamak in[42].In（[72],[73]）,Shabir,Jun and Nawaz characterized semigroups by（∈,∈ ∨qk）-fuzzy ideals and by（α,β）-fuzzy ideals.Jun generalized the idea of quasi-coincident of a fuzzy point with a fuzzy subset and defined（∈,∈ ∨qk）－fuzzy subgroup algebras in BCK/BCI-algebras.Ma and Zhan in[51],introduced（∈γ,∈γ ∨qδ）-fuzzy ideals of BCI-algebras.In[85],Zhan and Yin further generalizing the concept of（∈,∈ ∨qk）-fuzzy ideals defined（∈γ,∈γ ∨qδ）-fuzzy ideals of near-rings.Yin and Zhan in[83],gave the characterization of ordered semigroups in terms of（∈γ,∈γ ∨qδ）－fuzzy soft ideal.In[41],Khan introduced the generalized version of Jun’s cubic set and then applied it to the ideal theory of semigroups.He introduced the concept and investigated some related properties of（∈（γ1,γ2）,∈（γ1,γ2）∨q（δ1,δ2））-cubic ideals,（∈（γ1,γ2）,∈（γ1,γ2）Vq（δ1,δ2））-cubic bi-ideals and（∈（γ1,γ2）,∈（γ1,γ2）Vq（δ1,δ2））-cubic semiprime ideals in semi-groups.A recent and new extension to fuzzy sets has been introduced by Torra[74],so-called hesitant fuzzy sets to deal with hesitant situations which were not well managed by the previous extensions.Hesitant fuzzy sets have attracted quickly the attention of many researchers/mathematicians in a short time because hesitant situations are very common in different real world problems and this new approach facili-tates the management of uncertainty provoked by hesitation.Hesitant fuzzy sets have been extended from different points of view in（[65],[75],[78],[80],[82],[92]）.Chapter-wise studyThis thesis consists of six chapters.The structure of the thesis is as follows.Chapter 1 is of introductory nature,provides history,basic definitions and results,which are needed for our subsequent chapters.In Chapter 2,we have a new approach to ordered AG-groupoid theory via soft set theory.We introduce the concepts of soft inter-section ordered AG-groupoid,soft intersection left（resp.,right,two-sided）ideal,bi-ideal,generalized bi-ideal,interior ideal,quasi-ideal and soft semiprime ideal to study the structural properties of ordered AG-groupoids.We study some different relations between these concepts and characterized intra-regular ordered AG-groupoids by the properties of soft intersection ideals.In Chapter 3,we introduce the concept of（∈（γ1,γ2）,∈（γ1,γ2）∨q（δ1,δ2））－cubic soft AG-subgroupoids,（∈（γ1,γ2）,∈（γ1,γ2）∨q（δ1,δ2））-cubic softleft（resp.,right,bi-）ideals to study the algebraic structures and prop-erties of ordered AG-groupoids.We prove some fundamental results of these ideals.Some examples of（∈（γ1,γ2）,∈（γ1,γ2）∨q（δ1,δ2））-cubic soft AG-subgroupoids and（∈（γ1,γ2）,∈（γ1,γ2）∨q（δ1,δ2））-cubic soft left（resp.,right,bi-）ideals of an ordered AG-groupoid are given.Furthermore,we characterized intra-regular ordered AG-groupoids using the properties of（∈（γ1,γ2）,∈（γ1,γ2）∨q（δ1,δ2））-cubic soft ideals.In Chapter 4,we introduce the concept of（∈（γ1,γ2）,∈（γ1,γ2）∨q（δ1,δ2））-cubic soft AG-subgroupoid,∈（γ1,γ2）,∈（γ1,γ2）∨q（δ1,δ2）)-cubic soft left（resp.,right,two-sided）ideals in AG-groupoids,their examples are given and several basic properties are ivestigated.Moreover,we discuss some characterization of intra-regular AG-groupoids using the prop-erties of（∈（γ1,γ2）,∈（γ1,γ2）∨q（δ1,δ2））-)-cubic soft sets and（∈（γ1,γ2）,∈（γ1,γ2）∨q（δ1,δ2））-cubic soft right ideals.In Chapter 5,we apply the notion of hesitant fuzzy sets to the al-gebraic structures of AG-groupoids.We introduced the notions of hes-itant fuzzy AG-groupoids hesitant fuzzy left（resp.,right,two-sided）ideal,hesitant fuzzy bi-ideal,hesitant fuzzy interior ideal and hesitant fuzzy quasi-ideal on AG-groupoids,their examples are given and several basic properties are investigated.In Chapter 6,we characterize AG-groupoids by the properties of hesitant fuzzy ideals.Characterizations of intra-regualr,regular,com-pletely regular,weakly regular and quasi-regular AG-groupoids are given by the properties of their hesitant fuzzy left（resp.,right,two-sided）ideal,hesitant fuzzy bi-ideal,hesitant fuzzy interior ideal and hesitant fuzzy quasi-ideal.