An Innovative Approach Of Possibility Fuzzy Soft Ordered Semigroups And Its Extension Towards Various Ideals

In contemporary mathematics,the use of generalized techniques via fuzzy soft set theory can solve complicated problems in the domain of applied sciences.The Possibility fuzzy soft set(PFSS)theory is one of the aforementioned techniques.Ordered semigroups are the fundamental algebraic structures used in different fields such as coding theory,machine learning,formal language and many more,the diverse applications of algebraic structures in several applied branches forces the researchers to come up with some new subsystems.The main work of this dissertation is divided into four parts.1)A possibility fuzzy soft sets(PFSS)is used to solve various problems in decision making and medical science.The present theory focused on developing a new type of fuzzy subsystem called possibility fuzzy soft ordered semigroups(PFSOS).The author successfully developed this new theory with suitable examples.Various characterization results of ordered semigroups have been obtained,using possibility fuzzy soft sets under the basic operations(including Union,Intersection,AND/OR operations)and all the relations are validated with the help of examples.Next,we introduce the notions of left(resp.right)ideals and l-idealistic(resp.r-idealistic)possibility fuzzy soft ordered semigroups.The author has proved several algebraic properties along with suitable examples.2)A new generalization of possibility fuzzy soft sets named as possibility multi-fuzzy soft set(PMFSS)is discussed.The PMFSS theory is the most prominent tool that helps to solve uncertain problems more precisely.Practical examples from decision making and medical diagnosis are included that will increase researcher’s interest and give a better understanding of aforementioned topic.Taking into account the prior technique,a new generalized concept is introduced that combines the possibility multi-fuzzy soft set theory with ordered semigroups.Our aim is to investigate this new theory named as possibility multi-fuzzy soft ordered semigroups(PMFSOS).Possibility multi-fuzzy soft left(resp.right)ideals and l-idealistic(resp.r-idealistic)possibility multi-fuzzy soft ordered semigroups have been determined and various algebraic operations like union,intersection,AND & OR operations are investigated.For better understanding,all the new notions are supported by several examples.3)The concept of possibility fuzzy soft interior ideals is also broached up in this research.The various results are presented in the form of the theorems and validated with suitable examples.There is a wide applicability of the possibility fuzzy soft ordered semigroups as it will be a new tool that may help in providing an extra parameter in solving such problems in the modern life.Elementary and fundamental concepts are presented that include regular,intra-regular and simple ordered semigroups in terms of possibility fuzzy soft ordered semigroup.Later,the concept of left(resp.right)regular and left(resp.right)simple in terms of possibility fuzzy soft ordered semigroups are presented.The notion of possibility fuzzy soft semiprime ideals in an ordered semigroup is also defined and illustrated by theorems and example.4)Following the concept of possibility multi-fuzzy soft ordered semigroups we relate a novel approach towards possibility multi-fuzzy soft interior ideals and its relation with possibility multi-fuzzy soft ideals.Further,various classes of ordered semigroups are introduced,including simple,regular and intra-regular based on the innovative approach of PMFSOS.Various important conclusions are made using these concepts and are validated by appropriate examples.Finally,the notion of possibility multi-fuzzy soft ideals for semiprime ordered semigroups is also defined and supported by an example.