scholarly journals Ideal Theory in BCK/BCI-Algebras Based on Soft Sets and -Structures

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Young Bae Jun ◽  
Kyoung Ja Lee ◽  
Min Su Kang
Keyword(s):  
Ideal Theory ◽  
Closed Ideal ◽  
Soft Sets

Based on soft sets and -structures, the notion of (closed) -ideal over a BCI-algebra is introduced, and related properties are investigated. Relations between -BCI-algebras and -ideals are established. Characterizations of a (closed) -ideal over a BCI-algebra are provided. Conditions for an -ideal to be an -BCI-algebra are considered.

scholarly journals Ideal Theory in Semigroups Based on Intersectional Soft Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Seok Zun Song ◽  
Hee Sik Kim ◽  
Young Bae Jun
Keyword(s):  
Regular Semigroup ◽  
Ideal Theory ◽  
Soft Sets

The notions of int-soft semigroups and int-soft left (resp., right) ideals are introduced, and several properties are investigated. Using these notions and the notion of inclusive set, characterizations of subsemigroups and left (resp., right) ideals are considered. Using the notion of int-soft products, characterizations of int-soft semigroups and int-soft left (resp., right) ideals are discussed. We prove that the soft intersection of int-soft left (resp., right) ideals (resp., int-soft semigroups) is also int-soft left (resp., right) ideals (resp., int-soft semigroups). The concept of int-soft quasi-ideals is also introduced, and characterization of a regular semigroup is discussed.

scholarly journals Characterizations of Right Weakly Regular Semigroups in Terms of Generalized Cubic Soft Sets

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 293 ◽  
Author(s):  
Muhammad Gulistan ◽  
Feng Feng ◽  
Madad Khan ◽  
Aslıhan Sezgin
Keyword(s):  
Research Direction ◽  
Ideal Theory ◽  
Characteristic Functions ◽  
Algebraic Structures ◽  
Soft Sets ◽  
Regular Semigroups ◽  
Different Types ◽  
Associative Structures ◽  
New Research ◽  
The Ideal

Cubic sets are the very useful generalization of fuzzy sets where one is allowed to extend the output through a subinterval of [ 0 , 1 ] and a number from [ 0 , 1 ] . Generalized cubic sets generalized the cubic sets with the help of cubic point. On the other hand Soft sets were proved to be very effective tool for handling imprecision. Semigroups are the associative structures have many applications in the theory of Automata. In this paper we blend the idea of cubic sets, generalized cubic sets and semigroups with the soft sets in order to develop a generalized approach namely generalized cubic soft sets in semigroups. As the ideal theory play a fundamental role in algebraic structures through this we can make a quotient structures. So we apply the idea of neutrosophic cubic soft sets in a very particular class of semigroups namely weakly regular semigroups and characterize it through different types of ideals. By using generalized cubic soft sets we define different types of generalized cubic soft ideals in semigroups through three different ways. We discuss a relationship between the generalized cubic soft ideals and characteristic functions and cubic level sets after providing some basic operations. We discuss two different lattice structures in semigroups and show that in the case when a semigroup is regular both structures coincides with each other. We characterize right weakly regular semigroups using different types of generalized cubic soft ideals. In this characterization we use some classical results as without them we cannot prove the inter relationship between a weakly regular semigroups and generalized cubic soft ideals. This generalization leads us to a new research direction in algebraic structures and in decision making theory.

scholarly journals Fuzzy soft set approach to ideal theory of regular AG-groupoids

2016 ◽  
Vol 24 (1) ◽  
pp. 263-288 ◽  
Author(s):  
Feng Feng ◽  
Madad Khan ◽  
Violeta Leoreanu-Fotea ◽  
Saima Anis ◽  
Nadeem Ajaib
Keyword(s):  
Fuzzy Sets ◽  
Ideal Theory ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Algebraic Properties

Abstract This paper aims to apply fuzzy sets and soft sets in combination to investigate algebraic properties of regular AG-groupoids. We initiate (∈γ; ∈γ qδ)-fuzzy soft left ideals (right ideals, bi-ideals and quasi-ideals) over AG-groupoids and explore some related properties. Moreover, we give a number of characterizations for regular AG-groupoids by virtue of various types of fuzzy soft ideals over them.

scholarly journals Ideal Theory of BCK/BCI-algebras Based on Double-framed Soft Sets

2013 ◽  
Vol 7 (5) ◽  
pp. 1879-1887 ◽  
Author(s):  
Young Bae Jun ◽  
G. Muhiuddin ◽  
Abdullah M. Al-roqi
Keyword(s):  
Ideal Theory ◽  
Soft Sets

scholarly journals A Benchmark Generalization of Fuzzy Soft Ideals in Ordered Semigroups

2021 ◽  
Vol 29 (2) ◽  
pp. 155-171
Author(s):  
Faiz Muhammad Khan ◽  
Violeta Leoreanu-Fotea ◽  
Saifullah ◽  
Amanullah
Keyword(s):  
Real Life ◽  
Ideal Theory ◽  
Ordered Semigroup ◽  
Soft Sets ◽  
Ordered Semigroups ◽  
Binary Operations ◽  
Benchmark Study ◽  
Fuzzy Soft Sets

Abstract In real life, variability and inaccuracy are always presentand must be calculated by either possibilistic, probabilistic, polymorphic or other uncertainty approach. This benchmark study is about to construct new types of fuzzy soft ideals i.e., (∈, ∈ ∨qk )-FSR(L)Is of ordered semigroup(OSG). Based on this inception, fuzzy soft level subsets are defined which link ordinary ideals with (∈, ∈ ∨qk )-fuzzy soft left(right) ideals. Some binary operations like ◦ λ , intersection ∩ λ and union of fuzzy soft sets ∪ λ are given and various fundamental results of ideal theory are developed through these types of fuzzy soft ideals.

Utopophobia

2019 ◽  
Author(s):  
David Estlund
Keyword(s):  
Political Philosophy ◽  
Social Justice ◽  
Political Thought ◽  
Political Action ◽  
Ideal Theory ◽  
Theory Of Justice ◽  
Sound Theory ◽  
Theory Versus ◽  
History Of ◽  
Practical Guidance

Throughout the history of political philosophy and politics, there has been continual debate about the roles of idealism versus realism. For contemporary political philosophy, this debate manifests in notions of ideal theory versus nonideal theory. Nonideal thinkers shift their focus from theorizing about full social justice, asking instead which feasible institutional and political changes would make a society more just. Ideal thinkers, on the other hand, question whether full justice is a standard that any society is likely ever to satisfy. And, if social justice is unrealistic, are attempts to understand it without value or importance, and merely utopian? This book argues against thinking that justice must be realistic, or that understanding justice is only valuable if it can be realized. The book does not offer a particular theory of justice, nor does it assert that justice is indeed unrealizable—only that it could be, and this possibility upsets common ways of proceeding in political thought. The book's author engages critically with important strands in traditional and contemporary political philosophy that assume a sound theory of justice has the overriding, defining task of contributing practical guidance toward greater social justice. Along the way, it counters several tempting perspectives, including the view that inquiry in political philosophy could have significant value only as a guide to practical political action, and that understanding true justice would necessarily have practical value, at least as an ideal arrangement to be approximated. Demonstrating that unrealistic standards of justice can be both sound and valuable to understand, the book stands as a trenchant defense of ideal theory in political philosophy.

Application of Fuzzy Soft Sets in Job Requirement Problem

2019 ◽  
Vol 10 (1) ◽  
pp. 184-189
Author(s):  
S. Sandhiya ◽  
K. Selvakumari
Keyword(s):  
Soft Sets ◽  
Fuzzy Soft Sets

Soft sets and soft topology on nearness approximation spaces

Filomat ◽  
2017 ◽  
Vol 31 (13) ◽  
pp. 4117-4125 ◽  
Author(s):  
Hatice Tasbozan ◽  
Ilhan Icen ◽  
Nurettin Bagirmaz ◽  
Abdullah Ozcan
Keyword(s):  
Soft Sets ◽  
Approximation Spaces ◽  
Soft Topology

The Role of Ideal Theory

2018 ◽  
Author(s):  
Christie Hartley
Keyword(s):  
Ideal Theory ◽  
Racial Minorities ◽  
Gender Inequalities ◽  
Liberal Society ◽  
Social Categories ◽  
Ideal Society ◽  
Gender And Race ◽  
Theories Of Justice ◽  
Comprehensive Doctrines

This chapter discusses whether political liberalism’s commitment to ideal theory makes it ill-suited for theorizing about justice for socially subordinated groups such as women and racial minorities. It is shown that political liberalism’s commitment to ideal theory does not entail assuming away race or gender as social categories that give rise to concerns about justice. Even within a politically liberal well-ordered (ideal) society racial or gender inequalities may arise due to the role that beliefs about race or gender play in some persons’ comprehensive doctrines. Furthermore, it is argued that theories of justice developed for a well-ordered politically liberal society provide important guidance for correcting injustices on the basis of gender and race in nonideal societies.

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