scholarly journals Regular Ordered Ternary Semigroups in Terms of Bipolar Fuzzy Ideals

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 233 ◽  
Author(s):  
Shahida Bashir ◽  
Medhit Fatima ◽  
Muhammad Shabir
Keyword(s):  
Fuzzy Set ◽  
Fuzzy Point ◽  
Ternary Semigroup ◽  
Innovative Concept

Our main objective is to introduce the innovative concept of (α,ß)-bipolar fuzzy ideals and (α,ß)-bipolar fuzzy generalized bi-ideals in ordered ternary semigroups by using the idea of belongingness and quasi-coincidence of an ordered bipolar fuzzy point with a bipolar fuzzy set. In this research, we have proved that if a bipolar fuzzy set h = (S; hn, hp) in an ordered ternary semigroup S is the (∈,∈ ∨ q)-bipolar fuzzy generalized bi-ideal of S, it satisfies two particular conditions but the reverse does not hold in general. We have studied the regular ordered ternary semigroups by using the (∈,∈ ∨ q)-bipolar fuzzy left (resp. right, lateral and two-sided) ideals and the (∈,∈ ∨ q)-bipolar fuzzy generalized bi-ideals.

scholarly journals Regular and Intra-Regular Semigroups in Terms of m-Polar Fuzzy Environment

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2031
Author(s):  
Shahida Bashir ◽  
Ahmad N. Al-Kenani ◽  
Sundas Shahzadi ◽  
Muhammad Shabir
Keyword(s):  
Fuzzy Set ◽  
Research Paper ◽  
Regular Semigroups ◽  
Fuzzy Environment ◽  
Central Objective ◽  
Innovative Concept

The central objective of the proposed work in this research is to introduce the innovative concept of an m-polar fuzzy set (m-PFS) in semigroups, that is, the expansion of bipolar fuzzy set (BFS). Our main focus in this study is the generalization of some important results of BFSs to the results of m-PFSs. This paper provides some important results related to m-polar fuzzy subsemigroups (m-PFSSs), m-polar fuzzy ideals (m-PFIs), m-polar fuzzy generalized bi-ideals (m-PFGBIs), m-polar fuzzy bi-ideals (m-PFBIs), m-polar fuzzy quasi-ideals (m-PFQIs) and m-polar fuzzy interior ideals (m-PFIIs) in semigroups. This research paper shows that every m-PFBI of semigroups is the m-PFGBI of semigroups, but the converse may not be true. Furthermore this paper deals with several important properties of m-PFIs and characterizes regular and intra-regular semigroups by the properties of m-PFIs and m-PFBIs.

Characterizations of Fuzzy Sublattices Based on Fuzzy Point

2020 ◽  
pp. 105-127
Author(s):  
Chiranjibe Jana ◽  
Faruk Karaaslan
Keyword(s):  
Fuzzy Set ◽  
Cartesian Product ◽  
Inverse Image ◽  
Fuzzy Point ◽  
Fuzzy Ideal ◽  
The Relationship

In a lattice 𝔏, the authors used the concept of belongingness and quasi-coincidence of fuzzy point to a fuzzy set, and by this notion, (∈,∈∨q)-fuzzy sublattice, (∈,∈∨q)-fuzzy ideal, cartesian product of (∈,∈∨q)-fuzzy sublattice, (∈,∈∨q)-fuzzy complemented sublattice, and cartesian product of (∈,∈∨q)-fuzzy complemented sublattice are introduced, and their properties are briefly studied. The relationship between fuzzy sublattice and (∈,∈∨q)-fuzzy sublattice, fuzzy ideal and (∈,∈∨q)-fuzzy ideal of L are established. The authors prove that the cartesian product of two (∈,∈∨q)-fuzzy ideals of a lattice is not necessarily a fuzzy ideal of a lattice. The theory of image and inverse image of an (∈,∈∨q)-fuzzy sublattice and (∈,∈∨q)-fuzzy ideal, an (∈,∈∨q)-fuzzy complemented sublattice, and (∈,∈∨q)-fuzzy complemented ideal of 𝔏 on the basis of homomorphism of lattices are also significantly established.

scholarly journals PROPERTIES OF FUZZY DITANCE ON FUZZY SET

2016 ◽  
Vol 11 (6) ◽  
pp. 5286-5299
Author(s):  
Jehad R. Kider ◽  
Aisha J Hassan
Keyword(s):  
Fuzzy Set ◽  
Cauchy Sequence ◽  
Fuzzy Distance ◽  
Fuzzy Point ◽  
Definition Of ◽  
Fuzzy Convergence

In this paper we introduce the definition of fuzzy distance space on fuzzy set then we study and discuss several properties of  this space after some illustrative examples are given . Furthermore we introduce the definition of fuzzy convergence, fuzzy Cauchy sequence of fuzzy point and fuzzy bounded fuzzy distance space . 

scholarly journals Characterizations of Ordered Semigroups by New Type of Interval Valued Fuzzy Quasi-Ideals

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Jian Tang ◽  
Xiangyun Xie ◽  
Yanfeng Luo
Keyword(s):  
Fuzzy Set ◽  
Ordered Semigroups ◽  
Fuzzy Point ◽  
New Type ◽  
Interval Valued

The concept of non-k-quasi-coincidence of an interval valued ordered fuzzy point with an interval valued fuzzy set is considered. In fact, this concept is a generalized concept of the non-k-quasi-coincidence of a fuzzy point with a fuzzy set. By using this new concept, we introduce the notion of interval valued(∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals of ordered semigroups and study their related properties. In addition, we also introduce the concepts of prime and completely semiprime interval valued(∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals of ordered semigroups and characterize bi-regular ordered semigroups in terms of completely semiprime interval valued(∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals. Furthermore, some new characterizations of regular and intra-regular ordered semigroups by the properties of interval valued(∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals are given.

scholarly journals Extended Fuzzy Sets and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 770
Author(s):  
Bahram Farhadinia ◽  
Francisco Chiclana
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Algebraic Operations ◽  
Innovative Concept

This contribution deals with introducing the innovative concept of extended fuzzy set (E-FS), in which the S-norm function of membership and non-membership grades is less than or equal to one. The proposed concept not only encompasses the concept of the fuzzy set (FS), but it also includes the concepts of the intuitionistic fuzzy set (IFS), the Pythagorean fuzzy set (PFS) and the p-rung orthopair fuzzy set (p-ROFS). In order to explore the features of the E-FS concept, set and algebraic operations on E-FSs, average and geometric operations of E-FSs are studied and an E-FS score function is defined. The superiority of the E-FS concept is further confirmed with a score-based decision making technique in which the concepts of FS, IFS, PFS and p-ROFS do not make sense.

BI-IDEALS OF ORDERED SEMIGROUPS BASED ON THE INTERVAL-VALUED FUZZY POINT

2016 ◽  
Vol 78 (2) ◽  
Author(s):  
Hidayat Ullah Khan ◽  
Nor Haniza Sarmin ◽  
Asghar Khan ◽  
Faiz Muhammad Khan
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Real World ◽  
Fuzzy Set Theory ◽  
Fuzzy Subset ◽  
Ordered Semigroups ◽  
Fuzzy Point ◽  
Interval Valued ◽  
Real World Problems

Interval-valued fuzzy set theory (advanced generalization of Zadeh's fuzzy sets) is a more generalized theory that can deal with real world problems more precisely than ordinary fuzzy set theory. In this paper, we introduce the notion of generalized quasi-coincident with () relation of an interval-valued fuzzy point with an interval-valued fuzzy set. In fact, this new concept is a more generalized form of quasi-coincident with relation of an interval-valued fuzzy point with an interval-valued fuzzy set. Applying this newly defined idea, the notion of an interval-valued -fuzzy bi-ideal is introduced. Moreover, some characterizations of interval-valued -fuzzy bi-ideals are described. It is shown that an interval-valued -fuzzy bi-ideal is an interval-valued fuzzy bi-ideal by imposing a condition on interval-valued fuzzy subset. Finally, the concept of implication-based interval-valued fuzzy bi-ideals, characterizations of an interval-valued fuzzy bi-ideal and an interval-valued -fuzzy bi-ideal are considered. 

Regular (ϵ,ϵνqk) - Fuzzy Duo Ordered Semigroups

2013 ◽  
Vol 756-759 ◽  
pp. 3084-3088
Author(s):  
Qi Cheng ◽  
Feng Lian Yuan ◽  
Yun Qiang Yin ◽  
Qing Yan Chen
Keyword(s):  
Fuzzy Set ◽  
Ordered Semigroup ◽  
Ordered Semigroups ◽  
Fuzzy Point ◽  
Fuzzy Ideal ◽  
Characterization Theorems ◽  
The Ideal

In this paper, the ideal of quasi-coincidence of a fuzzy point with a fuzzy set is generalized and the concept of an - fuzzy ideal (bi-ideal, quasi-ideal) of an ordered semigroup is introduced. The the notion of - fuzzy duo ordered semigroups is introduced and some characterization theorems are presented in terms of - fuzzy ideals.

Certain type of covers of L-fuzzy point set and their connection with L-fuzzy i-covers of L-fuzzy set

2021 ◽  
Author(s):  
Sai Prasanthi G. ◽  
Pusuluri V. N. H. Ravi ◽  
Nistala V. E. S. Murthy
Keyword(s):  
Fuzzy Set ◽  
Fuzzy Point ◽  
Point Set

scholarly journals Fuzzy Set Field and Fuzzy Metric

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Gebru Gebray ◽  
B. Krishna Reddy
Keyword(s):  
Fuzzy Set ◽  
Fuzzy Metric ◽  
Fuzzy Point

The notation of fuzzy set field is introduced. A fuzzy metric is redefined on fuzzy set field and on arbitrary fuzzy set in a field. The metric redefined is between fuzzy points and constitutes both fuzziness and crisp property of vector. In addition, a fuzzy magnitude of a fuzzy point in a field is defined.

scholarly journals On the Fuzzy Convergence

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Abdul Hameed Q. A. Al-Tai
Keyword(s):  
Real Number ◽  
Fuzzy Set ◽  
Fuzzy Number ◽  
Triangular Fuzzy Number ◽  
Fuzzy Point ◽  
Fuzzy Convergence

The aim of this paper is to introduce and study the fuzzy neighborhood, the limit fuzzy number, the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence on the base which is adopted by Abdul Hameed (every real numberris replaced by a fuzzy numberr¯(either triangular fuzzy number or singleton fuzzy set (fuzzy point))). And then, we will consider that some results respect effect of the upper sequence on the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence.

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