scholarly journals m-Polar Fuzzy Sets: An Extension of Bipolar Fuzzy Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Juanjuan Chen ◽  
Shenggang Li ◽  
Shengquan Ma ◽  
Xueping Wang
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Real World ◽  
Ordinal Number ◽  
Information Uncertainty ◽  
Multi Index ◽  
Limit Process ◽  
Multi Agent ◽  
Bipolar Fuzzy Sets ◽  
Real World Problems

Recently, bipolar fuzzy sets have been studied and applied a bit enthusiastically and a bit increasingly. In this paper we prove that bipolar fuzzy sets and0,12-sets (which have been deeply studied) are actually cryptomorphic mathematical notions. Since researches or modelings on real world problems often involve multi-agent, multi-attribute, multi-object, multi-index, multi-polar information, uncertainty, or/and limit process, we put forward (or highlight) the notion ofm-polar fuzzy set (actually,0,1m-set which can be seen as a generalization of bipolar fuzzy set, wheremis an arbitrary ordinal number) and illustrate how many concepts have been defined based on bipolar fuzzy sets and many results which are related to these concepts can be generalized to the case ofm-polar fuzzy sets. We also give examples to show how to applym-polar fuzzy sets in real world problems.

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. 

scholarly journals Foldness of Bipolar Fuzzy Sets and Its Application in BCK/BCI-Algebras

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1036
Author(s):  
Young Bae Jun ◽  
Seok-Zun Song
Keyword(s):  
Information Processing ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Negative Information ◽  
Positive Information ◽  
Fuzzy Ideal ◽  
Recent Trends ◽  
Modern Information ◽  
Bipolar Fuzzy Sets

Recent trends in modern information processing have focused on polarizing information, and and bipolar fuzzy sets can be useful. Bipolar fuzzy sets are one of the important tools that can be used to distinguish between positive information and negative information. Positive information, for example, already observed or experienced, indicates what is guaranteed to be possible, and negative information indicates that it is impossible, prohibited, or certainly false. The purpose of this paper is to apply the bipolar fuzzy set to BCK/BCI-algebras. The notion of (translated) k-fold bipolar fuzzy sets is introduced, and its application in BCK/BCI-algebras is discussed. The concepts of k-fold bipolar fuzzy subalgebra and k-fold bipolar fuzzy ideal are introduced, and related properties are investigated. Characterizations of k-fold bipolar fuzzy subalgebra/ideal are considered, and relations between k-fold bipolar fuzzy subalgebra and k-fold bipolar fuzzy ideal are displayed. Extension of k-fold bipolar fuzzy subalgebra is discussed.

Complex bipolar fuzzy sets: An application in a transport’s company

2020 ◽  
pp. 1-17
Author(s):  
Muhammad Gulistan ◽  
Naveed Yaqoob ◽  
Ahmed Elmoasry ◽  
Jawdat Alebraheem
Keyword(s):  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Cartesian Product ◽  
Real Numbers ◽  
Wide Range ◽  
Fuzzy Aggregation ◽  
Bipolar Fuzzy Sets ◽  
Range Of Values

Zadeh’s fuzzy sets are very useful tool to handle imprecision and uncertainty, but they are unable to characterize the negative characteristics in a certain problem. This problem was solved by Zhang et al. as they introduced the concept of bipolar fuzzy sets. Thus, fuzzy set generalizes the classical set and bipolar fuzzy set generalize the fuzzy set. These theories are based on the set of real numbers. On the other hand, the set of complex numbers is the generalization of the set of real numbers so, complex fuzzy sets generalize the fuzzy sets, with wide range of values to handle the imprecision and uncertainty. So, in this article, we study complex bipolar fuzzy sets which is the generalization of bipolar fuzzy set and complex fuzzy set with wide range of values by adding positive membership function and negative membership function to unit circle in the complex plane, where one can handle vagueness in a much better way as compared to bipolar fuzzy sets. Thus this paper leads us towards a new direction of research, which has many applications in different directions. We develop the notions of union, intersection, complement, Cartesian product and De-Morgan’s Laws of complex bipolar fuzzy sets. Furthermore, we develop the complex bipolar fuzzy relations, fundamental operations on complex bipolar fuzzy matrices and some operators of complex bipolar fuzzy matrices. We also discuss the distance measure on complex bipolar fuzzy sets and complex bipolar fuzzy aggregation operators. Finally, we apply the developed approach to a numerical problem with the algorithm.

On 2-absorbing bipolar fuzzy ideals over LA -semigroups

2021 ◽  
Vol 41 (2) ◽  
pp. 3173-3181
Author(s):  
Pairote Yiarayong
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Bipolar Fuzzy Sets ◽  
The Relationship

The aim of this manuscript is to apply bipolar fuzzy sets for dealing with several kinds of theories in LA -semigroups. To begin with, we introduce the concept of 2-absorbing (quasi-2-absorbing) bipolar fuzzy ideals and strongly 2-absorbing (quasi-strongly 2-absorbing) bipolar fuzzy ideals in LA -semigroups, and investigate several related properties. In particular, we show that a bipolar fuzzy set A = ( μ A P , μ A N ) over an LA -semigroup S is weakly 2-absorbing if and only if [ B ⊙ C ] ⊙ D ⪯ A implies B ⊙ C ⪯ A or C ⊙ D ⪯ A or B ⊙ D ⪯ A for any bipolar fuzzy sets B = ( μ B P , μ B N ) , C = ( μ C P , μ C N ) and D = ( μ D P , μ D N ) . Also, we give some characterizations of quasi-strongly 2-absorbing bipolar fuzzy ideals over an LA -semigroup S by bipolar fuzzy points. In conclusion of this paper we prove that the relationship between quasi-strongly 2-absorbing bipolar fuzzy ideals over an LA -semigroup S and quasi-2-absorbing bipolar fuzzy ideals over S.

scholarly journals A note on different types of product of neutrosophic graphs

2021 ◽  
Author(s):  
Kartick Mohanta ◽  
Arindam Dey ◽  
Anita Pal
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Real World ◽  
Real Life ◽  
Neutrosophic Set ◽  
Total Degree ◽  
Decision Making Problem ◽  
Different Types ◽  
Neutrosophic Graph ◽  
Real World Problems

AbstractFuzzy set and neutrosophic set are two efficient tools to handle the uncertainties and vagueness of any real-world problems. Neutrosophic set is more capable than fuzzy set to deal the uncertainties of a real-life problem. This research paper introduces some new concept of single-valued neutrosophic graph (SVNG). We have also presented some different operations on SVNG such as rejection, symmetric difference, maximal product, and residue product with appropriate examples, and some of their important theorems are also described. Then, we have described the concept of total degree of a neutrosophic graph with some interesting examples. We have also presented an efficient approach to solve a decision-making problem using SVNG.

On 2-absorbing bipolar fuzzy ideals over LA -semigroups

2021 ◽  
pp. 1-9
Author(s):  
Pairote Yiarayong
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Bipolar Fuzzy Sets ◽  
The Relationship

The aim of this manuscript is to apply bipolar fuzzy sets for dealing with several kinds of theories in LA -semigroups. To begin with, we introduce the concept of 2-absorbing (quasi-2-absorbing) bipolar fuzzy ideals and strongly 2-absorbing (quasi-strongly 2-absorbing) bipolar fuzzy ideals in LA -semigroups, and investigate several related properties. In particular, we show that a bipolar fuzzy set A = ( μ A P , μ A N ) over an LA -semigroup S is weakly 2-absorbing if and only if [ B ⊙ C ] ⊙ D ⪯ A implies B ⊙ C ⪯ A or C ⊙ D ⪯ A or B ⊙ D ⪯ A for any bipolar fuzzy sets B = ( μ B P , μ B N ) , C = ( μ C P , μ C N ) and D = ( μ D P , μ D N ) . Also, we give some characterizations of quasi-strongly 2-absorbing bipolar fuzzy ideals over an LA -semigroup S by bipolar fuzzy points. In conclusion of this paper we prove that the relationship between quasi-strongly 2-absorbing bipolar fuzzy ideals over an LA -semigroup S and quasi-2-absorbing bipolar fuzzy ideals over S.

An Extended Relational Model & SQL for Fuzzy Multidatabases

2011 ◽  
pp. 185-219
Author(s):  
Awadhesh Kumar Sharma ◽  
A. Goswami ◽  
D.K. Gupta
Keyword(s):  
Query Processing ◽  
Fuzzy Sets ◽  
Real World ◽  
Relational Model ◽  
Ambiguous Information ◽  
Fuzzy Query ◽  
Algebraic Properties ◽  
Recent Trends ◽  
Real World Problems

Many real world problems involve imprecise and ambiguous information rather than crisp information. Recent trends in the database paradigm are to incorporate fuzzy sets to tackle imprecise and ambiguous information of real world problems. Fuzzy query processing in multidatabases have been extensively studied, however, the same has rarely been addressed for fuzzy multidatabases. This chapter attempts to extend the SQL to formulate a global fuzzy query on a fuzzy multidatabase under FTS relational model discussed earlier. The chapter provides architecture for distributed fuzzy query processing with a strategy for fuzzy query decomposition and optimization. Proofs of consistent global fuzzy operations and some of algebraic properties of FTS Relational Model are also supplemented.

scholarly journals A Decision-making Problem as an Applications of Intuitionistic Fuzzy Set

2019 ◽  
Vol 9 (2) ◽  
pp. 5259-5261
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Decision Making Problem ◽  
Real World Problems

The fuzzy sets and Intuitionistic fuzzy sets are very useful concepts to elaborate the vagueness in real world problems. The objective of our study is to apply fuzzy set theory and Intuitionistic fuzzy set theory in decision making process. In this paper, we identify in which society a person has to purchase a house in order to fulfil his requirement to maximum extent. In our study we use intuitionistic fuzzy sets to find a relation between the societies and the parameters. And then we find a relation between a person and the parameters. We calculate Normalized Euclidean distance between two Intuitionistic fuzzy sets to make a decision of purchasing house in a society.

scholarly journals Multi-Agent Systems of Inverse Reinforcement Learners in Complex Games

2017 ◽  
Author(s):  
Dave Mobley
Keyword(s):  
Reinforcement Learning ◽  
Real World ◽  
Computer Games ◽  
Computer Game ◽  
Role Playing ◽  
Multi Agent Systems ◽  
Role Playing Games ◽  
Starting Point ◽  
Multi Agent ◽  
Real World Problems

Real-world problems exhibit a few defining criteria that make them hard for computers to solve. Problems such as driving a car or flying a helicopter have primary goals of reaching a destination as well as doing it safely and timely. These problems must each manage many resources and tasks to achieve their primary goals. The tasks themselves are made up of states that are represented by variables or features. As the feature set grows, the problems become intractable. Computer games are smaller problems but also are representative of real-world problems of this type. In my research, I will look at a particular class of computer game, namely computer role-playing games (RPGs), which are made up of a collection of overarching goals such as improving the player avatar, navigating a virtual world, and keeping the avatar alive. While playing there are also subtasks such as combatting other characters and managing inventory which are not primary, but yet important to overall game play. I will be exploring tiered Reinforcement Learning techniques coupled with training from expert policies using Inverse Reinforcement Learning as a starting point on learning how to play a complex game while attempting to extrapolate ideal goals and rewards.

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