Bipolar Fuzzy Research Articles

Anti-Homomorphisms in Bipolar Fuzzy Ideals and Bi-Ideals of Γ-Near Rings

Anti-Homomorphisms in Bipolar Fuzzy Ideals and Bi-Ideals of Γ-Near Rings

Selection of Energy Trading Platform for Peer-to-Peer (P2P) Energy Trading by Using a Multi-Attribute Decision-Making Approach Based on Bipolar Fuzzy Aczel-Alsina Prioritized Aggregation Operators

Selection of Energy Trading Platform for Peer-to-Peer (P2P) Energy Trading by Using a Multi-Attribute Decision-Making Approach Based on Bipolar Fuzzy Aczel-Alsina Prioritized Aggregation Operators

A New Approach on Bipolar Second Degree Perfect Fuzzy Matching for Bipolar Fuzzy Graphs Based on Vertices

Graph is a visual representation of data. In mathematics, graph is a structure which creates the pairwise relation between objects. The objects are known as nodes or vertices and the connection between two nodes are known as links or edges. A graph is a symmetric binary relation on a non-empty set whereas Fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. Bipolar Fuzzy graph is a generalization of graph theory by using bipolar Fuzzy set. The bipolar Fuzzy sets are the extension of Fuzzy sets. Our main objective is to introduce Bipolar Second Degree Perfect Fuzzy Matching for Bipolar Fuzzy Graph based on vertices. Secondly, we proved the necessary conditions under which they are equivalent and also proved that for a particular condition a perfect second-degree fuzzy matching is not a regular bipolar fuzzy graph. Next, we discussed about perfect second-degree Fuzzy matching and second degree fuzzy matching number for bipolar fuzzy graph on the cycle.

Bipolar Fuzzy Multi-Criteria Decision-Making Technique Based on Probability Aggregation Operators for Selection of Optimal Artificial Intelligence Framework

Artificial intelligence (AI) frameworks are essential for development since they offer pre-built tools and libraries that speed up and simplify the production of AI models, leveraging symmetry to save time and effort. They guarantee effective computing by modifying code for particular hardware, facilitating quicker testing and deployment. The identification of a suitable and optimal AI framework for development is a multi-criteria decision-making (MCDM) dilemma, where the considered AI frameworks for development are evaluated by considering various criteria and these criteria may have dual aspects (positive and negative). Thus, in this manuscript, we diagnosed a technique of MCDM within the bipolar fuzzy set (BFS) for identification and selection of optimal AI framework for development. In this regard, we diagnosed probability aggregation operators (AOs) within BFS, such as probability bipolar fuzzy weighted averaging (P-BFWA), probability bipolar fuzzy ordered weighted averaging (P-BFOWA), immediate probability bipolar fuzzy ordered weighted averaging (IP-BFOWA), probability bipolar fuzzy weighted geometric (P-BFWG), probability bipolar fuzzy ordered weighted geometric (P-BFOWH), and immediate probability bipolar fuzzy ordered weighted geometric (IP-BFOWG) operators. The diagnosed technique would be based on these invented probably AOs. Afterward, in this manuscript, we took a case study and obtained the optimal AI framework for development by employing the diagnosed technique of MCDM. We also investigated the comparison of the devised theory with certain prevailing theories to reveal the dominance and significance of the devised theory.

Piecewise Approximation for Bipolar Fuzzy Initial Value Problem

In this work, a new solution for the bipolar-fuzzy initial value problem is proposed. This method is obtained by approximating the solution by piece-wise polynomial of order three. The existence and uniqueness of the solution and convergence of the method are discussed in detail. Finally, for more explanation, several numerical examples are solved.

Properties of Bipolar Fuzzy Automata

This work focuses on establishing the relationship between bipolar fuzzy automata, reverse bipolar fuzzy automata, and double bipolar fuzzy automata. It also introduces the concepts of bipolar fuzzy subsystems, reverse bipolar fuzzy subsystems, and double bipolar fuzzy subsystems, and explores various properties associated with these subsystems. Furthermore, the paper aims to introduce the categorical aspects of bipolar fuzzy automata and reverse bipolar fuzzy automata, along with their functorial relationship.

Retracted: Bipolar Fuzzy Implicative Ideals of BCK-Algebras

Retracted: Bipolar Fuzzy Implicative Ideals of BCK-Algebras

Some Characterizations of Whole Edge Domination in Bipolar Fuzzy Graphs

In this paper, Some bounds, theorems and results on whole edge domination number in bipolar fuzzy graph are established with support of some examples. The concepts of perfect, complete perfect and semi-perfect whole edge domination in bipolar fuzzy graph are discussed and investigated with some of their properties and also results on perfect contributed via the support of some examples.

Application of Bipolar Fuzzy Set to a Novel of Fuzzy Ideal in $\Gamma$-Semigroups

In this paper we define new types of bipolar fuzzy ideals, bipolar fuzzy almost ideals in $\Gamma$-semigroups. We discussed properties of bipolar fuzzy ideals, bipolar fuzzy almost ideals, minimal bipolar fuzzy ideal, minimal bipolar almost ideal in $\Gamma$-semigroups. Moreover, we prove connection between almost ideals and bipolar fuzzy almost ideals of $\Gamma$-semigroups.

A bipolar fuzzy [formula omitted]-competition graph based ARAS technique for prioritizing COVID-19 vaccines

A bipolar fuzzy competition graph helps to examine the competition between two vertices when they have a common out-neighbourhood. With this idea, the bipolar fuzzy p-competition graph (BFpCG) can be defined when two vertices have p common out-neighbourhood. In this study, the above-said concepts are defined along with certain characteristics such as low, high, semi-perfect and perfect competitive competition graphs based on the number of components, and certain important results are derived. Moreover, the extensions of BFpCG are discussed by considering various situations and illustrated by a food web problem of 13 species. Besides, an application is taken to find the competition among the COVID-19 vaccines against five mutations: Alpha, Beta, Gamma, Delta and Omicron. Multi-criteria decision-making (MCDM) techniques utilize to access the prioritization problems. The additive ratio assessment (ARAS) is a robust MCDM technique and it simplifies complex decision-making problems through the utility degree. An efficient outcome can be attained by this technique when it works with positive and negative perceptions. Therefore, this study constructs a novel bipolar fuzzy ARAS system based on the BFpCG. To demonstrate the applicability of the proposed system, an application is taken in prioritizing COVID-19 vaccines, where Moderna and CoronaVac resulted in first and last rank, respectively. For this purpose, the efficacy rate of the vaccines against severe disease is considered. Finally, the outcomes are validated through sensitivity and comparative analyses. Then, the managerial implications, future works and limitations of the study are provided to explore the proposed research.

Probabilistic hesitant bipolar fuzzy Hamacher prioritized aggregation operators and their application in multi-criteria group decision-making

Probabilistic hesitant bipolar fuzzy Hamacher prioritized aggregation operators and their application in multi-criteria group decision-making

An interpreter ranking index-based MCDM technique for COVID-19 treatments under a bipolar fuzzy environment

The entire world is currently fighting the severe and dangerous pandemic COVID-19, which is causing bodily suffering and mental distress due to the rapidly increasing number of infected patients and deaths worldwide. Many COVID-19 treatments are going on in India, and some treatments are under development for these patients. But, treatment selection for the COVID-19 patients is challenging in the present situation. Through the multi-criteria decision-making technique, they can select the COVID-19 treatments easily. Therefore, we have developed an MCDM technique to select COVID-19 treatments in India. This paper invented the value and ambiguity of bipolar fuzzy (BF) numbers. Additionally, some fundamental theorems and properties of BF-numbers are studied. A novel positive and negative interpreter ranking index of BF numbers has been introduced. In the present day, most human decision-making relies heavily on bipolar fuzzy information. Hence, we developed an MCDM technique with bipolar fuzzy details. A comprehensive range of human decisions for selecting COVID-19 treatments is based on positive and negative double-sided or bipolar judgemental thinking. To select COVID-19 treatments in India, we have applied the proposed MCDM technique with BTrF information. Moreover, to demonstrate the applicability of our proposed MCDM method, we have considered a numerical example with BF data. Finally, we give the comparison study to show the effectiveness of our proposed MCDM method with other existing decision-making methods.

A Genetic Algorithm for Solving Nonlinear Optimization Problem with Max-Archimedean Bipolar Fuzzy Relation Equations

This paper discusses a nonlinear optimization problem with the system of max-Archimedean bipolar fuzzy relation equations as constraints. Some results related to the structure of the solution set of max-Archimedean bipolar fuzzy relation equations are proved. Using these results, a genetic algorithm is proposed to solve the problem for obtaining optimal or converging solutions. The effectiveness of the algorithm is also compared with other methods found in the literature. The previous methods require conversion of the problem into 0-1 mixed integer optimization problem solvable by some nonlinear optimization solvers and thereby, the computational work may increase with the size of the problem. Some test problems are developed to evaluate the performance of the proposed algorithm.

Paper making raw materials assessed by bipolar fuzzy environment

Paper is one of the most versatile products of everyday life. It is indeed the primary material used for written communication and distribution of information. Paper is composed of cellulose fibers. Paper making technologyis the process of conversion of raw materials into pulp and paper products. Here PROMETHEE method based on bipolar fuzzy set is dealt with. To obtain the weights based on each criteria, an entropy measure on bipolar fuzzy set is developed. Further, bipolar fuzzy preference function is defined to form bipolar fuzzy preference and aggregated preference matrices. Finally, net outranking flow is calculated and the ranking of the alternative is determined. Here, paper made from wood pulp, rag pulp, grass, baggase and hemp are evaluated using bipolar fuzzy PROMETHEE method based on the properties brightness, durability, moisture content and smoothness. It is found using this method that the paper made from rag pulp is superior than the others.

Regular and Intra-Regular Ternary Semirings in Terms of m-Polar Fuzzy Ideals

In practical applications, the basic fuzzy set is used via symmetric uncertainty variables. In the research field, it is comparatively rare to discuss two-fold uncertainty due to its complication. To deal with the multi-polar uncertainty in real life problems, m-polar (multi-polar) fuzzy (m-PF) sets are put forward. The main objective of this paper is to explore the idea of m-PF sets, which is a generalization of bipolar fuzzy (BPF) sets, in ternary semirings. The major aspects and novel distinctions of this work are that it builds any multi-person, multi-period, multi-criteria, and complex hierarchical problems. The main focus of this study is to confine generalization of some important results of BPF sets to the results of m-PF sets. In this research, the notions of m-polar fuzzy ternary subsemiring (m-PFSS), m-polar fuzzy ideal (m-PFI), m-polar fuzzy generalized bi-ideal (m-PFGBI), m-polar fuzzy bi-ideal (m-PFBI), and m-polar fuzzy quasi-ideal (m-PFQI) in ternary semirings are introduced. Moreover, this paper deals with several important properties of m-PFIs and characterizes regular and intra-regular ternary semiring in terms of these ideals.

Essential Bipolar Fuzzy Ideals in Semigroups

In this paper, we give the concepts of essential bipolar fuzzy ideals in semigroups. We discuss the basic properties and relationships between essential bipolar fuzzy ideals and essential ideals in semigroups Finally, we extend to 0-essential bipolar fuzzy ideals in semigroups.

Retracted: Novel Concepts in Bipolar Fuzzy Graphs with Applications

Retracted: Novel Concepts in Bipolar Fuzzy Graphs with Applications

A decision-making strategy to combat CO$ _2 $ emissions using sine trigonometric aggregation operators with cubic bipolar fuzzy input

<abstract><p>A cubic bipolar fuzzy set (CBFS) is by far the most efficient model for handling bipolar fuzziness because it carries both single-valued (SV) and interval-valued (Ⅳ) bipolar fuzzy numbers at the same time. The sine trigonometric function possesses two consequential qualities, namely, periodicity and symmetry, both of which are helpful tools for matching decision makers' conjectures. This article aims to integrate the sine function and cubic bipolar fuzzy data. As a result, sine trigonometric operational laws (STOLs) for cubic bipolar fuzzy numbers (CBFNs) are defined in this article. Premised on these laws, a substantial range of aggregation operators (AOs) are introduced. Certain features of these operators, including monotonicity, idempotency, and boundedness, are explored as well. Using the proffered AOs, a novel multi-criteria group decision-making (MCGDM) strategy is developed. An extensive case study of carbon capture and storage (CCS) technology has been provided to show the viability of the suggested method. A numerical example is provided to manifest the feasibility of the developed approach. Finally, a comparison study is executed to discuss the efficacy of the novel MCGDM framework.</p></abstract>

Cayley bipolar fuzzy graphs associated with bipolar fuzzy groups

Recently, bipolar fuzzy graph is a growing research topic as it is the generalisation of fuzzy graphs. Let G be a non-trivial group and S be a non-empty subset of G such that not containing the identity element of G and S = S-1 = {s-1| s ∈ S}. The Cayley graph Γ = Cay (G, S) is the graph whose vertex set V(Γ) is G and edge set E(Γ) is {{g, gs}| g ∈ G, s ∈ S}. A non-empty subset S of G such that not containing the identity and S = S-1 is referred to as a Cayley subset of G, and the Cayley graph Γ = Cay (G, S) is referred to as a Cayley graph of G relative to S. In this paper, we introduce the concept of Cayley bipolar fuzzy graphs on the bipolar fuzzy groups. Also some properties of Cayley bipolar fuzzy graphs as connectivity and transitivity are provided.

Cubic bipolar fuzzy VIKOR and ELECTRE-II algorithms for efficient freight transportation in Industry 4.0

<abstract><p>The theory of cubic bipolar fuzzy sets (CBFSs) is a robust approach for dealing with vagueness and bipolarity in real-life circumstances. This theory provides a hybrid machine learning paradigm that can accurately describe two-sided contrasting features for medical diagnosis. The ELECTRE-II model, which is extensively used, is expanded in this article to include the cubic bipolar fuzzy (CBF) context. In order to produce a comprehensive preference ordering of actions, ELECTRE-II establishes two different forms of embedded outranking relations while taking into account the subjective human judgments. A huge number of applications have been created by its variations under various models, considering the CBF model's greater capacity to deal. For opinions in the adaptive CBF structure with unknown information, the CBF-ELECTRE-II group decision support method is described. With the use of proper CBF aggregation operations, the expert CBF views on each alternative and criterion are compiled in the first step. The approach then constructs weak and strong outranking relations and offers three distinct CBF outranking set kinds ("concordance", "indifferent" and "discordance" sets). Strong and weak outranking graphs serve as a visual depiction of the latter, which is finally studied by a rigorous iterative procedure that yields a preferred system. For these objectives, integrated CBF-VIKOR and CBF-ELECTRE-II techniques are developed for multi-criteria group decision making (MCDGM). Finally, suggested techniques are recommended to determine ranking index of efficient road freight transportation (FRT) in Industry 4.0. The ranking index and optimal decision are also computed with other techniques to demonstrate robustness of proposed MCDGM approach.</p></abstract>