Bipolar Fuzzy Sets Research Articles

TOPSIS method based on connection number of set pair analysis subject to bipolar fuzzy environment with application in decision making

In this manuscript, we develop TOPSIS (Technique for order of preference by similarity to ideal solution) method in the setting of bipolar fuzzy environment which has the ability to deal the data while keeping in view the positive and negative aspects. By using bipolar fuzzy sets, we establish the novel concept of rating the numerous preferences of any object described through the connection number(CN) of set pair analysis(SPA). In this regard, we extend the TOPSIS method based on the connection number(CN) of set pair analysis(SPA) in the frame of bipolar fuzzy sets. For the sake of verification, effectiveness and superiority of our method, we conduct the comparative study of some real life problem related to decision making theory. Moreover, we observe that our proposed method also fulfills the existing test criterions.

Anti homomorphism and homomorphism of bipolar valued multi Fuzzy HX-subgroups and it’s normal

In this article, homomorphism and anti-homomorphism bipolar valued multi normal fuzzy HX subgroup of a HX group is studied, discussed and their properties are introduced. The theorems presented in this article are considered a generalization of what has been publishedthrough the concept of fuzzy sets. As the concept of fuzzy sets was introduced by Zadeh in 1965, after that this concept, we expanded into more than one types, intuitionistic fuzzy set, bipolar fuzzy sets, tripolar fuzzy set, and bipolar valued multi fuzzy set are one of this.

Contemporary Algebraic Attributes of the q‐Rung Orthopair Complex Fuzzy Subgroups

A more advanced form of complex fuzzy sets is q‐rung orthopair complex fuzzy (q -ROCF) sets, which offer an additional and broad visualization of the uncertainty present in the unit disk. In comparison to complex intuitionistic fuzzy sets and complex bipolar fuzzy sets, the q -ROCF set is more appropriate and versatile. Their ability to describe a broader range of unclear information makes them distinguishable because the real part of a complex‐valued membership degree and the real part of a complex‐valued nonmembership degree have a sum of qth powers that is equal to or less than one (similarly for the imaginary part of a complex‐valued). In terms of the characteristics of the q -ROCF set, we propose the concept of q -ROCF subgroups and investigate some fundamental features under the q -ROCF set. Moreover, we show that every intuitionistic complex fuzzy subgroup is a q -ROCF subgroup. Also, we use this approach to define q -ROCF level subgroups, q -ROCF cosets, and q -ROCF normal subgroups of a certain group as well as to investigate some of their algebraic characteristics. Furthermore, we develop the concept of group homomorphism, images, and preimages under the influence of the q -ROCF subgroup.

Dynamic bipolar fuzzy aggregation operators: A novel approach for emerging technology selection in enterprise integration

<abstract> <p>Emerging technology selection is crucial for enterprise integration, driving innovation, competitiveness, and streamlining operations across diverse sectors like finance and healthcare. However, the decision-making process for technology adoption is often complex and fraught with uncertainties. Bipolar fuzzy sets offer a nuanced representation of uncertainty, allowing for simultaneous positive and negative membership degrees, making them valuable in decision-making and expert systems. In this paper, we introduce dynamic averaging and dynamic geometric operators under bipolar fuzzy environment. We also establish some of the fundamental crucial features of these operators. Moreover, we present a step by step mechanism to solve MADM problem under bipolar fuzzy dynamic aggregation operators. In addition, these new techniques are successfully applied for the selection of the most promising emerging technology for enterprise integration. Finally, a comparative study is conducted to show the validity and practicability of the proposed techniques in comparison to existing methods.</p> </abstract>

An application of fuzzy bipolar weighted correlation coefficient in decision-making problem.

Diagnosing and finding the disease in medical sciences is a complex procedure. The basic steps involved in finding starts with signs, symptoms, and test. This study is based on the diagnosis of a skin disorder. The identification of a disease has been made on the basis of symptoms that sometimes show bipolarity. To address this bipolarity, the bipolar fuzzy sets are used as bipolar fuzzy sets cover the positive as well as negative aspects of a specific symptom. It is combined with the idea of soft sets, which gives more precise results. We have proposed a new technique in which a correlation coefficient is used to measure bipolar fuzzy soft set, which has been applied for diagnosis. The BFSSs deal most effectively with dual and fuzzy information. The correlation coefficient and the weighted correlation coefficient of BFSSs are suggested in this research. Based on said techniques, the decision-making method is suggested under a bipolar fuzzy environment to resolve ambiguous and unclear information. The implementation and effectiveness of the proposed and existing strategy has been checked by numerical computation.

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.

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.

Mathematical depiction of costing perspectives allied with the dynamics of processed food supply chain

PurposeThis study aims to ground the assessment of the various costing perspectives associated with the dynamics of processed food supply chains (FSCs), for questing the avenues of profitability within a food processing enterprise.Design/methodology/approachThis study underpins the development of the relation hierarchical model, binding the cluster of the key costing enactors, with the various incurred costs in the food supply chain performance system. The developed model is seeded by the inputs gathered from the case enterprises under consideration, which is further contemplated by extending the fundamentals of bipolar fuzzy sets with the methodology of ELECTRE-II.FindingsSecured primacies owing to the mutual correspondence between the costing cluster reveal the impact of procurement cost in the dynamics of FSC. Furthermore, an inference is grounded relative to the other entities of total costs like investment, production, transportation, distribution and retailing by considering the perspective of a case enterprise. It yields that procurement costing procedurals need to be deliberated supremely, considering the vitality of the costing perspective associated with the other procedurals of the case enterprise.Originality/valueThe framework developed in the presented work clusters the various costing enactors along with the costings in processed FSCs, binding its holistic perspective rather than the discrete approach. The present research work provides an origin to explore the various miniatures more precisely succeeding to secure primacies for upscaling the profit-cost notions. As costing determines the avenues bundled with the production and consumption of various food commodities.

Pessimistic multigranulation rough bipolar fuzzy set and their application in medical diagnosis

Pessimistic multigranulation rough bipolar fuzzy set and their application in medical diagnosis

Computational bipolar fuzzy soft matrices with applications in decision making problems

A fuzzy soft matrix is a type of mathematical matrix that combines the principles of fuzzy set theory and soft set theory. It is used to handle uncertainty and vagueness in decision-making problems. Fuzzy soft matrix theory cannot handle negative information. To overcome this difficulty, we define the notion of bipolar fuzzy soft (BFS) matrices and study their fundamental properties. We define products of BFS matrices and investigate some useful properties and results. We also give an application of bipolar fuzzy soft matrices to decision-making problems. We propose a decision-making algorithm based on computer programs under the environment of the bipolar fuzzy soft sets.

A novel multigranulation roughness of bipolar fuzzy set over dual universes and its applications

In the world, multigranulation rough sets and bipolar fuzzy sets are the practical tools for dealing with the uncertainty, vagueness, and imperfection that frequently arise in decision making problems. The goal of multigranulation rough sets is to characterize uncertain situations in various granularity spaces, whereas bipolar fuzzy sets (BFSs) have the capacity to handle uncertainty as well as informational bipolarity in a variety of contexts. This article examines the optimistic multigranulation rough approximation of a BFS in the light of multi-soft binary relations across two different universes. We investigate some algebraic properties of our newly constructed optimistic multigranulation rough set scheme. Measures of accuracy and roughness are also covered in this paper. Finally, two decision algorithms are designed with respect to aftersets and foresets that are applied to a decision making problem in disease diagnoses, and the applicability of the method is illustrated by a numerical example.

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.

Topological structures on cubic bipolar fuzzy sets with linear assignment model and SIR method for healthcare

The idea of a cubic bipolar fuzzy set (CBFS) is a new hybrid extension of the cubic set (CS) and the bipolar fuzzy set (BFS). A CBFS is a strong model to deal with bipolarity and fuzziness in terms of positive membership grades (PMGs) and negative membership grades (NMGs). A positive interval and a positive numbers represent a PMG to express the degree of belongingness of a specific property, and a negative interval and a negative number represent a NMG which defines the degree of non-belongingness of the specific property (or satisfaction level of its counter property). The aim of this paper is to define the cubic bipolar fuzzy topology under P-order (CBFSP topology) as well as the cubic bipolar fuzzy topology under R-order (CBFSR topology). We investigate certain properties and results of CBFSP topology and CBFSR topology. Topological structures on CBFSs are helping in the development of new artificial intelligence (AI) techniques for healthcare domain strategies and investigating various critical diseases. Such techniques allow for the early detection and investigation of diseases, assisting clinicians in minimizing the possible risk factors. An extended linear assignment model (LAM) and superiority and inferiority ranking method (SIR method) are proposed for healthcare diagnosis based on newly developed structures. The proposed LAM and SIR method are successfully applied for investigation of critical diseases. Moreover, we discuss a comparison analysis of investigations made by suggested techniques with some existing approaches.

Quotient bipolar fuzzy soft sets of hypervector spaces and bipolar fuzzy soft sets of quotient hypervector spaces

In this paper, two related quotient structures are investigated utilizing the concept of coset. At first, a new hypervector space F/V = (F/V,\circ,\circledcirc,K) is created, which is composed of all cosets of a bipolar fuzzy soft set (F;A) over a hypervector space V . Then it will be shown that dim F/V = dim V/W, where the quotient hypervector space V/W includes all cosets of an especial subhyperspace W of V. Also, three bipolar fuzzy soft sets over the quotient hypervector space V/W are presented and in this way some new bipolar fuzzy soft hypervector spaces are defined.

Possibility neutrosophic bipolar fuzzy soft sets and their applications

In this work, the possibility neutrosophic bipolar soft sets interact with the possibility bipolar fuzzy soft sets, as well as complementation, union, intersection, AND, and OR. This paper extends the concept of bipolar neutrosophic soft sets to the possibility neutrosophic bipolar soft sets. Our main goal was to demonstrate De Morgan’s law, associate law and distributive law, which are all the laws related to the possibility neutrosophic bipolar soft sets. Also, we present an algorithm that uses a soft set model to solve the decision-making problem primarily in order to simplify the process.

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>

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>

Radial basis function bipolar fuzzy neural network

This paper deals with radial basis function neural network on bipolar fuzzy sets. Bipolar Gaussian positive and negative membership function acts as activation function in this network. An algorithm is developed based on Radial basis function bipolar fuzzy neural network. Further, an example is given based on the technique of injection molding process using thermoplastic raw materials, to select the highly durable plastic material product. Four thermoplastic materials such as Polyethylene terephthalate, Polyvinyl chloride, Polypropylene, Polystyrene with physical composition such as oxygen barrier, rigidity, moisture barrier, resistance to sunlight are examined. The plastic processing technology is compared with radial basis function bipolar fuzzy neural network. Considering the feeding section as the input layer, the processing section as hidden layer and ejecting section as output layer, the durability of the thermoplastic materials are estimated. It is found that Polyvinyl chloride bottles are more enduring than the other three thermoplastic material bottles.