Bipolar Fuzzy Research Articles

An Innovative Perspective on Bipolar Fuzzy Fantastic Ideals in BCK/BCI-Algebras

In this paper, we propose the concept of $(\in, \in \vee (\varphi^{\divideontimes}, \check{q_{\varphi}}))$-bipolar fuzzy ideals in BCK/BCI-algebras. We show that an $(\in, \in \vee \check{q_{\varphi}})$-bipolar fuzzy ideal is an $(\in, \in \vee (\varphi^{\divideontimes}, \check{q_{\varphi}}))$-bipolar fuzzy ideal. For a BCK/BCI-algebra, it has been shown that an $(\in, \in \vee (\varphi^{\divideontimes}, \check{q_{\varphi}})$-bipolar fuzzy ideal is an $(\in, \in \vee \check{q})$-bipolar fuzzy ideal of $\check{\aleph}$, but not conversely, and then an example is given. We introduce the concept of $(\in, \in \vee (\varphi^{\divideontimes}, \check{q_{\varphi}}))$-bipolar fuzzy fantastic ideals in BCK/BCI-algebras. It has been shown that an $(\in, \in \vee (\varphi^{\divideontimes}, \check{q_{\varphi}}))$-bipolar fuzzy fantastic ideal is an $(\in, \in)$-bipolar fuzzy ideal in BCK/BCI-algebras. Furthermore, the connection between $(\in, \in \vee (\varphi^{\divideontimes}, \check{q_{\varphi}}))$-bipolar fuzzy fantastic ideals and fantastic ideals are established.

Bipolar Expected Value-based MCDM Technique for Wastewater Management under Trapezoidal Bipolar Fuzzy Environment

: Kolkata is located on western bank of the Hooghly River. Wastewater from the city is discharged into this river and pollutes the river water. It causes maximum negative effects than positive impacts. Many uncertainties and bipolarity occur for this reason. Through the bipolar fuzzy concept, we can easily take the determination for this situation. A bipolar fuzzy expected is an effective tool for illustrating uncertainty and fuzziness in a decision-making problem. There-fore, in this paper, we have invented the bipolar expected value of bipolar fuzzy numbers. In addition, we have invented a few formulae and a theorem based on bipolar expected values. Using this bipolar expected value, we developed a novel MCDM technique, and it's employed for wastewater management problems in Kolkata city under a bipolar environment. Numerically, we have solved the wastewater management problem under a bipolar fuzzy environment.

Translation of a Bipolar Fuzzy Set in Hilbert Algebras

This study explores the application of bipolar fuzzy set theory within Hilbert algebras, introducing and examining the concept of bipolar fuzzy (β, α)-translations of a bipolar fuzzy set φ =(φ+, φ−) in two distinct forms: Type I and Type II. Fundamental properties of these bipolar fuzzy translations are investigated in depth, alongside the introduction of bipolar fuzzy extensions andintensities, broadening the utility and flexibility of bipolar fuzzy sets in capturing nuanced bipolar information. Moreover, this work addresses the intricate relationships between the complement of a bipolar fuzzy subalgebra, bipolar fuzzy ideal, and bipolar fuzzy deductive system with respect to their level cuts. The findings significantly contribute to the broader theoretical foundation and potential applications of bipolar fuzzy logic in Hilbert algebras, offering valuable insights for managing complex bipolar information in uncertain environments.

Characterizations of Regular and Intra-regular Ordered Semigroups by using Generalized Interval Valued Bipolar Fuzzy Quasi-Ideals

In this article, we introduce the concept of a generalized interval-valued bipolar fuzzy quasi-ideal and investigate its properties. We explore the relationship between generalized interval-valued bipolar fuzzy quasi-ideals and generalized interval-valued bipolar fuzzy ideals. Furthermore, we characterize regular and intra-regular ordered semigroups by utilizing generalized interval valued bipolar fuzzy quasi-ideals.

An Extension of VIKOR Approach for MCDM Using Bipolar Fuzzy Preference δ-Covering Based Bipolar Fuzzy Rough Set Model

Bipolarity highlights the positive and negative facets of a certain dilemma. This script aims to propose a novel multi-criteria decision-making (MCDM) approach based on bipolar fuzzy preference δ-covering based bipolar fuzzy rough set (BFPδC-BFRS) model by combining the VIKOR (VIseKriterijumska Optimizacija I Kompromisno Rasenje) scheme. The VIKOR scheme is viewed as a beneficial MCDM strategy, particularly in situations where an expert is incapable of making the right decision at the beginning of system design. The VIKOR method works well for problems with competing attributes because it operates under the presumptions that compromise is acceptable in conflict resolution, the expert seeks a solution that is extremely close to the best, and all developed attributes are taken into consideration when processing the various alternatives. In this study, firstly, we proposed an integrated MCDM based on BFPδC-BFRSs using the VIKOR methodology. Moreover, we solve a real-world illustration to show the effectiveness of the expanded VIKOR approach. Finally, we demonstrate a detailed comparative analysis of the proposed methodology with some prevalent decision-making approaches to substantiate the accountability of the recommended scheme.

MCDM Method for Managing the Water Resources Based on Possibility Theory under Bipolar Fuzzy Environment

Background: Uncertainty is a common factor in every real-life decision-making problem. Possibility theory is one uncertainty theory in Fuzzy sets (FS). The possibility-based decision-making under a fuzzy environment is a significant multi-criteria decision-making (MCDM) method. Methods: A bipolar FS is an extension of a fuzzy set. With the bipolarity concept, we can handle both positive and negative thoughts. In this study, we have provided a possibility mean of a bipolar fuzzy number. We have developed a ranking method for bipolar fuzzy numbers using this pos-sibility concept. A novel possibility MCDM method is suggested for solving the water resources management (WRM) in the Nagpur area, Maharashtra State, India. Results: The MCDM technique is an effective tool for solving WRM problems in an area. Many uncertainties and bipolarities occur together in Nagpur water resources. WRM technique with fuzzy is one approach that can be used to solve the area's water problem. We have used the pro-posed MCDM to address the water-related issues of this district. With this proposed MCDM method, numerically, we employed water resource problems under a bipolar fuzzy environ-ment. Conclusion: The Nagpur area is covered by Basaltic rock and faces water shortage. The district is experiencing severe water shortages. Groundwater, surface water, and rainfall are three water resources considered as alternatives. According to the proposed MCDM technique in Nagpur district, Groundwater is the best water source from three flanks: quality of water, affordability, and availability.

Second Order Bipolar Fuzzy Matrix and its Application in Medical Diagnosis

Second Order Bipolar Fuzzy Matrix and its Application in Medical Diagnosis

On Null Vertex in Bipolar Fuzzy Graphs

We present a novel vertex in Bipolar fuzzy graph, null vertex, which is distinct from boundary vertex and interior vertex and also attempt a study on null vertex in bipolar fuzzy closed helm graph CHn.

Multi-Q Cubic Bipolar Fuzzy Soft Sets and Cosine Similarity Methods for Multi-Criteria Decision Making

This study introduces a novel mathematical tool for representing imprecise and ambiguous data: the multi-q cubic bipolar fuzzy soft set. Building upon established bipolar fuzzy sets and soft sets, this paper fist defines the concept of multi-q cubic bipolar fuzzy sets and their fundamental properties. Mathematical operations such as complement, union, and intersection are then developed for these sets. The core contribution lies in the introduction of multi-q cubic bipolar fuzzy soft sets. This new tool allows for a more nuanced representation of imprecise data compared to existing approaches. Key operations for manipulating these sets, including complement, restriction, and expansion, are defined. The applicability of multi-q cubic bipolar fuzzy soft sets extends to various domains, including multi-criteria decision making and problem solving. Illustrative examples demonstrate the practical utility of this innovative concept.

The novel WASPAS method for roughness of bipolar fuzzy sets based bipolar fuzzy covering

The research employs Covering-based Rough Set and Fuzzy Set theories to handle uncertainty in data analysis. However, when dealing with data uncertainty and bipolarity in various scenarios, the Bipolar Fuzzy Set (BFS) theory proves advantageous by simultaneously managing positive and negative information. Other sets, such as traditional fuzzy sets, often fail to capture this duality, leading to less comprehensive data analysis. This study pioneers a new methodology called the Theory of Roughness of Bipolar Fuzzy Sets, integrating Fuzzy Covering, Monotone Fuzzy Covering, and Bipolar Fuzzy Covering to propose an innovative decision-making approach. This novel concept undergoes comprehensive structural analysis. By incorporating the bipolar fuzzy covering based bipolar fuzzy rough set ( BFCBFRS ) model into conventional decision-making methods like the WASPAS technique, the research introduces a fresh perspective to address Multi-Criteria Decision-Making ( MCDM ) challenges. The efficacy of this extended method is evaluated by applying it to agricultural diagnosis, demonstrating its superiority over existing approaches through comparative analysis.

Bipolar Fuzzy Commutative Ideals in BCK-algebras

This paper presents the concept of the notions of bipolar fuzzy commutative ideals of a BCK-algebra. We also study various properties regarding this concept. We prove various characterisations for bipolar fuzzy commutative ideals. Moreover, a relationship between bipolar fuzzy commutative ideals and bipolar fuzzy positive implicative ideals is presented. In addition, we present the notation of bipolar fuzzy characteristic commutative ideal. Then a relationship between a bipolar fuzzy characteristic commutative ideal and its level-cut commutative ideals is provided.

Resource allocation strategy selection for 5G network by using multi-attribute decision-making approach based on tangent trigonometric bipolar fuzzy aggregation operators

Resource allocation strategy selection for 5G network by using multi-attribute decision-making approach based on tangent trigonometric bipolar fuzzy aggregation operators

Domination on Bipolar Fuzzy Graph Operations: Principles, Proofs, and Examples

Bipolar fuzzy graphs, capable of capturing situations with both positive and negative memberships, have found diverse applications in various disciplines, including decision-making, computer science, and social network analysis. This study investigates the domain of domination and global domination numbers within bipolar fuzzy graphs, owing to their relevance in these aforementioned practical fields. In this study, we introduce certain operations on bipolar fuzzy graphs, such as intersection, join, and union of two graphs. Furthermore, we analyze the domination number and the global domination number for various operations on bipolar fuzzy graphs, including intersection, join, and union of fuzzy graphs and their complements.

A Study on Quotient Structures of Bipolar Fuzzy Finite State Machines

This article introduces different congruence relations on the bipolar fuzzy set associated with the bipolar fuzzy finite state machine. Each congruence relation associates a semigroup with the bipolar fuzzy finite automata. We also discuss characterizing a bipolar fuzzy finite state machine by defining an admissible relation.

A study on coopetition using bipolar fuzzy bunch graphs

Several methodologies have been proposed in the literature of graph theory for depicting collaboration among entities. However, in these studies, the measure of collaboration is taken based on the crisp graphical properties and discusses only its positive effects. In this manuscript, we discuss the simultaneous collaboration and competition that are observed among individuals, organizations, countries, communities and many others. The notion of bipolar fuzzy bunch graph (BFBG) is introduced in this study to effectively capture the positive and negative effects of both the terms collaboration and competition, which is jointly called coopetition. The goal of this paper is to introduce an improved representation and analytical measure for coopetition. To further enrich the literature on competition graphs, the notion of survival and winning competition among species has been introduced and also provides its bipolar fuzzy competition degrees. We also introduce two types of coopetition measures to understand the ranking structure of entities (i.e. which node batter collaborates and competes with other nodes) in the network: a) bipolar fuzzy coopetition degree and b) bipolar fuzzy coopatition index. In the form of a bipolar fuzzy coopetition graph, we find evidence to validate our framework and computations. We gathered research articles on COVID-19 and their citations over a specific time period from a specific journal. To demonstrate our approach, we displayed bipolar fuzzy collaboration and competition of various countries on COVID-19 and classified their rankings based on their positive and negative coopetition indices.

Intelligent decision support system for pulmonary tuberculosis detection using bipolar fuzzy utility matrix and bipolar Mamdani fuzzy inference system

Tuberculosis (TB) stands as the second leading global infectious cause of death, following closely behind the impact of COVID-19. The standard approach to diagnose TB involves skin tests, but these tests can yield inaccurate results due to limited access to healthcare and insufficient diagnostic resources. To enhance diagnostic accuracy, this study introduces a novel approach employing a Bipolar Fuzzy Utility Matrix Inference System (BFUMIS) and a Bipolar Mamdani Fuzzy Inference System (BMFIS) to assess TB disease levels. By considering factors associated with the causation of TB, the study devises suitable membership functions for bipolar fuzzy sets (BFS) using both triangular and trapezoidal fuzzy numbers. Using a point factor scale, the study clusters the rules systematically and assesses the level of uncertainty within these grouped rules by utilizing bipolar triangular fuzzy numbers (BTFN). To handle the BTFN, this study proposes converting bipolar triangular fuzzy into bipolar crisp score (CBTFBCS) algorithm as a defuzzification method. The optimal bipolar fuzzy utility sets (BFUS) are determined from the bipolar fuzzy utility matrix to identify patients’ TB disease levels. These sets play a pivotal role in characterizing the severity of TB disease levels in patients. Additionally, rigorous validation of the utility framework is accomplished through measures of bipolar fuzzy satisfactory factors and sensitivity analyses. Furthermore, the study introduces the BMFIS, which presents a novel perspective on the conventional fuzzy inference system. This innovative system integrates the Mamdani fuzzy inference system (MFIS) into a bipolar fuzzy context, enriching the diagnostic process with enhanced insights. To demonstrate the efficacy of the proposed methods, extensive validation is carried out using actual clinical data. The performance metrics used in this validation effectively demonstrate the superiority of the proposed approach.

Bipolar Fuzzy Supra Topology via (Q-) Neighborhood and Its Application in Data Mining Process

The aim of this study is to provide neighborhood structures in bipolar fuzzy supra topological space and to show the applicability of bipolar fuzzy supra topology to the medical diagnosis problem. Firstly, we give some properties related to bipolar fuzzy points and their neighborhood structure in bipolar fuzzy supra topological spaces. Then, we consider another important structure, “quasi-coincident”, in the case of bipolar fuzzy points and bipolar fuzzy sets. Then, we introduce the corresponding neighborhood structure called “Q-neighborhood system” by using the quasi-coincident relations. Furthermore, we also investigate the characterization of bipolar fuzzy supra topological space in terms of quasi-neighborhoods. Finally, we present a new method to solve medical diagnosis problems by using the bipolar fuzzy score function.

Neutrosophic bipolar fuzzy decision-based approach for developing sustainable circular business model innovation tools

The circular economy (CE) has been identified as a possible catalyst for sustainable development by business, academics, and policymakers. To aid company developers in creating and improving business models that incorporate circularity, a variety of tools for circular business model innovation (CBMI) have been proposed. Nevertheless, the existing tools failed to consider sustainability or CE in their advancements. Currently, there is no research that has presented a complete dataset including all potential tools that may be created based on the CE’ sustainability performance attributes. Moreover, there has been a dearth of research conducted to assess and model these tools in order to determine the most efficient ones, which has resulted in a research gap. This paper constructs a decision matrix of CBMI tools by intersecting 100 CBMI tools with 10 CE’ sustainability performance attributes. The modeling of CBMI tools falls under Multiple Attribute Decision Making (MADM) due to the presence of many attributes, varying importance levels of these attributes, and the and variation in data. Thus, the fuzzy weighted with zero inconsistency (FWZIC) method is reformulated under neutrosophic bipolar fuzzy sets (NBFS) to determine the weight of CE's sustainability performance attributes. The matrix that has been constructed and the resulting weight values are fed into the CODAS method in order to model CBMI tools and identify the most sustainable tool. The results indicate that the NBFS-FWZIC method gave a weight value of 0.1031 to A7, which is the greatest weight value. On the other hand, A3 had the lowest weight value of 0.0944. The CODAS method modeled the 100 CBMI tools, with Tool39 being identified as the most sustainable tool and Tool26 as the least sustainable tool. The robustness and durability of the proposed method are evaluated using a sensitivity analysis, Spearman's rank correlation test, and comparison analysis.

SOLVING BIPOLAR FULLY FUZZY SYLVESTER MATRIX EQUATIONS WITH NEGATIVE FUZZY NUMBERS

Sylvester matrix equations play a crucial role in control theory for controller design. Bipolar Fully Fuzzy Sylvester Matrix Equations (FFSME), incorporating both positive and negative components, are employed in controller design to address uncertainties that may affect a system’s performance and stability. However, there is not much existing research on combining bipolar fuzzy numbers and FFSME,and most of them mainly deal with positive coefficients. Thus, this paper presents a method that enables solving the negative coefficient of bipolar FFSME in the form of Left-Right (LR) triangular fuzzynumbers using an Associated Bipolar Linear System (ABLS). To obtain the ABLS, bipolar FFSME is transformed into a bipolar Fully Fuzzy Linear System (FFLS) using the Kronecker product and Vecoperator. Subsequently, the solution is derived through the inverse method, and the equation of the ABLS is rearranged as a bipolar fuzzy matrix. Additionally, this paper provides two numerical examples to illustrate the applicability of the constructed method.

Bipolar Fuzzy Almost Quasi-Ideals in Semigroups

The aim of paper, we give the concept bipolar fuzzy, almost quasi-ideal in semigroups. We present the properties of bipolar fuzzy, almost quasi-ideals in semigroups. Moreover, we prove the relationship between almost quasi-ideals and bipolar fuzzy quasi-ideals in semigroups.