M-polar Fuzzy Research Articles

New approach for performance score analysis of m-polar Fuzzy ELECTRE-I method

New approach for performance score analysis of m-polar Fuzzy ELECTRE-I method

Identification of desalination and wind power plants sites using m-polar fuzzy Aczel–Alsina aggregation information

Real-world decision-making problems often include multi-polar uncertainties dependent on multi-dimensional attributes. The m-polar fuzzy (mF) sets can efficiently handle such multi-faceted complications with T-norm based weighted aggregation techniques. The Aczel–Alsina T-norms offer comparatively flexible and accurate aggregation than the other well-known T-norm families. Consequently, this work introduced novel mF Aczel–Alsina aggregation operators (AOs), including weighted averaging (mFAAWA, mFAAOWA, mFAAHWA) and weighted geometric (mFAAWG, mFAAOWG, mFAAHWG) AOs. The fundamental properties, including boundedness, idempotency, monotonicity, and commutativity are investigated. Based on the proposed AOs, a decision-making algorithm is developed and implemented to solve two detailed multi-polar site selection problems (for desalination plant and for wind-power plant). Finally, a comparison with mF Dombi and mF Yager AOs reveals that different T-norm based AOs may yeild different solutions for the same problem.

Certain Types of Vertices in m-Polar Fuzzy Graphs

In this study, we explore the concept of m-polar fuzzy (mPF) detour g-eccentric nodes within m-polar fuzzy graphs (mPFGs). We delve into the idea of mPF detour g-interior nodes and mPF detour g-boundary nodes, examining their significance and properties. Additionally, we establish the relationship between mPF detour g-boundary vertices and mPF cut vertices.

Utilizing m-Polar Fuzzy Saturation Graphs for Optimized Allocation Problem Solutions

It is well known that crisp graph theory is saturated. However, saturation in a fuzzy environment has only lately been created and extensively researched. It is necessary to consider m components for each node and edge in an m-polar fuzzy graph. Since there is only one component for this idea, we are unable to manage this kind of circumstance using the fuzzy model since we take into account m components for each node as well as edges. Again, since each edge or node only has two components, we are unable to apply a bipolar or intuitionistic fuzzy graph model. In contrast to other fuzzy models, mPFG models produce outcomes of fuzziness that are more effective. Additionally, we develop and analyze these kinds of mPFGs using examples and related theorems. Considering all those things together, we define saturation for a m-polar fuzzy graph (mPFG) with multiple membership values for both vertices and edges; thus, a novel approach is required. In this context, we present a novel method for defining saturation in mPFG involving m saturations for each element in the membership value array of a vertex. This explains α-saturation and β-saturation. We investigate intriguing properties such as α-vertex count and β-vertex count and establish upper bounds for particular instances of mPFGs. Using the concept of α-saturation and α-saturation, block and bridge of mPFG are characterized. To identify the α-saturation and β-saturation mPFGs, two algorithms are designed and, using these algorithms, the saturated mPFG is determined. The time complexity of these algorithms is O(|V|3), where |V| is the number of vertices of the given graph. In addition, we demonstrate a practical application where the concept of saturation in mPFG is applicable. In this application, an appropriate location is determined for the allocation of a facility point.

Inverse Graphs in m-Polar Fuzzy Environments and Their Application in Robotics Manufacturing Allocation Problems with New Techniques of Resolvability

The inverse in crisp graph theory is a well-known topic. However, the inverse concept for fuzzy graphs has recently been created, and its numerous characteristics are being examined. Each node and edge in m-polar fuzzy graphs (mPFG) include m components, which are interlinked through a minimum relationship. However, if one wants to maximize the relationship between nodes and edges, then the m-polar fuzzy graph concept is inappropriate. Considering everything we wish to obtain here, we present an inverse graph under an m-polar fuzzy environment. An inverse mPFG is one in which each component’s membership value (MV) is greater than or equal to that of each component of the incidence nodes. This is in contrast to an mPFG, where each component’s MV is less than or equal to the MV of each component’s incidence nodes. An inverse mPFG’s characteristics and some of its isomorphic features are introduced. The α-cut concept is also studied here. Here, we also define the composition and decomposition of an inverse mPFG uniquely with a proper explanation. The connectivity concept, that is, the strength of connectedness, cut nodes, bridges, etc., is also developed on an inverse mPF environment, and some of the properties of this concept are also discussed in detail. Lastly, a real-life application based on the robotics manufacturing allocation problem is solved with the help of an inverse mPFG.

Doubt m-Polar Fuzzy Sets Based on BCK-Algebras

Doubt m-polar subalgebras (ideals) were introduced and some properties were investigated. Also, doubt m-polar positive implicative (commutative) ideals were defined and related results were proved.

Integrity on m-Polar Fuzzy Graphs and Its Application

Integrity for crisp graph theory is a well-defined topic. However, the integrity concept for fuzzy graphs has only recently been defined and extensively researched. However, in m-polar fuzzy graphs (mPFG), each node as well as edges has m components. So, defining integrity in the mPF environment needs a new concept. As in the m-polar fuzzy environment, each node and edge has m components, so we have more flexibility to address the uncertainty rather than fuzzy as well as other uncertain environments. In this article, we developed a brand-new idea known as node integrity on mPFG and went in-depth on a few of their related properties. We have thoroughly covered some of their related properties as well as a brand-new idea called dominating integrity on mPFG. Different types of integrity on mPFG such as node integrity, dominating integrity, and edge integrity are discussed thoroughly along with some of its interesting facts have been introduced. Under isomorphism, their properties have also been studied. We also discussed the interrelation between them. A new type of mPFG called efficient mPFG which is directly related to dominating integrity concept has also been introduced. Several facts about efficient mPFG have also been studied here along with details descriptions. Finally, a real-world mobile network application that is directly related to the integrity of the mPFG concept has been discussed.

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.

M-Polar Fuzzy Graphs and Deep Learning for the Design of Analog Amplifiers

The design of analog circuits is a complex and repetitive process aimed at finding the best design variant. It is characterized by uncertainty and multivariate approaches. The designer has to make different choices to satisfy a predefined specification with required parameters. This paper proposes a method for facilitating the design of analog amplifiers based on m-polar fuzzy graphs theory and deep learning. M-polar fuzzy graphs are used because of their flexibility and the possibility to model different real-life multi-attribute problems. Deep learning is applied to solve a regression task and to predict the membership functions of the m-polar fuzzy graph vertices (the solutions), taking on the role of domain experts. The performance of the learner is high since the obtained errors are very small: Root Mean Squared Error is from 0.0032 to 0.0187, Absolute Error is from 0.022 to 0.098 and Relative Error is between 0.27% and 1.57%. The proposed method is verified through the design of three amplifiers: summing amplifier, subtracting amplifier, and summing/subtracting amplifier. The method can be used for improving the design process of electronic circuits with the possibility of automating some tasks.

New Class of M-Polar Fuzzy Measure Ideals Algebra in BCK2/BCK1/BCI2

In this work, we introduced the concepts of fuzzy measure algebra of the M-polar electrode ambiguous ideals, and many of them have been investigated properties. Characterizations of the blurry M-polar measure sub-algebra and fuzzy (commutative) ideals of polarity are also looked at. Also, the relationships between M-polar fuzzy measure subalgebras, and M-polar ambiguous and ambiguous pole reciprocal ideals have been discussed. A new Concepts suggested here can be expanded to different types of ideals in BCK2, BCK1 and BCI2-algebras, for instance, a-ideal, implicated, n-fold and n-fold ideals, and commutative ideals. Besides, the properties of BCK2 (resp, BCK1 and BCI2) M-polar fuzzy measure algebra are discussed. Finally, the study also investigates the relationships between the mysterious BCK2 (resp, BCK1 and BCI2) M-polar fuzzy measure ideal. Some examples related to it are also given.

Group Decision Analysis Based on Complex m-Polar Fuzzy N-Soft Environment

This research article presents a novel multicriteria group decision-making (MCGDM) technique, namely, complex m-polar fuzzy N-soft TOPSIS (CmPFNS-TOPSIS), that incorporates the remarkable features of manipulating the complex two-dimensional data and the multipolarity of the modern era with the help of CmPFNSS and the multicriteria group decision making potential of the TOPSIS technique. This newly proposed technique shares a very general parametric structure of the CmPFMSS and enables us to make the suitable decisions in this multipolar complex two-dimensional domain. The incredible CmPFNS-TOPSIS technique works on the principle of finding the optimal solution nearest to the positive ideal solution (PSS) and farthest from the negative ideal solution (NIS) by evaluating the Euclidean distance between the alternatives and the optimal solutions. The support of complex m-polar fuzzy N-soft weighted averaging operator (CmPFNSWA), Euclidean distance, score function, and the revised closeness index is utilized for uncovering our optimal solutions. The alternatives, with respect to the revised closeness index, are arranged in the descending order and the alternative with the least closeness index is preferred. The methodology of the CmPFNS-TOPSIS technique is illustrated with the help of the flow chart. The proficiency of this technique is proved by considering a case study of selection of the suitable surgical equipment in the oncology department of Shaukat Khanum Hospital, Lahore (Pakistan). To prove its validity and credibility, a comparative analysis between CmPFNS-TOPSIS and m-polar fuzzy N-soft TOPSIS (mFNS-TOPSIS) is pictured with the help of a bar chart displaying the same end results of the CmPFNS-TOPSIS and mFNS-TOPSIS.

Pythagorean m-polar Fuzzy Neutrosophic Topology with Applications

Pythagorean m-polar Fuzzy Neutrosophic Topology with Applications

Novel multiple criteria decision-making analysis under m-polar fuzzy aggregation operators with application.

Aggregation is a very efficient indispensable tool in which several input values are transformed into a single output value that further supports dealing with different decision-making situations. Additionally, note that the theory of m-polar fuzzy (mF) sets is proposed to tackle multipolar information in decision-making problems. To date, several aggregation tools have been widely investigated to tackle multiple criteria decision-making (MCDM) problems in an m-polar fuzzy environment, including m-polar fuzzy Dombi and Hamacher aggregation operators (AOs). However, the aggregation tool to deal with m-polar information under Yager's operations (that is, Yager's t-norm and t-conorm) is missing in the literature. Due to these reasons, this study is devoted to investigating some novel averaging and geometric AOs in an mF information environment through the use of Yager's operations. Our proposed AOs are named as the mF Yager weighted averaging (mFYWA) operator, mF Yager ordered weighted averaging operator, mF Yager hybrid averaging operator, mF Yager weighted geometric (mFYWG) operator, mF Yager ordered weighted geometric operator and mF Yager hybrid geometric operator. The initiated averaging and geometric AOs are explained via illustrative examples and some of their basic properties, including boundedness, monotonicity, idempotency and commutativity are also studied. Further, to deal with different MCDM situations containing mF information, an innovative algorithm for MCDM is established under the under the condition of mFYWA and mFYWG operators. After that, a real-life application (that is, selecting a suitable site for an oil refinery) is explored under the conditions of developed AOs. Moreover, the initiated mF Yager AOs are compared with existing mF Hamacher and Dombi AOs through a numerical example. Finally, the effectiveness and reliability of the presented AOs are checked with the help of some existing validity tests.

Attributes reduction algorithms for m-polar fuzzy relation decision systems

Nowadays, attribute reduction has become a significant topic in relation decision systems. Their applications come from different domains of the computer sciences, including machine learning, data mining and pattern recognition, which often involve a large number of attributes in data. Several attribute reduction methods are presented in the literature in order to help solving decision-making problems efficiently. A common characterization for these approaches is still missing, that is, although attribute reduction methods of relation decision systems and fuzzy relation decision systems exist, a common generalization for them is still missing. This study presents a systematic discussion of attribute reduction based on m-polar fuzzy (mF, in short) relation systems and mF relation decision systems, which are respective extensions of fuzzy relation systems and fuzzy relation decision systems. This study provides mathematical results on the attribute reduction algorithms based upon mF relation systems and mF relation decision systems. Both are explained with numerical examples. The resulting algorithms permit to reinterpret the upshots of traditional reduction methods, providing them with larger generality and unification abilities. Afterwards, two real-life applications of the proposed attribute reduction approaches prove their validity and feasibility. Finally, the attribute reduction methods developed here are compared with some existing approaches to show their reliability.

An investigation on m-polar fuzzy tolerance graph and its application

An investigation on m-polar fuzzy tolerance graph and its application

Correlation Measures for Cubic m-Polar Fuzzy Sets with Applications

A cubic m -polar fuzzy set (CmPFS) is a new hybrid extension of m -polar fuzzy set and cubic set. A CmPFS is a robust model to express multipolar information in terms of m fuzzy intervals representing membership grades and m fuzzy numbers representing nonmembership grades. In this article, we explore some new operational laws of CmPFSs, produce some related results, and discuss their consequences. We propose relative informational coefficients and relative noninformational coefficients for CmPFSs. These coefficients are analyzed to investigate further properties of CmPFSs. Based on these coefficients, we introduce new correlation measures and their weighted versions for CmPFSs. The value of proposed correlation measures is symmetrical and lies between −1 and 1. Moreover, the applications of the proposed correlation in pattern recognition and medical diagnosis are developed. The feasibility and efficiency of suggested correlation measures is determined by respective illustrative examples.

Generalized Fuzzy Ideals of BCI-Algebras Based on Interval Valued m-Polar Fuzzy Structures

In this paper, first we introduce the concepts of interval valued m-polar fuzzy (briefly, IVmPF) p-ideals, IVmPF q-ideals and IVmPF a-ideals in BCI-algebras. Then we show that IVmPF p(q and a)-ideals are IVmPF ideals but the converse statements are not valid and an example is given in each case. We provide conditions under which an IVmPF ideal becomes an IVmPF p(q and a)-ideal. Further, the associated properties of IVmPF p-ideals, IVmPF q-ideals and IVmPF a-ideals are considered. Moreover, we characterize IVmPF p(q and a)-ideals in terms of fuzzy p(q and a)-ideals of BCI-algebras. Also, correspondences among IVmPF p(q and a)-ideals of BCI-algebras and p(q and a)-ideals of BCI-algebras are investigated.

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

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.

Menger’s theorem for m-polar fuzzy graphs and application of m-polar fuzzy edges to road network

The main objective of this research article is to classify different types of m-polar fuzzy edges in an m-polar fuzzy graph by using the strength of connectedness between pairs of vertices. The identification of types of m-polar fuzzy edges, including α-strong m-polar fuzzy edges, β-strong m-polar fuzzy edges and δ-weak m-polar fuzzy edges proved to be very useful to completely determine the basic structure of m-polar fuzzy graph. We analyze types of m-polar fuzzy edges in strongest m-polar fuzzy path and m-polar fuzzy cycle. Further, we define various terms, including m-polar fuzzy cut-vertex, m-polar fuzzy bridge, strength reducing set of vertices and strength reducing set of edges. We highlight the difference between edge disjoint m-polar fuzzy path and internally disjoint m-polar fuzzy path from one vertex to another vertex in an m-polar fuzzy graph. We define strong size of an m-polar fuzzy graph. We then present the most celebrated result due to Karl Menger for m-polar fuzzy graphs and illustrate the vertex version of Menger’s theorem to find out the strongest m-polar fuzzy paths between affected and non-affected cities of a country due to an earthquake. Moreover, we discuss an application of types of m-polar fuzzy edges to determine traffic-accidental zones in a road network. Finally, a comparative analysis of our research work with existing techniques is presented to prove its applicability and effectiveness.

Parameter reduction analysis under interval-valued m-polar fuzzy soft information

This paper formalizes a novel model that is able to use both interval representations, parameterizations, partial memberships and multi-polarity. These are differing modalities of uncertain knowledge that are supported by many models in the literature. The new structure that embraces all these features simultaneously is called interval-valued multi-polar fuzzy soft set (IVmFSS, for short). An enhanced combination of interval-valued m-polar fuzzy (IVmF) sets and soft sets produces this model. As such, the theory of IVmFSSs constitutes both an interval-valued multipolar-fuzzy generalization of soft set theory; a multipolar generalization of interval-valued fuzzy soft set theory; and an interval-valued generalization of multi-polar fuzzy set theory. Some fundamental operations for IVmFSSs, including intersection, union, complement, “OR”, “AND”, are explored and investigated through examples. An algorithm is developed to solve decision-making problems having data in interval-valued m-polar fuzzy soft form. It is applied to two numerical examples. In addition, three parameter reduction approaches and their algorithmic formulation are proposed for IVmFSSs. They are respectively called parameter reduction based on optimal choice, rank based parameter reduction, and normal parameter reduction. Moreover, these outcomes are compared with existing interval-valued fuzzy methods; relatedly, a comparative analysis among reduction approaches is investigated. Two real case studies for the selection of best site for an airport construction and best rotavator are studied.