Concept Of Fuzzy Sets Research Articles

Complex Linear Diophantine Fuzzy Sets over AG-Groupoids with Applications in Civil Engineering

Intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PFS), and q-rung orthopair fuzzy sets (q-ROFS) are among those concepts which are widely used in real-world applications. However, these theories have their own limitations in terms of membership and non-membership functions, as they cannot be obtained from the whole unit plane. To overcome these restrictions, we developed the concept of a complex linear Diophantine fuzzy set (CLDFS) by generalizing the notion of a linear Diophantine fuzzy set (LDFS). This concept can be applied to real-world decision-making problems involving complex uncertain information. The main motivation behind this paper is to study the applications of CLDFS in a non-associative algebraic structure (AG-groupoid), which has received less attention as compared to associative structures. We characterize a strongly regular AG-groupoid in terms of newly developed CLDF-score left (right) ideals and CLDF-score (0,2)-ideals. Finally, we construct a novel approach to decision-making problems based on the proposed CLDF-score ideals, and some practical examples from civil engineering are considered to demonstrate the flexibility and clarity of the initiated CLDF-score ideals.

Analysis of Hamming and Hausdorff 3D distance measures for complex pythagorean fuzzy sets and their applications in pattern recognition and medical diagnosis

AbstractSimilarity measures are very effective and meaningful tool used for evaluating the closeness between any two attributes which are very important and valuable to manage awkward and complex information in real-life problems. Therefore, for better handing of fuzzy information in real life, Ullah et al. (Complex Intell Syst 6(1): 15–27, 2020) recently introduced the concept of complex Pythagorean fuzzy set (CPyFS) and also described valuable and dominant measures, called various types of distance measures (DisMs) based on CPyFSs. The theory of CPyFS is the essential modification of Pythagorean fuzzy set to handle awkward and complicated in real-life problems. Keeping the advantages of the CPyFS, in this paper, we first construct an example to illustrate that a DisM proposed by Ullah et al. does not satisfy the axiomatic definition of complex Pythagorean fuzzy DisM. Then, combining the 3D Hamming distance with the Hausdorff distance, we propose a new DisM for CPyFSs, which is proved to satisfy the axiomatic definition of complex Pythagorean fuzzy DisM. Moreover, similarly to some DisMs for intuitionistic fuzzy sets, we present some other new complex Pythagorean fuzzy DisMs. Finally, we apply our proposed DisMs to a building material recognition problem and a medical diagnosis problem to illustrate the effectiveness of our DisMs. Finally, we aim to compare the proposed work with some existing measures is to enhance the worth of the derived measures.

A Theoretical Development of Cubic Pythagorean Fuzzy Soft Set with Its Application in Multi-Attribute Decision Making

Scientific progression has allowed researchers to develop novel and innovative ways to deal with uncertainty in data, allowing for the development of more precise and accurate data representation models. This paper aims to extend an already reported concept of Cubic Pythagorean fuzzy set to Cubic Pythagorean Fuzzy Soft Set (CPFSs) as it incorporates both interval-valued Pythagorean fuzzy sets (IVPFS) and Pythagorean fuzzy sets (PFS) at the same time, providing a more targeted approach to deal with uncertainty. This hybrid structure can better handle data in comparison to the ones in the literature by having the characteristics of PFS and soft sets, leading to a more targeted approach to handle attributes in decision-making studies. In this study, we defined various internals and externals of CPFSs, set operators, aggregation operators, and developed an algorithm based on distance measures for (CPFSs), which are applied in a disease diagnostic decision-making problem.

Gas Cooled Graphite Moderated and Pressurized Water Reactor the Optimal Choice for Nuclear Power Plants Based on a New Group Decision-Making Technique

The aim of this work is to introduce the novel concept of an m-polar fuzzy soft set, including various types of algorithms and their fundamental operations. We created mathematical modeling to analyze operational rules and discuss the advantages, disadvantages, and natural aspects of algorithms for six types of nuclear power plants. It has been determined that emerging trends and the benefits of algorithms are increasing step by step. The suggested modeling with an m-polar fuzzy soft set is integrated into the fuzzy mean environment to analyze the effect of the correlation between decision factors and decision results without an excessive duty cycle, thus minimizing energy use and other adverse effects. Based on a new group decision-making technique considering an asymmetric weight vector, we proved that Gas Cooled, Graphite-Moderated, and Pressurized Water Reactors are the optimal choices for nuclear power plants. In the end, a numerical illustration is provided for selecting the best photo to demonstrate the use of the generated technique and to exhibit its adequacy.

Cubic Intuitionistic Fuzzy Topology with Application to Uncertain Supply Chain Management

The concept of the cubic intuitionistic fuzzy set is an effective hybrid model for modeling uncertainties with an intuitionistic fuzzy set and an interval-valued intuitionistic fuzzy set, simultaneously. The primary objective of this study is to develop a topological structure on cubic intuitionistic fuzzy sets with P-order and R-order as well as to define some fundamental characteristics and significant results with illustrations. Taking advantage of topological data analysis with cubic intuitionistic information, novel multicriteria group decision-making methods are developed for an uncertain supply chain management. Algorithms 1 and 2 are proposed for extensions of the weighted product model and the choice value method towards a cubic intuitionistic fuzzy environment, respectively. A comparative analysis is also given to discuss the validity and advantages of the proposed techniques.

Q-rung orthopair triangular fuzzy linguistic Frank aggregation operators and their application

The aim of this paper is to introduce a Frank operator in the q-rung orthopair triangular fuzzy linguistic environment on the basis of the notion of the Frank operator and the q-rung orthopair fuzzy set. Firstly, the concept of a q-rung orthopair triangular fuzzy linguistic set (q-ROTrFLS) is proposed, then several basic operations, score, and accuracy functions to compare the q-ROTrFLS values are defined. Secondly, a series of q-rung orthopair triangular fuzzy linguistic Frank aggregation operators are developed, such as q-rung orthopair triangular fuzzy linguistic Frank weighted average (q-ROTrFLWA)operator,q-rung orthopair triangular fuzzy linguistic Frank weighted geometric (q-ROTrFLWG) operator, and we introduce several relevant properties of these operators and prove their validity, and show the relevant relationship between some operators. Thirdly, two different decision-making approaches are constructed in the q-rung orthopair triangular fuzzy linguistic environment. Furthermore, a practical example is given to explain the developed methods. Finally, a comparative study is conducted, and the relevant sensitivity analysis is also discussed, and the outcome shows the prominence and the effectiveness of the developed methods compared to previous studies.

Towards Interval Type-3 Intuitionistic Fuzzy Sets and Systems

In this work, several types of intuitionistic fuzzy sets, inspired by Type-2 and Type-3 concepts, are introduced. In particular, the newly proposed interval Type-3 intuitionistic sets are very interesting as they extend the opportunities of both interval Type-3 fuzzy sets and intuitionistic sets when capturing specific forms of uncertainty. A comparative study of interval Type-3 with respect to intuitionistic fuzzy is presented. Based on this comparison, a novel concept of an interval Type-3 intuitionistic fuzzy set is put forward to enhance the capabilities of modeling uncertainty with respect to the individual Type-3 and intuitionistic concepts. Basically, the secondary and tertiary membership functions are added to the intuitionistic fuzzy sets to build an interval Type-3 intuitionistic fuzzy set. An illustrative example dealing with controlling the imaging system of televisions is provided to envision the potential applicability and advantages of interval Type-3 intuitionistic fuzzy sets in real problems. For this application, the intuitionistic Type-3 approach shows the potential to outperform previous approaches in controlling this system.

An Additive Consistency and Consensus Approach for Group Decision Making With Probabilistic Hesitant Fuzzy Linguistic Preference Relations and Its Application in Failure Criticality Analysis.

In this article, probabilistic hesitant fuzzy linguistic preference relations (PHFLPRs) are proposed to present the qualitative pairwise preference information of decision makers (DMs) with hesitation and probability uncertainty assessments. The measurements and improvements of additive consistency and consensus of PHFLPRs are investigated in group decision making (GDM). First, a new concept of probabilistic hesitant fuzzy linguistic term sets is defined. Second, the consistency and consensus measurements are established to survey the additive consistency and consensus levels of PHFLPRs. Subsequently, an optimization model is developed to improve the unacceptably additive consistent PHFLPR. By optimizing the unacceptable consensual PHFLPRs with repeating additive consistency improvement, the acceptably additive consistent and consensual PHFLPRs are obtained, based on which DMs' weights are determined objectively and then, the collective PHFLPR is aggregated from individual PHFLPRs. Alternatives' priority weights are derived from the collective PHFLPR as GDM. Finally, an example about failure criticality analysis is given, and a comparison analysis is presented.

Multi-Criteria Decision Making to Logarithmic Pythagorean Fuzzy Entropy Measure Under TOPSIS Approach

One of the most essential ideas for tracing the best objects among a set of possible ones is decision-making theory. We make decisions to gain a wide range of advantages from them based on our previous experiences. The concept of Pythagorean fuzzy sets (PFS) was first established by Yager to provides a new technique to describe ambiguity with great precision when compared to intuitionistic fuzzy sets (IFS) and fuzzy sets (FS). The study of PFS is recently gaining importance due to its wide application in situations involving ambiguity. It can easily be merged with MADM techniques to solve real-life problems. However, many of these measures for PFS are ineffective in the sense that they have fundamental shortcomings that restrict them from providing reliable and consistent results. This paper provides a novel Pythagorean fuzzy entropy measure and its application to decision-making problem using technique for order preference by similarity of ideal solution (TOPSIS) on some real-life environment. Comparative study is also done for validation of the proposed measure.

Topological Data Analysis of m-Polar Spherical Fuzzy Information with LAM and SIR Models

The concept of m-polar spherical fuzzy sets (mPSFS) is a combination of m-polar fuzzy sets (mPFS) and spherical fuzzy sets (SFS). An mPSFS is an optimal strategy for addressing multipolarity and fuzziness in terms of ordered triples of positive membership grades (PMGs), negative membership grades (NMGs), and neutral grades (NGs). In this study, the innovative concept of m-polar spherical fuzzy topology (mPSF-topology) is proposed for data analysis and information aggregation. We look into the characteristics and results of mPSF-topology with the help of several examples. Topological structures on mPSFSs help with both the development of new artificial intelligence (AI) tools for different domain strategies and the study of different kinds of uncertainty in everyday life problems. These strategies make it possible to recognise and look into a situation early on, which helps professionals to reduce certain risks. In order to address various group decision-making issues in the m-polar spherical fuzzy domain, one suggestion has been to apply an extended linear assignment model (LAM) along with the SIR method known as superiority and inferiority ranking methodology in order to analyze road accident issues and dispute resolution. In addition, we examine the symmetry of optimal decision and perform a comparative study between the research carried out using the suggested methodology and several existing methods.

Multi-Attribute Decision Making with Einstein Aggregation Operators in Complex Q-Rung Orthopair Fuzzy Hypersoft Environments

The purpose of our research is to extend the formal representation of the human mind to the concept of the complex q-rung orthopair fuzzy hypersoft set (Cq-ROFHSS), a more general hybrid theory. A great deal of imprecision and ambiguity can be captured by it, which is common in human interpretations. It provides a multiparameterized mathematical tool for the order-based fuzzy modeling of contradictory two-dimensional data, which provides a more effective way of expressing time-period problems as well as two-dimensional information within a dataset. Thus, the proposed theory combines the parametric structure of complex q-rung orthopair fuzzy sets and hypersoft sets. Through the use of the parameter q, the framework captures information beyond the limited space of complex intuitionistic fuzzy hypersoft sets and complex Pythagorean fuzzy hypersoft sets. By establishing basic set-theoretic operations, we demonstrate some of the fundamental properties of the model. To expand the mathematical toolbox in this field, Einstein and other basic operations will be introduced to complex q-rung orthopair fuzzy hypersoft values. The relationship between it and existing methods demonstrates its exceptional flexibility. The Einstein aggregation operator, score function, and accuracy function are used to develop two multi-attribute decision-making algorithms, which prioritize based on the score function and accuracy function to ideal schemes under Cq-ROFHSS, which captures subtle differences in periodically inconsistent data sets. The feasibility of the approach will be demonstrated through a case study of selected distributed control systems. The rationality of these strategies has been confirmed by comparison with mainstream technologies. Additionally, we demonstrate that these results are compatible with explicit histograms and Spearman correlation analyses. The strengths of each approach are analyzed in a comparative manner. The proposed model is then examined and compared with other theories, demonstrating its strength, validity, and flexibility.

A DSS Framework for Advanced Traffic Signal Control System Investment Planning

This article presents ongoing research on the initial development of a decision support system (DSS) framework for integrated emergency vehicle preemption and transit priority system investment planning. A conceptual intelligent DSS framework provides a holistic framework to perform analytical assessments of integrated emergency vehicle preemption and transit priority systems. Three analytical tools are presented for incorporation into future DSS design: the first addresses the potential impact of transit travel time reduction on transit operating costs; the second addresses the potential impact of reduced emergency vehicle crashes at signalized intersections on fire and rescue operating costs; and the third integrates fuzzy sets concepts and multiattribute decision-making methods to rank order transit signal priority strategy alternatives at the intersection level.

Self-organizing map with granular competitive learning: Application to microarray clustering

Self-organizing map (SOM) models perform clustering process based on a competitive learning. The learning methods of these models involve neighborhood function such as Gaussian in the output layer, where the Euclidean distance from winning node to an output node is used. In this study, a granular competitive learning of SOM (SOMGCL) involving a fuzzy distance, the distance based granular neighborhood function and fuzzy initial connection weights is developed using the concepts of fuzzy rough set. The fuzzy distance between a winning node and an output node of SOM is computed where the average of memberships belonging to the lower approximations and boundary regions of a cluster obtained at the node is used. The fuzzy distance is incorporated into a Gaussian function to define the proposed neighborhood function. Dependency values of features using fuzzy rough sets are encoded into SOM as its fuzzy initial connection weights. Here, the concepts of fuzzy rough set are based on a new fuzzy strict order relation. While the fuzzy distance defines similarity measure in clustering process, the distance based granular neighborhood function handles uncertainty in cluster boundary regions. The effectiveness of SOMGCL is demonstrated in clustering of both the samples and genes in microarrays having the large number of genes and classes in terms of cluster evaluation metrics and quantization error. Further, biological meaning of gene clusters obtained using SOMGCL is elucidated using gene-ontology.

T-Intuitionistic Fuzzy Structures on PMS-Ideals of a PMS-Algebra

In this article, we apply the concept of a t -intuitionistic fuzzy set to PMS-ideals in PMS-algebras. The notion of the t -intuitionistic fuzzy PMS-ideal of PMS-algebra is introduced, and several related properties are studied. The relationships between a t -intuitionistic fuzzy PMS-ideal and a t -intuitionistic fuzzy PMS-subalgebra of a PMS-algebra, as well as the relationships between an intuitionistic fuzzy PMS-ideal and a t -intuitionistic fuzzy PMS-ideal are discussed in detail. A condition for an intuitionistic fuzzy set to be a t -intuitionistic fuzzy PMS-ideal is provided. The t -intuitionistic fuzzy PMS-ideals of PMS-algebra are described using their α , β level cuts. The homomorphism of a t -intuitionistic fuzzy PMS-ideal of a PMS-algebra is studied, and its homomorphic image and inverse image are explored. The Cartesian product of any two t -intuitionistic fuzzy PMS-ideals is discussed, and some related results are derived. The Cartesian product of the t -intuitionistic fuzzy PMS-ideals is also characterized using its α , β level cuts. The strongest t -intuitionistic fuzzy PMS-relation in a PMS-algebra is defined. Finally, the relationships between the strongest t -intuitionistic fuzzy PMS-relation and t -intuitionistic fuzzy PMS-ideal are studied.

Some Studies of Multi-Polar Fuzzy Ideals in LA-Semigroups

This article’s main goal is to investigate the concept of multi-polar fuzzy sets (MPF-sets) in LA-semi-groups, which is an extension of bi-polar fuzzy sets (BPF-sets) in LA-semigroups. The main objective of this research is to extend certain significant BPF-set results to MPF-sets results. This article introduces the concepts of multi-polar fuzzy sub LA-semigroups, multi-polar fuzzy quasi-ideals, multi-polar fuzzy bi-ideals, multi-polar fuzzy generalized bi-ideals, and multi-polar fuzzy interior ideals in LA-semigroups. This article also discusses a number of fundamental aspects of multi-polar fuzzy ideals, and we use these aspects to define regular LA-semigroups.

Q-Rung orthopair fuzzy soft aggregation operators based on Dombi t-norm and t-conorm with their applications in decision making

Recently, some improvement has been made in the dominant notion of fuzzy set that is Yager investigated the generalized concept of fuzzy set, Intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS) and called it q-rung orthopair fuzzy (q-ROF) set (q-ROFS). The aim of this manuscript is to present the concept of q-ROF soft (q-ROFSt) set (q-ROFStS) based on the Dombi operations. Since Dombi operational parameter possess natural flexibility with the resilience of variability. Some new operational laws are defined based on hybrid study of soft sets and q-ROFS. The advantage of Dombi operational parameter is very important to express the experts’ attitude in decision making. In this paper, we present q-ROFSt Dombi average (q-ROFSt DA) aggregation operators including q-ROFSt Dombi weighted average (q-ROFSt DWA), q-ROFSt Dombi ordered weighted average (q-ROFSt DOWA) and q-ROFSt Dombi hybrid average (q-ROFSt DHA) operators. Moreover, we investigate q-ROFSt Dombi geometric (q-ROFSt DG) aggregation operators including q-ROFSt Dombi weighted geometric (q-ROFSt DWG), q-ROFSt Dombi ordered weighted geometric (q-ROFSt DOWG), and q-ROFSt Dombi hybrid geometric (q-ROFSt DHG) operators. The basic properties of these operators are presented with detail such us Idempotency, Boundedness, Monotonicity, Shift invariance, and Homogeneity. Thus from the analysis and advantages of proposed model, it is clear that the investigated q-ROFSt DWA operator is the generalized form of IF St DWA, PFSt DWA and q-ROFDWA operators. Similarly, the investigated q-ROFSt DWG operator is the generalized form of IF St DWG, PFSt DWG and q-ROFDWG operators. By applying the develop approach, this manuscript contains the technique and algorithm for multicriteria decision making (MCDM). Further a numerical example is developed to illustrate the flexibility and applicability of the developed operators.

An (α,β)-Hesitant Fuzzy Set Approach to Ideal Theory in Semigroups

The aim of this manuscript is to introduce the \((\alpha,\beta)\)-hesitant fuzzy set and apply it to semigroups. In this paper, as a generalization of the concept of hesitant fuzzy sets to semigroup theory, the concept of \((\alpha,\beta)\)-hesitant fuzzy subsemigroups of semigroups is introduced, and related properties are discussed. Furthermore, we define and study \((\alpha,\beta)\)-hesitant fuzzy ideals on semigroups. In particular, we investigate the structure of \((\alpha,\beta)\)-hesitant fuzzy ideal generated by a hesitant fuzzy ideal in a semigroup. In addition, we also introduce the concepts of \((\alpha,\beta)\)-hesitant fuzzy semiprime sets of semigroups, and characterize regular semigroups in terms of \((\alpha,\beta)\)-hesitant fuzzy left ideals and \((\alpha,\beta)\)-hesitant fuzzy right ideals. Finally, several characterizations of regular and intra-regular semigroups by the properties of \((\alpha,\beta)\)-hesitant ideals are given.

Quantifying individual scientific output in terms of a new intuitionistic fuzzy sets based author-level metrics (IFALM)

The present paper proposes the idea of formulating a new author-level citation metrics, quantifying the individual’s scientific output, which uses the concept of intuitionistic fuzzy sets. This new metrics gives more visibility to the proportion of direct self-citations and hidden (co-author or collaborative) self-citations in the form of an intuitionistic fuzzy pair. Examples are given retrieving the necessary information from Scopus, one of the largest databases of peer-reviewed literature, which algorithmically enables retrieval of one’s citations including and excluding their own or their co-authors’ self-citations, as well as the calculation of three different values of one’s h-index with and without these respectively. Linear and triangular graphical representations are given, as well as comparisons with the concept proposed in 2005 by Jorge E. Hirsch, the now famous h-index, and ideas for future elaboration of the concept of the new intuitionistic fuzzy sets based author-level metrics, or shortly IFALM.

Inverse packet fuzzy sets and its characteristics

Based on inverse packet sets and fuzzy set, the concept of inverse packet fuzzy sets is proposed in this paper by means of introducing dynamic characteristics into a fuzzy set A and improving the fuzzy set A. The inverse packet fuzzy sets is composed of a pair of fuzzy sets generated by the fuzzy set A and has dynamic characteristic and fuzzy characteristic. Furthermore, on certain conditions, it can be restored to the fuzzy set A or the inverse packet sets generated by the Cantor set X=ker⁡(A). As a result, an inverse packet fuzzy sets can be expressed as a series of inverse packet sets by defining its scalar multiplication and its cut sets. Meanwhile some attribute-dependent characteristics of inverse packet fuzzy sets are obtained. The new set model will both enrich the set theory and provide a new basic tool for further practical applications.

Robust intuitionistic fuzzy clustering with bias field estimation for noisy image segmentation

The concept of intuitionistic fuzzy set has been found to be highly useful to handle vagueness in data. Based on intuitionistic fuzzy set theory, intuitionistic fuzzy clustering algorithms are proposed and play an important role in image segmentation. However, due to the influence of initialization and the presence of noise in the image, intuitionistic fuzzy clustering algorithm cannot acquire the satisfying performance when applied to segment images corrupted by noise. In order to solve above problems, a robust intuitionistic fuzzy clustering with bias field estimation (RIFCB) is proposed for noisy image segmentation in this paper. Firstly, a noise robust intuitionistic fuzzy set is constructed to represent the image by using the neighboring information of pixels. Then, initial cluster centers in RIFCB are adaptively determined by utilizing the frequency statistics of gray level in the image. In addition, in order to offset the information loss of the image when constructing the intuitionistic fuzzy set of the image, a new objective function incorporating a bias field is designed in RIFCB. Based on the new initialization strategy, the intuitionistic fuzzy set representation, and the incorporation of bias field, the proposed method preserves the image details and is insensitive to noise. Experimental results on some Berkeley images show that the proposed method achieves satisfactory segmentation results on images corrupted by different kinds of noise in contrast to conventional fuzzy clustering algorithms.