Fuzzy Set Operations Research Articles

Intuitionistic fuzzy normal bi-topological space-approach of intuitionistic fuzzy open sets

This paper provides nine newly proposed notions of intuitionistic fuzzy normal bi-topological spaces (IFNBTS) based on the concept of most explored field fuzzy bi-topological spaces using intuitionistic fuzzy open sets (IFOS). Further, the authors establish implications among the prescribed notions and show that these notions are good extensions of normal and fuzzy normal bi-topological spaces. Finally, the authors study the image and pre-image of IFNBTS, demonstrating that they are also IFNBTS in the sense of IFOS.

Revolutionizing diabetes care with innovative decision-making using cubic intuitionistic fuzzy Schweizer and Sklar power aggregation operators

The cubic intuitionistic fuzzy set is an expansion of the cubic fuzzy set that displays massive information to demonstrate interval-valued intuitionistic fuzzy sets and intuitionistic fuzzy sets. This increment informs limitations essential in existing frameworks, primarily focusing on the significance of embracing our access for more accurate decisions in compound and unresolved structures. The Schweizer and Sklar (SS) operations are engaged in promoting strong aggregation operators for cubic intuitionistic fuzzy sets through this research. Operators such as cubic intuitionistic fuzzy Schweizer and Sklar power weighted average (CIFSSPWA) and cubic intuitionistic fuzzy Schweizer and Sklar power weighted geometric (CIFSSPWG) are offered that enhance the workability of data aggregation within the cubic intuitionistic fuzzy (CIF) environment when compared to surviving methods. The proposed operators may assist in patient treatment and handling by upgrading decision-making in medical sectors like diabetes care. Moreover, to determine the stability and reliance of the outcomes, sensitivity and comparison studies are richly absorbed by this approach.

Optimizing decision-making in electric power system selection: A generalized approach based on Hamacher aggregation operators for q-rung orthopair fuzzy soft sets

Identifying the most suitable power source that is cost-effective, environmentally friendly, socially accepted, and capable of ensuring long-term sustainability represents a critical decision-making (DM) problem. Existing models based on traditional fuzzy sets and specific norms cannot describe complex issues such as selecting the best electric power system (EPS). These decision models can also be challenging, especially when transparency and regulatory compliance are required. This study introduces a novel operational framework based on Hamacher aggregation operators for q-rung orthopair fuzzy set soft sets. It aims to help decision-makers identify appropriate policies to overcome the shortfall of electric power. The advantages of the introduced decision support tool are better discrimination ability, well suited for handling extreme values in data, greater flexibility in representing complex DM scenarios, and parametrization. We also demonstrate the practical application of our approach to a real-world problem related to selecting the most suitable EPS in Pakistan. The selection is made from the set of five EPSs and is based on critical aspects like social acceptance, environmental impact, and cost-effectiveness. The findings show that the developed approach effectively identifies the best EPS. Tuning variables like q and ℓ allows for testing the sensitivity of the developed operators. The results showed that higher values of q make the uncertainty more evenly represented, which is essential for specific uses. The comparison with the existing approaches suggests the superiority of the proposed analytic framework.

A Novel Method for Failure Mode and Effect Analysis Based on the Fermatean Fuzzy Set and Bonferroni Mean Operator

Failure mode and effects analysis (FMEA) helps to identify the weak points in the processing, manufacturing, and assembly of products and plays an important role in improving product reliability. To address the shortcomings of the existing FMEA methods in terms of the uncertainty treatment of information and not considering the weights and correlations between risk factors, we propose a new FMEA method. In this paper, the Fermatean fuzzy Z-number (FFZN) is proposed by fusing the Fermatean fuzzy number and Z-number. Extending it to the Bonferroni mean (BM) operator, the Fermatean fuzzy Z-number-weighted Bonferroni mean (FFZWBM) operator is proposed. A new FMEA method is proposed based on this operator. In order to overcome the factors not considered in the FMEA method, two new risk factors are proposed and added. The ability of experts to express fuzzy information is enhanced by introducing the FFS. The weights and correlations between the influencing factors can be handled by aggregating the evaluation information using the FFZWBM operator. Finally, the proposed method is applied to an arithmetic example and the accuracy of the proposed method is proved by teaming it with other methods.

Power Dombi Aggregation Operators for Complex Pythagorean Fuzzy Sets and Their Applications in Green Supply Chain Management

Power Dombi Aggregation Operators for Complex Pythagorean Fuzzy Sets and Their Applications in Green Supply Chain Management

Hamacher interaction aggregation operators for complex intuitionistic fuzzy sets and their applications in green supply chain management

A complex intuitionistic fuzzy (CIF) set contains the membership and non-membership in the shape of a complex number whose amplitude term and phase term are covered in the unit interval. Moreover, Hamacher interaction aggregation operators are the combination of two major operators, called Hamacher aggregation operators and interaction aggregation operators, and they are used to aggregate the collection of information into one value. In this manuscript, we present the concept of Hamacher interaction operational laws for CIF sets (CIFSs). Further, we develop the CIF Hamacher interaction weighted averaging (CIFHIWA) operator, CIF Hamacher interaction ordered weighted averaging (CIFHIOWA) operator, CIF Hamacher interaction weighted geometric (CIFHIWG) operator, and CIF Hamacher interaction ordered weighted geometric (CIFHIOWG) operator. For these operators, we also discuss some basic properties, such as idempotency, monotonicity, and boundedness. Additionally, we develop a MADM method based on the developed operators and apply it to solve the green supply chain management problems, which can implement environmentally friendly practices to minimize carbon emissions, resource consumption, and waste generation while promoting long-term sustainability. Finally, we verify the superiority and effectiveness of the proposed method based on a comparative analysis between the proposed techniques and existing methods.

Archimedean Heronian mean operators based on complex intuitionistic fuzzy sets and their applications in decision-making problems

In this article, we derive the Archimedean aggregation operators for complex intuitionistic fuzzy sets, for this, first, we evaluate some Archimedean operational laws based on complex intuitionistic fuzzy values and then we discuss their special cases because the Archimedean norms are the general form of all existing norms, for instance, algebraic, Einstein, Hamacher, and Frank operational laws. Furthermore, we present the complex intuitionistic fuzzy Archimedean Heronian aggregation operator and complex intuitionistic fuzzy weighted Archimedean Heronian aggregation operator. Several special cases and the basic properties of the above-proposed operators are also diagnosed, because proposing the Heronian mean operators based on Archimedean norms are very challenging and complicated tasks, because of their features and structure. Additionally, a decision-making process is developed under the identified operators by using complex intuitionistic fuzzy information. Finally, we illustrate several examples to show the multi-attribute decision-making technique is more flexible than the prevailing works with the help of sensitive analysis between explored and certain prevailing works.

Hamacher Maclaurin symmetric mean aggregation operators and WASPAS method for multiple criteria group decision making under [formula omitted] - spherical fuzzy environment

T-spherical fuzzy sets can accurately represent fuzzy information and effectively simulate real-world decision making scenarios by adjusting the parameter t. The Maclaurin symmetric mean can combine multiple arguments by considering the relationships between them in any decision making process. The main goal of this paper is to develop Maclaurin symmetric mean aggregation operators based on the Hamacher operations of T-spherical fuzzy sets. The developed operators are thoroughly examined through their fundamental properties. The defined operators are adopted to develop a decision making methodology called WASPAS (Weighted Aggregated Sum Product ASsessment) for solving multiple criteria group decision making problems in a T-spherical fuzzy environment. A real-life example of project assessment is illustrated to demonstrate the practicality of the proposed decision making approach. Sensitivity analysis of the parameters is carried out to check their effect on the decision results. A comparison analysis with existing methods confirms the accessibility of the developed approach.

Gamified approach towards optimizing supplier selection through Pythagorean Fuzzy soft-max aggregation operators for healthcare applications

<abstract><p>The soft-max function, a well-known extension of the logistic function, has been extensively utilized in numerous stochastic classification methodologies, such as linear differential analysis, soft-max extrapolation, naive Bayes detectors, and neural networks. The focus of this study is the development of soft-max based fuzzy aggregation operators (AOs) for Pythagorean fuzzy sets (PyFS), capitalizing on the benefits provided by the soft-max function. In addition to introducing these novel AOs, we also present a comprehensive approach to multi-attribute decision-making (MADM) that employs the proposed operators. To demonstrate the efficacy and applicability of our MADM method, we applied it to a real-world problem involving Pythagorean fuzzy data. The analysis of supplier selection has been extensively examined in many academic works as a crucial component of supply chain management (SCM), recognised as a significant MADM challenge. The process of choosing healthcare suppliers is a pivotal element that has the potential to greatly influence the efficacy and calibre of healthcare provisions. In addition, we given a numerical example to rigorously evaluate the accuracy and dependability of the proposed procedures. This examination demonstrates the effectiveness and potential of our proposed soft-max based AOs and their applicability in Pythagorean fuzzy environments.</p></abstract>

β-b-REGULARITY IN FUZZY SETTING

This paper deals with a new type of fuzzy open-like set, viz., fuzzy β-b-open set, the class of which is strictly larger than that of fuzzy open set as well as fuzzy preopen set [11], fuzzy semiopen set [1], fuzzy α-open set [4] and fuzzy β-open set [6]. However, three different types of fuzzy continuous-like functions are introduced and studied and also the mutual relationships of these functions are established. Afterwards, two new types of separation axioms and a new type of compactness are introduced and studied. It is shown that in a fuzzy β-b-regular space, fuzzy β-b-open set coincides with fuzzy open set. In the last section some applications of the functions defined here are established.

Characterizations of generalized Fuzzy γ∗-closed sets

Generalized fuzzy open sets are playing a vital role in the study of fuzzy topological space as well as that of fuzzy bitopological space since its inception. More often, it is reported that fuzzy closed sets are always included in the family of generalized fuzzy closed sets. Very recently, it has appeared that fuzzy γ∗ -open sets are incomparable with fuzzy open sets. This paper aims to present three different kinds of fuzzy generalized closed sets in the light of fuzzy γ∗ -open set and associated closure operators with the terminologies- generalized fuzzy γ∗ -closed set, γ∗ -generalized fuzzy closed set and γ∗ -generalized fuzzy γ∗-closed set and it is found that the relation between any two concepts is not necessarily linear. Also, the interrelationships among them are established along with suitable counter examples which are properly placed to make the paper self-sufficient.

Stronger Forms of Fuzzy Pre-Separation and Regularity Axioms via Fuzzy Topology

It is common knowledge that fuzzy topology contributes to developing techniques to address real-life applications in various areas like information systems and optimal choices. The building blocks of fuzzy topology are fuzzy open sets, but other extended families of fuzzy open sets, like fuzzy pre-open sets, can contribute to the growth of fuzzy topology. In the present work, we create some classifications of fuzzy topologies which enable us to obtain several desirable features and relationships. At first, we introduce and analyze stronger forms of fuzzy pre-separation and regularity properties in fuzzy topology called fuzzy pre-Ti,i=0,12,1,2,3,4, fuzzy pre-symmetric, and fuzzy pre-Ri,i=0,1,2,3 by utilizing the concepts of fuzzy pre-open sets and quasi-coincident relation. We investigate more novel properties of these classes and uncover their unique characteristics. By presenting a wide array of related theorems and interconnections, we structure a comprehensive framework for understanding these classes and interrelationships with other separation axioms in this setting. Moreover, the relations between these classes and those in some induced topological structures are examined. Additionally, we explore the hereditary and harmonic properties of these classes.

On basic arithmetic operations for interval-valued intuitionistic fuzzy sets using the Hamming distance with their application in decision making

Atanassov’s intuitionistic fuzzy sets play a vital role in handling vagueness and uncertainty successfully as they associate an additional non-membership degree to each element of the universal set. Interval-valued intuitionistic fuzzy (IVIF) sets are more generalized quantities in this direction as they use intervals (⊂[0,1]) to define the membership and non-membership grades of each element of the set. However, without defining basic arithmetic operations on the IVIF values/sets, the study is incomplete. This paper broadly examines the division and subtraction operations over any arbitrary IVIF values/sets using the concept of Hamming distance between them. A deterministic linear optimization model is proposed and solved in order to obtain the complete expressions for these operations. Next, various fundamental properties and relationships are examined and proved for the proposed arithmetic operations over IVIF values/sets. Furthermore, an example of a multi-criteria decision-making problem under uncertain conditions is studied and analyzed using the developed arithmetic operations on IVIF numbers.

Weaker Form of Fuzzy Minimal Open Sets and a Stronger Form of Fuzzy Mean Open Sets

In a fuzzy topological space, this article introduces fuzzy locally minimal open, fuzzy s-mean open sets at certain fuzzy points. Additionally, several of those fuzzy open sets attributes are expanded. Fuzzy mean open sets are weaker than the fuzzy s-mean open. We note that for each of its fuzzy points, a fuzzy minimum open is a fuzzy locally minimal open set.

A prospect theory-based MABAC algorithm with novel similarity measures and interactional operations for picture fuzzy sets and its applications

Picture fuzzy set (PFS) is one the reliable tool to handle the uncertainties in the data as compared to the intuitionistic fuzzy set (IFS) or fuzzy set. PFS simultaneously handle the four degrees namely, membership, neutrality, non-membership, and refusal, and thus widely applicable to solve the real-life decision-making problems more accurately. Keeping their advantages, in this paper, we present some interactive operational laws for the picture fuzzy numbers (PFNs) to aggregate picture fuzzy information. Also, we state some new information measures namely picture fuzzy similarity measures (PFSimMs) based on fuzzy strict negations, which can overcome the various drawbacks of the existing PFSimMs. The various properties and their features are studied in detail to show their advantages. Finally, we develop a prospect theory-based multi-attributive border approximation area comparison (MABAC) method under picture fuzzy environment by using the proposed operational laws and PFSimMs to solve the decision-making problems. The applicability of the developed algorithm is explained through a numerical example and show its superiorities.

FUZZY PRE β-OPEN SET AND ITS APPLICATIONS

This paper deals with a new type of fuzzy open-like set, viz., fuzzy pre β-open set, the class of which is strictly larger than that of fuzzy preopen set [7]. Using fuzzy pre β-open set as a basic tool, here we introduce fuzzy pre β-regular space in which fuzzy open set and fuzzy pre β-open set coincide. Here we introduce two new types of functions, viz., fuzzy pre β-continuous function, fuzzy pre β-irresolute function. The applications of these two functions on fuzzy pre β-regular space are discussed here

An Innovative Decision Model Utilizing Intuitionistic Hesitant Fuzzy Aczel-Alsina Aggregation Operators and Its Application

The intuitionistic hesitant fuzzy set is a significant extension of the intuitionistic fuzzy set, specifically designed to address uncertain information in decision-making challenges. Aggregation operators play a fundamental role in combining intuitionistic hesitant fuzzy numbers into a unified component. This study aims to introduce two novel approaches. Firstly, we propose a three-way model for investors in the business domain, which utilizes interval-valued equivalence classes under the framework of intuitionistic hesitant fuzzy information. Secondly, we present a multiple-attribute decision-making (MADM) method using various aggregation operators for intuitionistic hesitant fuzzy sets (IHFSs). These operators include the IHF Aczel–Alsina average (IHFAAA) operator, the IHF Aczel–Alsina weighted average (IHFAAWAϣ) operator, and the IHF Aczel–Alsina ordered weighted average (IHFAAOWAϣ) operator and the IHF Aczel–Alsina hybrid average (IHFAAHAϣ) operators. We demonstrate the properties of idempotency, boundedness, and monotonicity for these newly established aggregation operators. Additionally, we provide a detailed technique for three-way decision-making using intuitionistic hesitant fuzzy Aczel–Alsina aggregation operators. Furthermore, we present a numerical case analysis to illustrate the pertinency and authority of the esteblished model for investment in business. In conclusion, we highlight that the developed approach is highly suitable for investment selection policies, and we anticipate its extension to other fuzzy information domains.

Prioritized Aggregation Operators for Complex Intuitionistic Fuzzy Sets Based on Aczel-Alsina T-norm and T-conorm and Their Applications in Decision-Making

Prioritized Aggregation Operators for Complex Intuitionistic Fuzzy Sets Based on Aczel-Alsina T-norm and T-conorm and Their Applications in Decision-Making

On some new aggregation operators for T-spherical fuzzy hypersoft sets with application in renewable energy sources

On some new aggregation operators for T-spherical fuzzy hypersoft sets with application in renewable energy sources

Evaluating the Quality of Medical Services Using Intuitionistic Hesitant Fuzzy Aczel–Alsina Aggregation Information

In modern civilization, individuals are increasingly concerned with evaluating the quality of medical services. Evaluation of the quality of medical services enables medical care providers to monitor and improve their service quality. The evaluation of medical service quality is efficiently addressed by the novel concept of Aczel–Alsina operators in an intuitionistic hesitant fuzzy (IHF) environment as multicriteria decision-making (MCDM) problem. Thus, this paper presents the IHF Aczel–Alsina weighted geometric operators for IHF information. We first apply the Aczel–Alsina norms to IHF scenarios and present novel operations of intuitionistic hesitant fuzzy sets. This article develops a unique strategy for evaluating the quality of medical services based on the specified operators, including a quantitative framework for evaluating medical service quality and a novel MCDM technique. Finally, this article presents a numerical example of the novel approach used to evaluate medical services for hospitals and compares it to conventional MCDM methods to highlight the suggested superiority method. According to the comparative results, our strategy outperforms the insufficiency of lacking decision flexibility in the existing MAGDM method.