Complex Intuitionistic Fuzzy Sets Research Articles

Multi-criteria Radio Frequency Identification Approach for Manufacturing Company Selection Based on Partitioned Maclaurin Symmetric Mean Operators Under Complex Intuitionistic Fuzzy Set Environment

Multi-criteria Radio Frequency Identification Approach for Manufacturing Company Selection Based on Partitioned Maclaurin Symmetric Mean Operators Under Complex Intuitionistic Fuzzy Set Environment

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.

Novel Complex Intuitionistic Hesitant Fuzzy Distance Measures for Solving Decision-Support Problems

The key objective of this article is to introduce the innovative idea of a complex intuitionistic hesitant fuzzy set (CIHFS), which blends the intuitionistic hesitant fuzzy set with the complex fuzzy set to address the uncertain information in real-life complex problems. In CIHFS, the range of the membership functions is extended from the subset of the real number to the unit disc under the hesitant environment. To determine how well the CIHFSs can be distinguished from one another, we first propose generalized distance measures and weighted generalized distance measures based on the Hamming, Euclidean, and Hausdorff metrics. Some interesting properties and their relationships are thoroughly discussed. Furthermore, a decision-making framework for selecting the optimal option from the feasible set has been proposed, which is grounded in these distance metrics. For the purpose of proving the method’s efficacy, we included examples from pattern recognition and medical diagnostics.

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.

Innovative approaches to solar cell selection under complex intuitionistic fuzzy dynamic settings

<abstract> <p>The need to meet current energy demands while protecting the interests of future generations has driven people to adopt regulatory frameworks that promote the careful use of limited resources. Among these resources, the sun is an everlasting source of energy. Solar energy stands out as a prime example of a renewable and environmentally friendly energy source. An imperative requirement exists for precise and dependable decision-making methods for the selection of the most efficacious solar cell. We aimed to address this particular issue. The theory of complex intuitionistic fuzzy sets (CIFS) adeptly tackles ambiguity, encompassing complex problem formulations characterized by both intuitionistic uncertainty and periodicity. We introduced two aggregation operators: The complex intuitionistic fuzzy dynamic ordered weighted averaging (CIFDOWA) operator and the complex intuitionistic fuzzy dynamic ordered weighted geometric (CIFDOWG) operator. Noteworthy features of these operators were stated, and significant special cases were meticulously outlined. An updated score function was devised to address the deficiencies, identified in the current score function within the context of CIF knowledge. In addition, we devised a methodical strategy for managing multiple attribute decision-making (MADM) problems that involve CIF data by implementing the proposed operators. To demonstrate the efficacy of the formulated algorithm, we presented a numerical example involving the selection of solar cells together with a comparative analysis with several well-established methodologies.</p> </abstract>

Exploring static rebalancing strategies for dockless bicycle sharing systems based on multi-granularity behavioral decision-making

In the continuously evolving context of urbanization, more people flock to cities for job opportunities and an improved quality of life, resulting in undeniable pressure on transportation networks. This leads to severe daily commuting challenges for residents. To mitigate this urban traffic pressure, most cities have adopted urban dockless bicycle sharing systems (UDBSS) as an effective measure. However, making accurate decisions regarding UDBSS demand in different city locations is crucial, as incorrect choices can worsen transportation problems, causing difficulties in finding bicycles or excessive deployments leading to disorderly accumulation. To address this decision-making challenge, it is essential to consider uncertain factors like daily weather, temperature, and workdays. To tackle this effectively, we construct an adjustable multi-granularity (MG) complex intuitionistic fuzzy (CIF) information system using complex intuitionistic fuzzy sets (CIFSs). This system objectively determines classification thresholds using an evaluation-based three-way decision (TWD) method, creating adjustable MG CIF probability rough sets (PRSs). Additionally, to recognize the irrationality of decision-makers (DMs), we propose a method that combines prospect theory (PT) with regret theory (RT), providing a more comprehensive understanding of the influence of DMs' psychological factors on decision outcomes. Building upon these foundations, we present static rebalancing strategies for UDBSS based on MG PRSs and prospect-regret theory (P-RT) within the CIF information system. Finally, using UDBSS data collected from various sensors, we conduct experimental analysis to verify its feasibility and stability. In summary, this approach considers residents’ daily usage preferences, including bicycles utilization and return, with the aim of minimizing unmet resident demands and predicting usage patterns for the next day. It effectively addresses the issue of UDBSS distribution inefficiencies and holds a significant advantage in prediction, making it suitable for broader applications in transportation systems and contributing to the establishment of more advanced modern intelligent transportation systems (MITSs) in the future.

Modeling uncertainties associated with multi-attribute decision-making based evaluation of cooling system using interval-valued complex intuitionistic fuzzy hypersoft settings

<abstract><p>Academics encounter a challenge regulating data-driven unpredictability in numerous complicated decision scenarios. Regulating the cyclical nature of appraisal attributes, determining lower and higher limitations, granting multi-parametric values as a means of assessing argumentation, and modeling uncertainty are a few examples of these problems. It requires the incorporation of complex plane settings, interval-valued intuitionistic fuzzy settings, and hypersoft settings. Inspired by these kinds of scenarios, the goal of this research was to articulate a new theoretical framework, the interval-valued complex intuitionistic fuzzy hypersoft set ($ \Gamma $-set), which can handle these kinds of problems as a whole under the umbrella of a single framework. First, the concepts of $ \Gamma $-set, as well as its set operations and aggregations, such as decision matrix, cardinal matrix, aggregate matrix, and cardinality set, were examined. The second phase offers an appealing algorithm that consists of nine steps that go from taking into account necessary set construction to making the best choice. A prototype case study analyzing eighteen evaluation qualities and thirty-four sub-attributes for determining an optimal cooling system ($ \mathbb{CSYS}) $ for a factory validates the provided algorithm. Informative comparison analysis and preferred study features were provided as essential components of research to assist academics in making significant advances regarding their field and gradually, but thoroughly, advancing their specialization.</p></abstract>

Selection of Optimal Approach for Cardiovascular Disease Diagnosis under Complex Intuitionistic Fuzzy Dynamic Environment

Cardiovascular disease (CVD) is a leading global health concern. There is a critical need for accurate and reliable decision-making tools to select the optimal approach for diagnosing cardiovascular disease (CVD). In this study, we have addressed this pressing issue. Complex intuitionistic fuzzy set (CIFS) theory is adept at encapsulating vagueness due to its capability to encompass comprehensive problem specifications characterized by both intuitionistic uncertainty and periodicity. Within the scope of this article, we present two novel aggregation operators: the complex intuitionistic fuzzy dynamic weighted averaging (CIFDWA) operator and the complex intuitionistic fuzzy dynamic weighted geometric (CIFDWG) operator. Some intriguing characteristics of these operators are elucidated, and important special cases are also defined in detail. We devise an enhanced score function to rectify the deficiencies observed in the existing score function under complex intuitionistic fuzzy knowledge. Furthermore, these operators are employed in the development of a systematic approach for the handling of multiple attribute decision-making (MADM) scenarios involving complex intuitionistic fuzzy data. Moreover, we undertake the resolution of an MADM problem, wherein we ascertain the optimal approach for diagnosing cardiovascular disease (CVD) through the utilization of the proposed operators, thereby substantiating their utility in decision-making processes. Finally, we conduct a comprehensive comparative analysis, pitting the presented operators against an array of existing counterparts, in order to demonstrate the reliability and stability inherent in the derived methodologies.

Innovative discussion of decision-making model based on complex cubic picture fuzzy information and geometric aggregation operators with applications

This article presents a novel concept of complex cubic picture fuzzy sets (CCPFS) and introduces one more new idea of complex interval-valued picture fuzzy sets (CIVPFS) as foundational framework of CCPFS. The proposed CCPFS combines CIVPFS and complex picture fuzzy sets (CPFS), where CPFS extends the complex intuitionistic fuzzy set by incorporating a neutral membership degree. This unique model offers an expanded range of values using degrees of membership, neutral membership, and non-membership, within the unit disk of a complex plane. Additionally, we introduce two more new ideas of internal complex cubic picture fuzzy sets (ICCPFS) and external complex cubic picture fuzzy sets (ECCPFS) to further enhance the versatility of the approach. To facilitate practical applications, complement, score, and accuracy functions are developed and defined for CCPFS. Moreover, three types of averaging aggregation operators based on complex cubic picture fuzzy sets are introduced, including complex cubic picture fuzzy weighted geometric (CCPFWG) operators, complex cubic picture fuzzy ordered weighted geometric (CCPFOWG) operator, and complex cubic picture fuzzy hybrid weighted geometric (CCPFHWG) operator. The CCPFHWG operator generalizes both CCPFWG and CCPFOWG operators, providing a comprehensive framework for aggregating complex cubic picture fuzzy data. To demonstrate the practicality of the proposed approach, a multi-criteria decision-making (MCDM) problem is presented, showcasing its effectiveness in addressing today's complex decision structures. The utilization of complex cubic picture fuzzy sets and the corresponding aggregation operators in MCDM highlights their applicability and relevance in tackling real-world complexities.

Identification and Classification of Multi-Attribute Decision-Making Based on Complex Intuitionistic Fuzzy Frank Aggregation Operators

Invented by Frank in 1979, Frank’s t-norm and t-conorm operations possess improved modifications and can be applied more generally than the existing algebraic t-norm and t-conorm. The major objective of this article is to determine Frank’s operational laws based on complex intuitionistic fuzzy (CIF) information. Moreover, we examine the Frank aggregation operators (averaging and geometric) based on CIF set theory and Frank operational laws, such as the CIF Frank weighted averaging (CIFFWA) operator, CIF Frank ordered weighted averaging (CIFFOWA) operator, CIF Frank hybrid averaging (CIFFHA) operator, CIF Frank weighted geometric (CIFFWG) operator, CIF Frank ordered weighted geometric (CIFFOWG) operator and CIF Frank hybrid geometric (CIFFHG) operator. Some dominant and feasible properties of the invented techniques are also stated. Additionally, to evaluate the problem of osteoporosis in human bodies based on their causes and risk factors, we illustrate an application of the multi-attribute decision-making (MADM) technique with consideration of the invented methods to show the supremacy and validity of the derived techniques. Finally, we aim to compare the proposed scenarios with some valid existing or prevailing techniques to increase the value of the presented approaches.

Complex Intuitionistic Fuzzy Subrings

In this paper, we defined the complex intuitionistic fuzzy subring and introduced some new concepts like Intuitionistic fuzzy sets and homogeneous complex intuitionistic fuzzy sets. Then, we investigated some of characteristics of complex intuitionistic fuzzy subring. The relationship between complex intuitionistic fuzzy subring and intuitionistic fuzzy subring is also investigated. It is found that every complex intuitionistic fuzzy subring yields two intuitionistic fuzzy subring. Finaly, we defined the image and inverse image of complex intuitionistic fuzzy subring under ring homomorphism, and thus studied their elementary properties.

Complex interval-valued intuitionistic fuzzy decision support system with application to COVID-19 healthcare facilities

The complex interval-valued intuitionistic fuzzy set (CIIFS), as an extension of the complex intuitionistic fuzzy set (CIFS), is one of the better tools for dealing with time-periodic information in a single set of two-dimensional information. So, this paper makes some new operators based on Aczel-Alsina’s t-norm and t-conorm in the CIIFS environment. First, some Aczel-Alsina t-norm and t-conorm operational laws are defined for complex interval-valued intuitionistic fuzzy numbers (CIIFNs). Then, using the proposed operational laws, Aczel-Alsina The operators Complex interval-valued intuitionistic Aczel-Alsina weighted average (CIIFAAWA), Complex interval-valued intuitionistic Aczel-Alsina weighted geometric (CIIFAAWG), Complex interval-valued intuitionistic Aczel-Alsina ordered weighted average (CIIFAAOWA), and Complex interval-valued intuitionistic Aczel-Alsina ordered weighted geometric (CIIFAAOWG) are developed. Further, some properties of the proposed operators are discussed and investigated in detail. A group decision-making method is also suggested based on developed operators in the CIIFS environment. The proposed operators are more adaptable and give more accurate results than existing ones. Furthermore, a multi-criteria decision-making technique is developed based on the proposed operators. A decision-making problem for healthcare facilities in public hospitals is provided to demonstrate the benefits and applicability of the proposed method. Finally, a comparative study is also investigated using the existing methods.

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

Frank Prioritized Aggregation Operators and WASPAS Method Based on Complex Intuitionistic Fuzzy Sets and Their Application in Multi-Attribute Decision-Making

Complex intuitionistic fuzzy (CIF) information covers the degree of membership and the degree of non-membership in the form of polar coordinates with a valuable and dominant characteristic where the sum of the real parts (the same rule for the imaginary parts) of the pair must be contained in the unit interval. In this paper, we first derive the Frank operational laws for CIF information and then examine the prioritized aggregation operators based on Frank operational laws for managing the theory of CIF information. These are the CIF Frank prioritized averaging (CIFFPA) operator, the CIF Frank prioritized ordered averaging (CIFFPOA) operator, the CIF Frank prioritized geometric (CIFFPG) operator, and the CIF Frank prioritized ordered geometric (CIFFPOG) operator with properties of idempotency, monotonicity, and boundedness. Furthermore, we derive the WASPAS (weighted aggregates sum product assessment) under the consideration or presence of the CIF information and try to justify it with the help of a suitable example. Additionally, we illustrate some numerical examples in the presence of the MADM (multi-attribute decision-making) procedures for evaluating the comparison between the proposed operators with some well-known existing operators to show the validity and worth of the proposed approaches.

Power aggregation operators based on Yager t-norm and t-conorm for complex q-rung orthopair fuzzy information and their application in decision-making problems

AbstractThe complex q-rung orthopair fuzzy (CQ-ROF) set can describe the complex uncertain information. In this manuscript, we develop the Yager operational laws based on the CQ-ROF information and Yager t-norm and t-conorm. Furthermore, in aggregating the CQ-ROF values, the power, averaging, and geometric aggregation operators have played a very essential and critical role in the environment of fuzzy set. Inspired from the discussed operators, we propose the CQ-ROF power Yager averaging (CQ-ROFPYA), CQ-ROF power Yager ordered averaging (CQ-ROFPYOA), CQ-ROF power Yager geometric (CQ-ROFPYG), and CQ-ROF power Yager ordered geometric (CQ-ROFPYOG) operators. These operators are the modified version of the Power, Yager, averaging, geometric, and the combination of these all based on fuzzy set (FS), intuitionistic FS, Pythagorean FS, q-rung orthopair FS, complex FS, complex intuitionistic FS, and complex Pythagorean FS. Moreover, we also discuss the main properties of the proposed operators. Additionally, we develop a multi-attribute decision-making (MADM) method based on the developed operators. To show the supremacy and validity of the proposed method, the comparison between the proposed method and some existing methods is done by some examples, and results show that the proposed method is better than the others in terms of generality and effectiveness.

Geometric Aggregation Operators for Solving Multicriteria Group Decision-Making Problems Based on Complex Pythagorean Fuzzy Sets

The Complex Pythagorean fuzzy set (CPyFS) is an efficient tool to handle two-dimensional periodic uncertain information, which has various applications in fuzzy modeling and decision making. It is known that the aggregation operators influence decision-making processes. Algebraic aggregation operators are the important and widely used operators in decision making techniques that deal with uncertain problems. This paper investigates some complex Pythagorean fuzzy geometric aggregation operators, such as complex Pythagorean fuzzy weighted geometric (CPyFWG), complex Pythagorean fuzzy ordered weighted geometric (CPyFOWG), complex Pythagorean fuzzy hybrid geometric (CPyFHG), induced complex Pythagorean fuzzy ordered weighted geometric (I-CPyFOWG), and induced complex Pythagorean fuzzy hybrid geometric (I-CPyFHG), and their structure properties, such as idempotency, boundedness, and monotonicity. In addition, we compare the proposed model with their existing models, such as complex fuzzy set and complex intuitionistic fuzzy set. We analyze an example involving the selection of an acceptable location for hospitals in order to demonstrate the effectiveness, appropriateness, and efficiency of the novel aggregation operators.

Aczel–Alsina Power Aggregation Operators for Complex Picture Fuzzy (CPF) Sets with Application in CPF Multi-Attribute Decision Making

Complex picture fuzzy sets are the updated version of the complex intuitionistic fuzzy sets. A complex picture fuzzy set covers three major grades such as membership, abstinence, and falsity with a prominent characteristic in which the sum of the triplet will be contained in the unit interval. In this scenario, we derive the power aggregation operators based on the Aczel–Alsina operational laws for managing the complex picture of fuzzy values. These complex picture fuzzy power aggregation operators are complex picture fuzzy Aczel–Alsina power averaging, complex picture fuzzy Aczel–Alsina weighted power averaging, complex picture fuzzy Aczel–Alsina power geometric, and complex picture fuzzy Aczel–Alsina weighted power geometric operators. We also investigate their theoretical properties. To justify these complex picture fuzzy power aggregation operators, we illustrate a procedure of a decision-making technique in the presence of complex picture fuzzy values and derive an algorithm to evaluate some multi-attribute decision-making problems. Finally, a practical example is examined to illustrate the decision-making procedure under the consideration of derived operators, and their performance is compared with that of various operators to show the supremacy and validity of the proposed approaches.

On Cohesive Fuzzy Sets, Operations and Properties with Applications in Electromagnetic Signals and Solar Activities

In the present communication, a new concept of a cohesive fuzzy set (CHFS) has been proposed as a synchronized generalization of complex fuzzy sets and hesitant fuzzy sets in a systematic way. The novelty of the introduced notion lies in the selection of the best alternative among the available multiple favorable situations, where the possibility of its range is in the extended unit circle of the complex plane. We study the relationship between the CHFS and the complex intuitionistic fuzzy set (CIFS), along with validation of the obtained results. On the basis of the proposed notion, various properties, operations, and identities have been established with their necessary proof. The applications of CHFS in the process of filtering the signals for obtaining the reference signal using the necessary Fourier cosine transform or inverse Fourier cosine transform and identifying the maximum number of sunspots in a particular interval of solar activity have been suitably discussed with illustrative numerical examples. Some advantages of incorporating the proposed notion have also been tabulated for better understanding.

Multi-attribute decision-making methods based on Aczel–Alsina power aggregation operators for managing complex intuitionistic fuzzy sets

Multi-attribute decision-making methods based on Aczel–Alsina power aggregation operators for managing complex intuitionistic fuzzy sets

Operation properties and $$(\alpha ,\beta )$$-equalities of complex intuitionistic fuzzy sets

Operation properties and $$(\alpha ,\beta )$$-equalities of complex intuitionistic fuzzy sets