Complex Fuzzy Sets Research Articles

Bipolar complex fuzzy credibility aggregation operators and their application in decision making problem

<abstract><p>A bipolar complex fuzzy credibility set (BCFCS) is a new approach in computational intelligence and decision-making under uncertainty. Bipolar complex fuzzy credibility (BCFC) information has been employed as a strategy for dealing with confusing and unreliable situations that arise in everyday life. In this paper, we used the concept of aggregation operators to diagnose the well-known averaging and geometric aggregation operators, as well as evaluate some properties and related results. Using described operators, an algorithm for multiple criteria group decision making is proposed. Then, a numerical example of a case study of Hospital selection is discussed. Lastly, the comparative analysis of suggested operators with existing operators are also given to discuss the rationality, efficiency and applicability of these operators.</p></abstract>

Dombi Bonferroni Mean Operators Under Bipolar Complex Fuzzy Environment and Their Applications in Internet World

Internet is almost a necessary facility and tool to solve daily life problems in every field life. Whether at the individual level or national and international level sale purchase of any kind of object has always been of much importance, especially after Corona Pandemic, when online business is at its peak. Because of the enhancement of online sales and purchases, various businessmen are looking for suitable internet websites for their businesses, and the selection of the most suitable internet websites is one of the multi-attribute decision-making (MADM) dilemmas. Thus, in this script, we take benefits of three various concepts that are Bonferroni mean (BM) operator which is a significant technique to catch the interrelatedness among any number of inputs, Dombi operations which are based on Dombi t-norm and t-conorm and the ability to create an aggregation procedure more flexible because of the parameter, bipolar complex fuzzy set (BCFS) which is an outstanding model for tackling two-dimensional information with negative aspect and interpret bipolar complex fuzzy (BCF) Dombi Bonferroni mean (BCFDBM), BCF weighted Dombi Bonferroni mean (BCFWDBM), BCF Dombi geometric Bonferroni mean (BCFDGBM), and BCF weighted Dombi geometric Bonferroni mean (BCFWDGBM) operators. After ward, in this script, for tackling MADM dilemmas in the setting of BCFS, we investigate a MADM procedure based on the investigated operators and solve a MADM dilemma (selection of a suitable internet website for businessmen). Further, to display the superiority and efficiency of our work, we compare our approach and operators with a few current approaches and operators.

Prioritization and selection of operating system by employing geometric aggregation operators based on Aczel-Alsina t-norm and t-conorm in the environment of bipolar complex fuzzy set

<abstract> <p>Aczel-Alsina t-norm and t-conorm are great substitutes for sum and product and recently various scholars developed notions based on the Aczel-Alsina t-norm and t-conorm. The theory of bipolar complex fuzzy set that deals with ambiguous and complex data that contains positive and negative aspects along with a second dimension. So, based on Aczel-Alsina operational laws and the dominant structure of the bipolar complex fuzzy set, we develop the notion of bipolar complex fuzzy Aczel-Alsina weighted geometric, bipolar complex fuzzy Aczel Alsina ordered weighted geometric and bipolar complex fuzzy Aczel Alsina hybrid geometric operators. Moreover, multi-attribute border approximation area comparison technique is a valuable technique that can cover many decision-making situations and have dominant results. So, based on bipolar complex fuzzy Aczel-Alsina aggregation operators, we demonstrate the notion of a multi-attribute border approximation area comparison approach for coping with bipolar complex fuzzy information. After that, we take a numerical example by taking artificial data for various types of operating systems and determining the finest operating system for a computer. In the end, we compare the deduced multi-attribute border approximation area comparison approach and deduced aggregation operators with numerous prevailing works.</p> </abstract>

Analyzing the effect of different types of pollution with bipolar complex fuzzy power Bonferroni mean operators

When any amount of harmful materials (any substance or any type of energy) is introduced into the climate at a rate quicker than it very well may be scattered or securely put away, then pollution occurs. These harmful materials are known as pollutants which can be natural and can also be manmade such as trash generated by factories. These harmful materials harm the quality of land, air, and water and cause various types of pollution, which affects the environment. In this article, we analyze the effect of various types of pollution on the environment and evaluate the most harmful type of pollution through an illustrative example by employing power Bonferroni mean (BM) operators in the setting of the bipolar complex fuzzy set (BCFS), like bipolar complex fuzzy (BCF) power BM (BCFPBM), BCF weighted power BM (BCFWPBM), BCF power geometric BM (BCFPGBM), and BCF weighted power geometric BM (BCFWPGBM) operators and a decision-making (DM) procedure created on these operators in the environment of the BCFS which are introduced in this article. Furthermore, we illustrate that the introduced operators and a DM procedure in the environment of the BCFS are more effective and have a wide model and advantages than certain prevailing works.

Analysis and application of Aczel-Alsina aggregation operators based on bipolar complex fuzzy information in multiple attribute decision making

Bipolar complex fuzzy information is a new idea that can easily depict awkward and vague information in real life problems. The main theory of the bipolar complex fuzzy set is the fusion of two different theories, called bipolar fuzzy set and complex fuzzy set. The bipolar complex fuzzy set contained two different grades, called positive membership grade which is considered a positive aspect of the problem, and negative membership grade which is considered a negative aspect of the problem, both contain in a unit square of complex plane. The major analysis of this theory is to diagnose the interrelationship among any number of attributes. For this, we defined various Aczel-Alsina operational laws and proved their influential results. Further, by using the Aczel-Alsina operational laws and bipolar complex fuzzy information, we diagnosed the theory of bipolar complex fuzzy Aczel-Alsina weighted averaging (BCFAAWA), bipolar complex fuzzy Aczel-Alsina ordered weighted averaging (BCFAAOWA), and bipolar complex fuzzy Aczel-Alsina hybrid averaging (BCFAAHA) operators. To modify the influence of the explored work, we discussed various important results and some properties (Idempotency, Monotonicity, and Boundedness) of the proposed work. Additionally, we computed a multi-attribute decision-making rule under the presence of the initiated approaches and tried to justify it with the help of some examples. Finally, to evaluate the influence and dominancy of the diagnosed work, we compared our deliberated work with various prevailing approaches and also described their geometrical representations.

Development of complex cubic q-rung orthopair fuzzy aggregation operators and their application in group decision-making

In view of the fact that the uncertainty and vagueness of decision data and the changes to the phase (periodicity) of the data may occur simultaneously, a new hybrid model is first proposed by combining cubic q-rung orthopair fuzzy set (Cq-ROFS) and complex fuzzy set, which is called complex cubic q-rung orthopair fuzzy set (CCq-ROFS). Then, some algebraic operations of CCq-ROFS are defined, and the distance measure, score function, accuracy function, comparison method and desirable properties are studied in detail. Further, we develop weighted average and geometric aggregation operators based on CCq-ROFS information, and propose a new decision method for complex decision-making problems. Finally, the proposed method is applied to the actual evaluation decision, and the validity and feasibility of the method are verified by parameter analysis and comparison of several decision-making methods.

Complex intuitionistic fuzzy ordered weighted distance measure

Compared with the complex fuzzy set (CFS) and the intuitionistic fuzzy set (IFS), the complex intuitionistic fuzzy set (CIFS) can handle the two-dimensional and uncertain information simultaneously, and thus strengthen the capability of capturing useful information. In this paper, we consider the situation with complex intuitionistic fuzzy environment, where the importance of certain information is also taken into consideration. To deal with these situations, we develop the complex intuitionistic fuzzy ordered weighted distance (CIFOWD) measure and investigate its main properties. We find that the CIFOWD measure provides a parameterized family of aggregation distance measures, which includes, for example, complex intuitionistic fuzzy ordered weighted geometric distance (CIFOWGD) measure, complex intuitionistic fuzzy ordered weighted Hamming distance (CIFOWHD) measure, and complex intuitionistic fuzzy ordered weighted Euclidean distance (CIFOWED) measure as special types. The CIFOWD measure is capable of alleviating the influence of excessively large or excessively small deviations on the aggregation results via weight vector. Based on these distance measures, a multiple criteria group decision-making approach is presented under the CIFSs environment. An illustrative example regarding coronavirus vaccine selection on COVID-19 is taken for demonstrating the effectiveness of the proposed approach. Finally, the proposed results are compared with the results obtained from the existing methods.

Retraction Note: Extentions of neutrosophic cubic sets via complex fuzzy sets with application

Retraction Note: Extentions of neutrosophic cubic sets via complex fuzzy sets with application

A Novel Solution for $Z$-Numbers Based on Complex Fuzzy Sets and Its Application in Decision-Making System

<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Z$</tex-math></inline-formula> -numbers have been proven to be advantageous in revealing uncertain information. This article focuses on applying uncertain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Z$</tex-math></inline-formula> -numbers to engineering practice. Considering that various uncertain data are inevitable in the process of addressing actual problems, uncertain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Z$</tex-math></inline-formula> -numbers are introduced to express information and measure information reliability. Powerful tools are essential when dealing with uncertain information; then, complex fuzzy sets (CFSs) are employed. First, the parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$B$</tex-math></inline-formula> in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Z$</tex-math></inline-formula> -numbers is interpreted from the perspective of the phase term, and uncertain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Z$</tex-math></inline-formula> -numbers are transformed to interval-valued CFSs. Next, arithmetic operators, aggregation operator, generalized entropy, distance measure, and similarity measure are defined. Besides, a multicriteria group decision-making method is suggested by combining the proposed entropy, distance measure, and aggregation operator. The algorithm is applied to select the brand of the inertial navigation system. The comparison analysis with other widely used methods is conducted to verify the feasibility and validity of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Z$</tex-math></inline-formula> -information in the application.

An algorithm for identifying reference signals under the environment of complex fuzzy sets

In this paper, we have discussed some new operations and results of set theory for complex fuzzy sets (CFSs). Moreover, we developed the basic results of CFSs under the basic operations such as complex fuzzy simple difference, bounded sum, bounded difference, dot product, bounded product, union, intersection, and Cartesian product. We explored the CFSs and discussed the related properties with examples such as complex fuzzy bounded sum over the intersection, complex fuzzy dot product over the union, etc. Identifying the reference signals under the environment of CFSs have always been a challenging. Many algorithms based on set theoretic operations and distance measures have been proposed for identifying a reference signal using any common system. But linear time invariant (LTI) system is considered easy to analyze the linear and time-varying signals. We used CFSs in signals and systems. We developed an algorithm based on convolution product and LTI system under the complex fuzzy environment. We identified a high degree of resemblance (reference signal) of the received signals to the reference signal in a linear time-invariant (LTI) system that receives an input signal and produces an output signal.

Complex q-rung orthopair fuzzy Frank aggregation operators and their application to multi-attribute decision making

The complex q-rung orthopair fuzzy sets (Cq-ROFSs) can serve as a generalization of q-rung orthopair fuzzy sets (q-ROFSs) and complex fuzzy sets FS (CFSs). Cq-ROFSs provide more freedom for people handling uncertainty and vagueness by the truth and falsity grades on the condition that the sum of the q-powers of the real part and imaginary part is within the unit interval. Further, Frank operational laws are an extended form of Archimedes' T mode and Archimedes' S mode and Frank aggregation operators have a certain parameter which makes them more flexible and more generalized than many other aggregation operators in the process of information fusion. The objectives of this paper are to extend the Frank operations to the complex q-rung orthopair fuzzy environment and to introduce their score function and accuracy function. Meanwhile, some complex q-rung fuzzy Frank aggregation operators are developed, such as the complex q-rung orthopair fuzzy Frank weighted averaging (Cq-ROFFWA) operator, the complex q-rung orthopair fuzzy Frank weighted geometric (Cq-ROFFWG) operator, and the complex q-rung orthopair fuzzy Frank ordered weighted averaging (Cq-ROFFOWA) operator, and their special cases are discussed. In addition, an innovative MADM method is introduced according to the propounded operators to deal with multi-attribute decision-making problems under the complex q-rung orthopair fuzzy environment. Consequently, the practicability and effectiveness of the created methods are proposed by parameter exploration and comparative analysis.

Some Characterizations of Certain Complex Fuzzy Subgroups

The complex fuzzy environment is an innovative tool to handle ambiguous situations in different mathematical problems. In this article, we commence the abstraction of (ρ,η)-complex fuzzy sets, (ρ,η)-complex fuzzy subgroupoid, (ρ,η)-complex fuzzy subgroups and describe important examples of the symmetric group under (ρ,η)-complex fuzzy sets. Additionally, we discuss the conjugacy class of the group with respect to (ρ,η)-complex fuzzy normal subgroups. We define (ρ,η)-complex fuzzy cosets and elaborate upon the certain operation of this analog to group theoretic operation. We prove that factors regarding the (ρ,η)-complex fuzzy normal subgroup form a group and establish an ordinary homomorphism. Moreover, we create the (ρ,η)-complex fuzzy subgroup of the factor group.

Novel distance measures based on complex fuzzy sets with applications in signals

Novel distance measures based on complex fuzzy sets with applications in signals

Bipolar Complex Fuzzy Subgroups

In this study, firstly, we interpret the level set, support, kernel for bipolar complex fuzzy (BCF) set, bipolar complex characteristic function, and BCF point. Then, we interpret the BCF subgroup, BCF normal subgroup, BCF conjugate, normalizer for BCF subgroup, cosets, BCF abelian subgroup, and BCF factor group. Furthermore, we present the associated examples and theorems, and prove these associated theorems. After that, we interpret the image and pre-image of BCF subgroups under homomorphism and prove the related theorems.

The generalized dice similarity measures for bipolar complex fuzzy set and its applications to pattern recognition and medical diagnosis

The generalized dice similarity measures for bipolar complex fuzzy set and its applications to pattern recognition and medical diagnosis

An Optimized Decision Support Model for COVID-19 Diagnostics Based on Complex Fuzzy Hypersoft Mapping

COVID-19 has shaken the entire world economy and affected millions of people in a brief period. COVID-19 has numerous overlapping symptoms with other upper respiratory conditions, making it hard for diagnosticians to diagnose correctly. Several mathematical models have been presented for its diagnosis and treatment. This article delivers a mathematical framework based on a novel agile fuzzy-like arrangement, namely, the complex fuzzy hypersoft (CFHS) set, which is a formation of the complex fuzzy (CF) set and the hypersoft set (an extension of soft set). First, the elementary theory of CFHS is developed, which considers the amplitude term (A-term) and the phase term (P-term) of the complex numbers simultaneously to tackle uncertainty, ambivalence, and mediocrity of data. In two components, this new fuzzy-like hybrid theory is versatile. First, it provides access to a broad spectrum of membership function values by broadening them to the unit circle on an Argand plane and incorporating an additional term, the P-term, to accommodate the data’s periodic nature. Second, it categorizes the distinct attribute into corresponding sub-valued sets for better understanding. The CFHS set and CFHS-mapping with its inverse mapping (INM) can manage such issues. Our proposed framework is validated by a study establishing a link between COVID-19 symptoms and medicines. For the COVID-19 types, a table is constructed relying on the fuzzy interval of [0,1]. The computation is based on CFHS-mapping, which identifies the disease and selects the optimum medication correctly. Furthermore, a generalized CFHS-mapping is provided, which can help a specialist extract the patient’s health record and predict how long it will take to overcome the infection.

An intelligent sv-neutrosophic parameterized MCDM approach to risk evaluation based on complex fuzzy hypersoft set for real estate investments

PurposeIn this article, the elementary notions and aggregation operations of single-valued neutrosophic parameterized complex fuzzy hypersoft set (sv-NPCFHSS) are characterized initially. Then by using matrix version of sv-NPCFHSS, a decision-support system is constructed for the evaluation of real estate residential projects by observing various risk factors.Design/methodology/approachTwo approaches are utilized in this research: set-theoretic approach and algorithmic approach. The first approach is used to investigate the notions of sv-NPCFHSS and its some aggregations whereas the second approach is used to propose an algorithm for designing its decision-support system by using the aggregation operations like reduced fuzzy matrix, decision matrix, etc. of sv-NPCFHSS. The adopted algorithm is validated in real estate scenario for the selection of residential project by observing various risk factors to avoid any expected investment loss.FindingsThe proposed approach is more flexible and reliable as it copes with the shortcomings of literature on sv-neutrosophic set, sv-neutrosophic soft set and other fuzzy soft set-like structures by considering hypersoft setting, complex setting and neutrosophic setting collectively.Research limitations/implicationsIt has limitations for complex intuitionistic fuzzy hypersoft set, complex neutrosophic hypersoft set and other complex neutrosophic hypersoft set-like models.Practical implicationsThe scope of this research may cover a wide range of applications in several fields of mathematical sciences like artificial intelligence, optimization, MCDM, theoretical computer science, soft computing, mathematical statistics etc.Originality/valueThe proposed model bears the characteristics of most of the relevant existing fuzzy soft set-like models collectively and fulfills their limitations.

A faster algorithm for identifying signals using complex fuzzy sets

A faster algorithm for identifying signals using complex fuzzy sets

Complex probabilistic fuzzy set and their aggregation operators in group decision making extended to TOPSIS

Randomness and fuzziness create uncertainty in the system at the same time. To combine randomness and cognitive uncertainty into a single paradigm and incorporate more data, this article focuses on developing complex probabilistic fuzzy set. The main intention of this article is to develop a method that can solve both statistical and non-statistical uncertainties. Statistical uncertainty depicts the type of uncertainty concerning the possibility of a future event occurring and non-statistical uncertainties denote the concept of partial truth and imprecise reason. Here, statistical uncertainty is given through probability and non-statistical uncertainty is denoted via the complex fuzzy sets and are incorporated together to form the complex probabilistic fuzzy set. This combination summarizes the importance of this article as they could depict the real life situations more precisely. Proposing the complex probabilistic fuzzy set and studying its basic operations are the article’s main contributions. Also, various aggregation operators are developed for the same and their essential properties are duely explained. Further on, these operators are extended to TOPSIS which is utilized for a group decision making problem with data obtained in the form of complex probabilistic fuzzy number to find the best site for construction of ethanol plant to produce biofuel. The main reason for considering TOPSIS here is because it is a concept that formulates a scalar value taking into consideration both the best and worst alternatives, it represents the rationale of human choice in a more simplistic and straightforward logic and also, it takes less computation time.

Amplitude interval-valued complex Pythagorean fuzzy sets with applications in signals processing

In this paper, we introduce the notion of amplitude interval-valued complex Pythagorean fuzzy sets (AIVCPFSs). The motivation for this extension is the utility of interval-valued complex fuzzy sets in membership and non-membership degree which can express the two dimensional ambiguous information as well as the interaction among any set of parameters when they are in the form of interval-valued. The principle of AIVCPFS is a mixture of the two separated theories such as interval-valued complex fuzzy set and complex Pythagorean fuzzy set which covers the truth grade (TG) and falsity grade (FG) in the form of the complex number whose real part is the sub-interval of the unit interval. We discuss some set-theoretic operations and laws of the AIVCPFSs. We study some particular examples and basic results of these operations and laws. We use AIVCPFSs in signals and systems because its behavior is similar to a Fourier transform in certain cases. Moreover, we develop a new algorithm using AIVCPFSs for applications in signals and systems by which we identify a reference signal out of the large number of signals detected by a digital receiver. We use the inverse discrete Fourier transform for the membership and non-membership functions of AIVCPFSs for incoming signals and a reference signal. Thus a method for measuring the resembling values of two signals is provided by which we can identify the reference signal.