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

Aggregation operators are the standard mathematical tool for the combination of several inputs into one unique output. This paper presents some aggregation operators for complex intuitionistic fuzzy (CIF) information. Complex intuitionistic fuzzy set (CIFS) theory has a large ability to capture vagueness since it can represent the complete specifications of problems with both intuitionistic uncertainty and periodicity. We introduce the CIF Hamacher weighted averaging (CIFHWA) operator, CIF Hamacher ordered weighted averaging (CIFHOWA) operator, CIF Hamacher weighted geometric (CIFHWG) operator and CIF Hamacher ordered weighted geometric (CIFHOWG) operator. We bring to light some remarkable properties of these operators and explicitly state some noteworthy special cases. Moreover, we contribute to the advancement of multi-attribute decision-making (MADM) with a novel proposal of an algorithm in the CIF environment. Furthermore, we consider and solve a MADM problem that finds the best source for generation of electricity with the aid of the proposed operators, thus proving their usefulness for the purpose of decision-making. Finally, we check the effectiveness of these operators by a validity test.

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.

Machine learning language is very valuable for depicting different problems, especially computer language, data mining, data sciences, and machine language. The circular intuitionistic fuzzy set (C-IFS) is a flexible approach to fuzzy sets and intuitionistic fuzzy sets. Keep in mind the flexibility of C-IFS, decision-maker used C-IFS to cope with incomplete and redundant human opinions accurately. Furthermore, power operators are used for depicting or aggregating the collection of data into a singleton set. In this manuscript, we explore the power operators for circular intuitionistic fuzzy (C-IF) information, such as C-IF power weighted averaging (C-IFPWA) operator, C-IF power weighted ordered averaging (C-IFPWOA) operator, C-IF power weighted geometric (C-IFPWG) operator, and C-IF power weighted ordered geometric (C-IFPWOG) operator. Some properties of the above information are also stated. Additionally, we evaluate the procedure of the multi-attribute decision-making (MADM) technique for resolving the utilization of the most suitable part of machine learning in complicated scenarios. Finally, we illustrate some numerical examples for addressing the comparison between proposed techniques and existing methods to show the effectiveness and reliability of the presented operators.

Complex intuitionistic fuzzy set (CIFS) is a special intuitionistic fuzzy set where the membership and non-membership degrees are expressed by a complex-valued membership degree and can more easily describe the vagueness and uncertainty in the real world. Archimedean t-conorm and t-norm (ATT), as an important class of the t-norm (TN) and t-conorm (TC), have greater flexibility in the information fusion process. In this paper, we extend the ATT to CIFSs and present some generalized geometric aggregation operators, which can be used to handle the multiple criteria decision-making (MCDM) problems. For it, we firstly define some new operational laws of the CIFSs based on ATT, then some weighted geometric aggregation operators based on proposed operations are proposed. Further, some desirable properties and special cases of them are studied. Finally, a decision-making approach is developed for the MCDM problem with complex intuitionistic fuzzy information. A practical example is given to show the availability and advantages of the proposed method by comparison with some existing methods. The proposed aggregation operators are more generalized than the existing ones to utilize the uncertain and imprecise information. Several existing operators are considered as special cases of the proposed one. Finally, the proposed method will offer various choices to the decision-maker to access the finest alternatives.

An m-polar fuzzy set is a powerful mathematical model to analyze multipolar, multiattribute, and multi-index data. The m-polar fuzzy sets have appeared as a useful tool to portray uncertainty in multiattribute decision making. The purpose of this article is to analyze the aggregation operators under the m-polar fuzzy environment with the help of Dombi norm operations. In this article, we develop some averaging and geometric aggregation operators using Dombi t-norm and t-conorm to handle uncertainty in m-polar fuzzy (mF, henceforth) information, which are mF Dombi weighted averaging (mFDWA) operator, mF Dombi ordered weighted averaging (mFDOWA) operator, mF Dombi hybrid averaging (mFDHA) operator, mF Dombi weighted geometric (mFDWG) operator, mF Dombi weighted ordered geometric operator, and mF Dombi hybrid geometric (mFDHG) operator. We investigate properties, namely, idempotency, monotonicity, and boundedness, for the proposed operators. Moreover, we give an algorithm to solve multicriteria decision-making issues which involve mF information with mFDWA and mFDWG operators. To prove the validity and feasibility of the proposed model, we solve two numerical examples with our proposed models and give comparison with mF-ELECTRE-I approach (Akram et al. 2019) and mF Hamacher aggregation operators (Waseem et al. 2019). Finally, we check the effectiveness of the developed operators by a validity test.

In this paper, we define aggregation operators for trapezoidal cubic linguistic fuzzy sets which includes generalized cubic linguistic fuzzy averaging (geometric) operator, generalized trapezoidal cubic linguistic fuzzy weighted averaging (GTrCLFWA) operator, generalized trapezoidal cubic linguistic fuzzy weighted geometric (GTrCFWG) operator, generalized trapezoidal cubic linguistic fuzzy ordered weighted average (GTrCLFOWA) operator, generalized trapezoidal cubic linguistic fuzzy ordered weighted geometric (GTrCLFOWG) operator, generalized trapezoidal cubic linguistic fuzzy hybrid averaging (GTrCLFHA) operator and generalized trapezoidal cubic linguistic fuzzy hybrid geometric (GTrCLFHG) operator. Furthermore, we relate these aggregation operators to develop an approach to multiple attribute group decision-making with trapezoidal cubic linguistic fuzzy information. Finally, a numerical example is providing to demonstrate the submission of the established approach.

In the context of fuzzy relations, symmetry refers to a property where the relationship between two elements remains the same regardless of the order in which they are considered. Natural language processing (NLP) in engineering documentation discusses the application of computational methods or techniques to robotically investigate, analyze, and produce natural language information for manufacturing contents. The NLP plays an essential role in dealing with large amounts of textual data normally recovered in engineering documents. In this paper, we expose the idea of a bipolar complex hesitant fuzzy (BCHF) set by combining the bipolar fuzzy set (BFS) and the complex hesitant fuzzy set (CHFS). Further, we evaluate some algebraic and Schweizer-Sklar operational laws under the presence of BCHF numbers (BCHFNs). Additionally, using the above information as well as the idea of prioritized (PR) operators, we derive the idea of BCHF Schweizer-Sklar PR weighted averaging (BCHFSSPRWA) operator, BCHF Schweizer-Sklar PR ordered weighted averaging (BCHFSSPROWA) operator, BCHF Schweizer-Sklar PR weighted geometric (BCHFSSPRWG) operator, and BCHF Schweizer-Sklar PR ordered weighted geometric (BCHFSSPROWG) operator. Basic properties for the above operators are also discussed in detail, such as idempotency, monotonicity, and boundedness. Moreover, we evaluate the best way in which NLP can be applied to engineering documentations with the help of the proposed operators. Therefore, we illustrate the major technique of multi-attribute decision-making (MADM) problems based on these derived operators. Finally, we use some existing operators and try to compare their ranking results with our proposed ranking results to show the supremacy and validity of the investigated theory.

The objective of this paper is to investigate three new methods to regulate and analyze the spreading of coronavirus disease (COVID-19). COVID-19 started in the city of Wuhan, China at the end of 2019 and spread to the whole world in a short time. This infection caused millions of infected cases globally and still poses a disturbing situation for the people. Recently, some mathematical models have been constructed for better understanding of the coronavirus infection. Mostly, these models are based on classical integer-order derivative using real numbers which cannot capture the fading memory. So, at the current position, it is a challenge for the world to control the spreading of COVID-19. Therefore, the aim of this paper is to utilize fuzzy logic to control the transmission and spreading of COVID-19. Here, we develop three new methods such as the generalized interval-valued intuitionistic fuzzy Einstein weighted geometric (GIVIFEWG) operator, the generalized interval-valued intuitionistic fuzzy Einstein ordered weighted geometric (GIVIFEOWG) operator, and the generalized interval-valued intuitionistic fuzzy Einstein hybrid geometric (GIVIFEHG) operator. Intuitionistic fuzzy information for interval-valued is the moral and decent method to precise the fuzzy information for judgment or decision and Einstein operations are the best approximations, and the generalized aggregation operators are a generalization of most aggregation operators so, in these notes, we can spread the Einstein operations to aggregate the interval-valued intuitionistic fuzzy information based on the generalized aggregation operators. At the end of the paper, an illustration of the emergency situation of COVID-19 is given for demonstrating the effectiveness of the suggested approach, showing the feasibility and reliability of the new methods.

Hesitant triangular fuzzy information aggregation based on Einstein operations and their application to multiple attribute decision making

In this article, the authors investigate the multiple attribute decision making problems with picture 2-tuple linguistic information. The utilized power average and power geometric operations used to develop some picture 2-tuple linguistic power aggregation operators: picture 2-tuple linguistic power weighted average (P2TLPWA) operator, picture 2-tuple linguistic power weighted geometric (P2TLPWG) operator, picture 2-tuple linguistic power ordered weighted average (P2TLPOWA) operator, picture 2-tuple linguistic power ordered weighted geometric (P2TLPOWG) operator, picture 2-tuple linguistic power hybrid average (P2TLPHA) operator and picture 2-tuple linguistic power hybrid geometric (P2TLPHG) operator. The prominent characteristic of these proposed operators is studied. This article has utilized these operators to develop some approaches to solve the picture 2-tuple linguistic multiple attribute decision making problems. Finally, a practical example for enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

As a generalization of complex fuzzy set (CFS), complex hesitation fuzzy set (CHFS) is a powerful tool to express two-dimensional fuzzy information, but it ignores the randomness that exists widely in real life. Considering the randomness and ambiguity often simultaneously occur in real-world problems, we come up with an innovative fuzzy set called complex probabilistic hesitant fuzzy set (CPHFS) in this article, which is a joint extension of CFS and probabilistic hesitant fuzzy set (PHFS). Moreover, we establish four basic operations for complex probabilistic hesitant fuzzy element(CPHFE) and a series of useful operational laws are also developed. Secondly, several aggregation operators including complex probabilistic hesitant fuzzy weighted averaging operator(CPHFWA), complex probabilistic hesitant fuzzy weighted geometric operator(CPHFWG), complex probabilistic hesitant fuzzy Heronian Mean operator(CPHFHM) and complex probabilistic hesitant fuzzy Geometric Heronian Mean operator(CPHFGHM) as well as their weighted forms that can reflect the interrelationship among all decision attributes are proposed, which is of great use in multi-attribute decision making(MADM) or in multi-attribute group decision making(MAGDM) issues when we want to synthesize multiple evaluation values into one. Besides, we also present a number of valuable properties of these provided aggregation operators. Thirdly, a MADM process is built in the CPHF environment step by step based on the aggregation operators we have just established. Furthermore, we provide an example about purchasing a most suitable car to demonstrate the effectiveness and practicability of the proposed decision process. Finally, we point out the superiorities of MADM in working under the CPHF environment through comparing it with the existing method and also offer some possible prospects for further research. The method displayed in this work can effectively solve the MADM problems where the decision-making information is described by CPHFEs and the attributes are interactive.

With respect to multiple periods multiple attribute decision making problems with intuitionistic fuzzy information, some operational laws, score function and accuracy function of intuitionistic fuzzy numbers are introduced, and a new operator called dynamic intuitionistic fuzzy weighted geometric (DIFWG) operator is presented. A model based on DIFWG operator is developed to solve the multiple periods multiple attribute decision making problems where all the decision making information about attribute values takes the form of intuitionistic fuzzy numbers collected t different periods. Then the intuitionistic fuzzy weighted geometric (IFWG) operator is utilized to aggregate the overall intuitionistic fuzzy information corresponding to each alternative, and then rank the alternatives and select the most desirable one(s) according to the score function and accuracy function. Finally, an illustrative example about supplier selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Since traffic congestion is a major issue worldwide, particularly in urban areas due to the increasing population on a daily basis, it negatively impacts human life, leading to time wastage, health problems, and economic repercussions. Therefore, establishing a sustainable transportation system in densely populated urban areas is crucial. To overcome this challenge, various factors on which a sustainable transportation system depends must be deeply analyzed. However, this analysis may involve fuzziness and vagueness due to imprecise data and incomplete information. In this regard, a mathematical framework called the Complex Intuitionistic Fuzzy Hypersoft Set (CIFHSS) is introduced in this research. This article presents and thoroughly investigates essential set-theoretical operations based on the complex intuitionistic fuzzy hypersoft set, using appropriate examples. Furthermore a novel Multi-Attribute Decision Making approach, based on the CIFHSS is developed. This approach incorporates decision-valued matrices (both maximum and minimum), a scoring framework for CIFHSS, and matrix-based aggregations, such as the core matrix. Moreover, the algorithm is implemented in a real-world scenario to solve traffic congestion in urban areas, demonstrating the versatility of the proposed algorithm. The model assigns scores of 0.6161 to the Electric Bus Rapid Transit system, 0.6089 to the Expanded Bicycle Lane Network, 0.6571 to Light Rail Transit, and 0.7627 to the Hybrid Car-Sharing Program, identifying the latter as the most suitable option. A sensitivity analysis of the proposed model is also presented using statistical tools. Finally, a detailed conclusion and future directions for the application of this research are provided.

Aggregation operators (AOs) are utilized to overcome the influence of uncertain and vague information in different fuzzy environments. A multi-attribute decision-making (MADM) technique plays a vital role in several fields of different environments such as networking analysis, risk assessment, cognitive science, recommender systems, signal processing, and many more domains in ambiguous circumstances. In this article, we elaborated the notion of Aczel–Alsina t-norm (TNM) and t-conorm (TCNM) under the system of complex Pythagorean fuzzy (CPyF) sets (CPyFSs). Some basic operational laws of Aczel–Alsina TNM and TCNM are established including Aczel–Alsina sum, product, scalar multiplication, and power operations based on CPyFSs. We established several AOs of CPyFSs such as CPyF Aczel–Alsina weighted average (CPyFAAWA), and CPyF Aczel–Alsina weighted geometric (CPyFAAWG) operators. The proposed CPyFAAWA and CPyFAAWG operators are symmetric in nature and satisfy the properties of idempotency, monotonicity, boundedness and commutativity. To solve an MADM technique, we established an illustrative example to select a suitable candidate for a vacant post in a multinational company. To see the advantages of our proposed AOs, we compared the results of existing AOs with the results of newly established AOs.

The digital green concept refers to the devotion to digital technology, i.e., techniques of procedures in the area of ecological or sustainable conservation. It contains leveraging digital techniques, procedures, and new tools to evaluate environmental problems and promote sustainable development. The major influence of this article is to evaluate the selection of the best digital green technology. For this, we aim to propose the idea of Maclaurin symmetric mean (MSM) operators based on interaction operational laws for T-spherical fuzzy (TSF) information, such as TSF interaction weighted averaging (TSFIWA), generalized TSF interaction weighted averaging (GTSFIWA), TSF interaction weighted geometric averaging (TSFIWGA), TSF interaction MSM (TSFIMSM), TSF interaction Bonferroni mean (TSFIBM), and TSF interaction weighted Maclaurin symmetric mean (TSFIWMSM) operators. Some dominant and reliable properties are also invented for evaluation. Moreover, to address the best digital green innovation (DGI) among the top five DGIs, we illustrate the procedure of the multi-attribute decision-making (MADM) technique under the presence of the derived operators. Finally, we demonstrate a numerical example for evaluating the comparative study between the proposed and existing or prevailing operators to enhance the worth of the derived theory.