Applications of Fermatean Uncertainty weighted Average Accumulation operator to Multiple attribute group Decision Making

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.

Intuitionistic fuzzy geometric aggregation operators in the framework of Aczel-Alsina triangular norms and their application to multiple attribute decision making

This article uses the Aczel-Alsina t-norm and t-conorm to make several new linguistic interval-valued intuitionistic fuzzy aggregation operators. First, we devised some rules for how linguistic interval-valued intuitionistic fuzzy numbers should work. Then, using these rules as a guide, we created a set of operators, such as linguistic interval-valued intuitionistic fuzzy Aczel-Alsina weighted averaging (LIVIFAAWA) operator, linguistic interval-valued intuitionistic fuzzy Aczel-Alsina weighted geometric (LIVIFAAWG) operator, linguistic interval-valued intuitionistic fuzzy Aczel-Alsina ordered weighted averaging (LIVIFAAOWA) operator, linguistic interval-valued intuitionistic fuzzy Aczel-Alsina ordered weighted geometric (LIVIFAAOWG) operator, linguistic interval-valued intuitionistic fuzzy Aczel-Alsina hybrid weighted averaging (LIVIFAAHWA) operator and linguistic interval-valued intuitionistic fuzzy Aczel-Alsina hybrid weighted geometric (LIVIFAAHWG) operators are created. Several desirable qualities of the newly created operators are thoroughly studied. Moreover, a multi-criteria group decision-making (MCGDM) method is proposed based on the developed operators. The proposed operators are then applied to real-world decision-making situations to demonstrate their applicability and validity to the reader. Finally, the suggested model is contrasted with the currently employed method of operation.

For the multiple attribute group decision-making problems where attribute values are the interval-valued Pythagorean fuzzy numbers, the group decision-making method based on generalized Einstein geometric aggregation operators is developed. First, induced generalized interval-valued Pythagorean fuzzy Einstein ordered weighted geometric (I-GIVPFEOWG) aggregation operator and induced generalized interval-valued Pythagorean fuzzy Einstein hybrid weighted geometric (I-GIVPFEHWG) aggregation operator, were proposed. Some general properties of these operators, such as idempotency, commutativity, monotonicity, and boundedness, were discussed, and some special cases in these operators were analyzed. Furthermore, the method for multiple attribute group decision-making problems based on these operators was developed, and the operational processes were illustrated in detail. The main advantage of using the proposed methods and operators is that these operators and methods give a more complete view of the problem to the decision makers. These methods provide more general, more accurate, and precise results. Therefore, these methods play a vital role in real-world problems. Finally the proposed operators have been applied to decision-making problems to show the validity, practicality, and effectiveness of the new approach.

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.

In some multi-attribute decision-making (MADM) models studying attributes’ interactive phenomena is very important for the minimizing decision risks. Usually, the Choquet integral type aggregations are considered in such problems. However, the Choquet integral aggregations do not consider all attributes’ interactions; therefore, in many cases, when these interactions are revealed in less degree, they do not perceive these interactions and their utility in MADM problems is less useful. For the decision of this problem, we create the Choquet integral-based new aggregation operators’ family which considers all pair interactions between attributes. The problem under the discrimination q-rung picture linguistic and q-rung orthopair fuzzy environments is considered. Construction of a 2-order additive fuzzy measure (TOAFM) involves pair interaction indices and importance values of attributes of a MADM model. Based on the attributes’ pair interactions for the identification of associated probabilities of a 2-order additive fuzzy measure, the Shapley entropy maximum principle is used. The associated probabilities q-rung picture linguistic weighted averaging (APs-q-RPLWA) and the associated probabilities q-rung picture linguistic weighted geometric (APs-q-RPLWG) aggregation operators are constructed with respect to TOAFM. For an uncertainty pole of experts’ evaluations on attributes regarding the possible alternatives, the associated probabilities of a fuzzy measure are used. The second pole of experts’ evaluations as arguments of the aggregation operators by discrimination q-rung picture linguistic values is presented. Discrimination q-rung picture linguistic evaluations specify the attribute’s dominant, neutral and non-dominant impacts on the selection of concrete alternative from all alternatives. Constructed operators consider the all relatedness between attributes in any consonant attribute structure. Main properties on the rightness of extensions are showed: APs-q-RPLWA and APs-q-RPLWG operators match with q-rung picture linguistic Choquet integral averaging and geometric operators for the lower and upper capacities of order two. The conjugation among the constructed operators is also considered. Connections between the new operators and the compositions of dual triangular norms (Tp,Spq) and (Tmin,Smax) are also constructed. Constructed operators are used in evaluation of a selection reliability index (SRI) of candidate service centers in the facility location selection problem, when small degree interactions are observed between attributes. In example MADM, the difference in optimal solutions is observed between the Choquet integral aggregation operators and their new extensions. The difference, however, is due to the need to use indices of all interactions between attributes.

Methods for aggregating interval-valued intuitionistic fuzzy information are investigated. Some operational laws of interval-valued intuitionistic fuzzy numbers, score function and accuracy function of interval-valued intuitionistic fuzzy numbers are intriduced. Based on these operational laws, some aggregation operators, including interval-valued intuitionistic fuzzy ordered weighted geometric aggregation (IIFOWGA) operator and interval-valued intuitionistic fuzzy hybrid geometric aggregation (IIFHGA) operator, are proposed. An approach to multiple attribute group decision making (MAGDM) with interval-valued intuitionistic fuzzy information is developed based on the IIFWGA and the IIFHGA operators. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

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.

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

In this paper, we extend the Hamacher operations to aggregate the dual hesitant fuzzy elements (DHFEs). Firstly, operational rules of DHFEs based on Hamacher t-norm and t-conorm are proposed. Then, we develop some dual hesitant fuzzy Hamacher aggregation operators based on the operational rules of DHFEs, such as dual hesitant fuzzy Hamacher weighted averaging (DHFHWA) operator, dual hesitant fuzzy Hamacher weighted geometric (DHFHWG) operator, dual hesitant fuzzy Hamacher ordered weighted averaging (DHFHOWA) operator, dual hesitant fuzzy Hamacher ordered weighted geometric (DHFHOWG) operator, dual hesitant fuzzy Hamacher hybrid averaging (DHFHHA) operator and dual hesitant fuzzy Hamacher hybrid geometric (DHFHHG) operator are proposed. Some desirable properties of these operators such as idempotency and boundedness are discussed, and some special cases of these operators are analyzed. Furthermore, a method to multiple attribute decision making (MADM) based on the proposed operators is developed. Finally, a practical example is given to illustrate the developed method and a comparison analysis is also conducted, which further demonstrates the practicality and effectiveness of the proposed approach.

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.

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic, geometric aggregation operators and Hamacher operations with picture fuzzy information. Then, motivated by the ideal of traditional arithmetic, geometric aggregation operators and Hamacher operations, we have developed some aggregation operators for aggregating picture fuzzy information: picture fuzzy Hamacher aggregation operators, picture fuzzy Hamacher geometric aggregation operators, picture fuzzy Hamacher correlated aggregation operators, induced picture fuzzy Hamacher aggregation operators, induced picture fuzzy Hamacher correlated aggregation operators, picture fuzzy Hamacher prioritized aggregation operators, picture fuzzy Hamacher power aggregation operators. Then, we have utilized these operators to develop some approaches to solve the picture fuzzy 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.

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.

The theme of this work is to present some new operational laws for intuitionistic fuzzy numbers and their averaging and geometric aggregation operators under the completely unknown attribute weights. To accomplish this, firstly the shortcoming of the existing operations has been highlighted, and then, they have been mitigated by defining intuitionistic fuzzy Hamacher interaction weighted averaging and geometric aggregation operators by considering the pairs of membership functions. Some of the desirable properties of the proposed operators are stated. The attribute weight vector used for aggregating the decision maker’s preferences has been computed by using the entropy function. Finally, a decision-making approach has been presented and illustrated with a numerical example to demonstrate the superiority of the approach over the existing operators.