Generalized trapezoidal cubic linguistic fuzzy ordered weighted average operator and group 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.

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.

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.

Aggregation operators are important tools for solving multi-attribute group decision-making (MAGDM) problems. The main challenging issue for aggregating data in a MAGDM problem is how to develop a symmetric aggregation operator expressing the decision makers’ behavior. In the literature, there are some methods dealing with this difficulty; however, they lack an effective approach for multi-polar inputs. In this study, a new aggregation operator for m-polar fuzzy soft sets (M-pFSMWM) reflecting different agreement scenarios within a group is presented to proceed MAGDM problems in which both attributes and experts have different weights. Moreover, some desirable properties of M-pFSMWM operator, such as idempotency, monotonicity, and commutativity (symmetric), that means being invariant under any permutation of the input arguments, are studied. Further, m-polar fuzzy soft induced ordered weighted average (M-pFSIOWA) operator and m-polar fuzzy soft induced ordered weighted geometric (M-pFSIOWG) operator, which are extensions of IOWA and IOWG operators, respectively, are developed. Two algorithms are also designed based on the proposed operators to find the final solution in MAGDM problems with weighted multi-polar fuzzy soft information. Finally, the efficiency of the proposed methods is illustrated by some numerical examples. The characteristic comparison of the proposed aggregation operators shows the M-pFSMWM operator is more adaptable for solving MAGDM problems in which different cases of agreement affect the final outcome.

The aim of this paper is to define some new operation laws for trapezoidal cubic hesitant fuzzy (TrCHF) numbers and define some new aggregation operators. In order to extend these operational laws of the trapezoidal cubic hesitant fuzzy numbers (TrCHFNs), we constructed a series of aggregation operator so called trapezoidal cubic hesitant fuzzy averaging and geometric aggregation operators. Furthermore, these aggregation operators applied to group decision making. Finally, a numerical example is used to illustrate the validity of the proposed approach in group decision-making problems.

The key objective of the proposed work in this paper is to introduce a generalized form of linguistic picture fuzzy set, so-called linguistic spherical fuzzy set (LSFS), combining the notion of linguistic fuzzy set and spherical fuzzy set. In LSFS we deal with the vague and defective information in decision making. LSFS is characterized by linguistic positive, linguistic neutral and linguistic negative membership degree which satisfies the conditions that the square sum of its linguistic membership degrees is less than or equal to 1. In this paper, we investigate the basic operations of linguistic spherical fuzzy sets and discuss some related results. We extend operational laws of aggregation operators and propose linguistic spherical fuzzy weighted averaging and geometric operators based on spherical fuzzy numbers. Further, the proposed aggregation operators of linguistic spherical fuzzy number are applied to multi-attribute group decision-making problems. To implement the proposed models, we provide some numerical applications of group decision-making problems. In addition, compared with the previous model, we conclude that the proposed technique is more effective and reliable.

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.

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

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.

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.

In this article, fermatean uncertainty weighted Averaging Aggregation operator has been studied along their several properties namely impotency, boundedness and monotonicity. Secondly we applied this proposed operator to deal with multiple attribute group decision making problem under fermatean uncertainty information. Finally, we constructed an algorithm for multiple attribute group decision making problems with suitable example. Introduction: Xu demonstrated several operators such as intuitionist uncertainty weighted averaging (IFWA), intuitionist uncertainty ordered weighted averaging (IFOWA) and intuitionist uncertainty hybrid Averaging (IFHA) operators. Xu and Yager explored geometric addition operators such as intuitionistic uncertainty weighted geometric (IFWG) operator, intuitionist uncertainty hybrid geometric (IFWG) operators. They also applied them to multiple alternate group decision making (MAGDH) based on intuitionist fuzzy set (IFS). The advantage of the aggregation operators in this work, we familiarize the noted of (3, 2) Uncertainty weighted averaging aggregation of operator and also discuss some of their basic properties. Conclusions: The main advantage of using the proposed method and operator is that this method provides more general, accurate and precise results. Therefore, the suggested methodology can be used for any type of selection problem involving any number of selection attributes. This method plays a vital role in real world situations. We ended the paper with an application of fermatean uncertainty decision making problem. In future, some author may develop this gives operators in various fuzzy Environment.

With respect to the multi-attribute group decision-making (MAGDM) problems with the interval grey uncertain linguistic variables (IGULVs), the MAGDM method based on the interval grey uncertain linguistic generalized hybrid averaging (IGULGHA) operator is proposed. Firstly, the operation rules, the properties and the comparing method of the IGUVs are introduced. Then, some aggregation operators such as interval grey uncertain linguistic generalized ordered weighted aggregation (IGULGOWA) operator and interval grey uncertain linguistic generalized hybrid aggregation (IGULGHA) operator are defined, and some properties such as idempotency, commutativity, monotonicity and boundedness are proved, and then, the decision-making methods based on these operators are presented to solve the group decision-making problems. Finally, a numerical example is used to show the proposed method, and the influence of the different position weight vector w and the different parameter � on decision-making is analysed. The result shows that the method is simple and effective.

With respect to intuitionistic linguistic information aggregation problems, we first define a new score function and a new accuracy function of intuitionistic linguistic number (ILN) and present a simple method for the comparison between two ILNs. Then, based on the intuitionistic linguistic weighted geometric averaging (ILWGA) operator, we propose two new intuitionistic linguistic geometric operators, such as the intuitionistic linguistic ordered weighted geometric (ILOWG) operator and intuitionistic linguistic hybrid geometric (ILHG) operator, and establish various properties of these operators. Furthermore, we apply the ILHG and ILWGA operators to solve multi-criteria group decision making problems, in which the criterion values take the form of ILNs and the criterion weight information is known completely. Finally, an illustrative example is given to demonstrate the feasibility and effectiveness of the developed approach.