Some Generalized Dual Hesistant Fuzzy Geometric Aggregation Operators and Applications

We investigate the multiple attribute decision making (MADM) problems with dual hesitant fuzzy information. We first introduce some basic concepts and operations on dual hesitant fuzzy sets. Then, we develop some generalized dual hesitant fuzzy aggregation operators which encompass some existing operators as their particular cases and discuss their basic properties. Next, we apply the generalized dual hesitant fuzzy Choquet ordered aggregation (GDHFCOA) operator to deal with multiple attribute decision making problems under dual hesitant fuzzy environment. Finally, an illustrative example is given to show the developed method and demonstrate its practicality and effectiveness.

Xu and Yager (2006) proposed some geometric aggregation operators based on intuitionistic fuzzy sets (IFS) and introduced the concept of sub-interval of membership values to define IFS. Based on the sub-interval, they defined various geometric aggregation operators such as intuitionistic fuzzy weighted geometric (IFWG) operator, intuitionistic fuzzy ordered weighted geometric (IFOWG) operator, and intuitionistic fuzzy hybrid geometric (IFHG) operator. In this paper, we propose these geometric aggregation operators (IFWG, IFOWG, and IFHG) based on IFS using the sub-interval of non-membership values. These operators can be used in an environment where the arguments are presented as intuitionistic fuzzy sets. Numerical examples are given to illustrate the operators. We also present an algorithm to show the application of the IFHG operator to multiple attribute decision making (MADM) problems based on intuitionistic fuzzy sets. Finally the algorithm has also been illustrated through a numerical example.

Induced aggregation operators are more suitable for aggregating the individual preference relations into a collective fuzzy preference relation. Therefore, in this paper, we introduce the notion of some new types induced aggregation operators, namely induced interval-valued Pythagorean fuzzy ordered weighted geometric aggregation operator, induced interval-valued Pythagorean fuzzy hybrid geometric aggregation operator, induced generalized interval-valued Pythagorean fuzzy ordered weighted geometric aggregation operator and induced generalized interval-valued Pythagorean fuzzy hybrid geometric aggregation operator. Furthermore, these operators are applied to decision-making problems in which experts provide their preferences in the Pythagorean fuzzy environment to show the validity, practicality and effectiveness of the new approach. We also study the applicability in a decision-making problem concerning strategic selection of the best information system and give an illustrative example to show the effectiveness of the developed methods and operators.

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.

Multi-criteria decision making (MCDM) technique and approach have been a trending topic in decision making and systems engineering to choosing the probable optimal options. The primary purpose of this article is to develop prioritized operators to multi-criteria decision making (MCDM) based on Archimedean t-conorm and t-norms (At-CN&t-Ns) under interval-valued dual hesitant fuzzy (IVDHF) environment. A new score function is defined for finding the rank of alternatives in MCDM problems with IVDHF information based on priority levels of criteria imposed by the decision maker. This paper introduces two aggregation operators: At-CN&t-N-based IVDHF prioritized weighted averaging (AIVDHFPWA), and weighted geometric (AIVDHFPWG) aggregation operators. Some of their desirable properties are also investigated in details. A methodology for prioritization-based MCDM is derived under IVDHF information. An illustrative example concerning MCDM problem about a Chinese university for appointing outstanding oversea teachers to strengthen academic education is considered. The method is also applicable for solving other real-life MCDM problems having IVDHF information.

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.

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.

The interval‐valued q‐rung orthopair fuzzy set (IVq‐ROFS) and complex fuzzy set (CFS) are two generalizations of the fuzzy set (FS) to cope with uncertain information in real decision making problems. The aim of the present work is to develop the concept of complex interval‐valued q‐rung orthopair fuzzy set (CIVq‐ROFS) as a generalization of interval‐valued complex fuzzy set (IVCFS) and q‐rung orthopair fuzzy set (q‐ROFS), which can better express the time‐periodic problems and two‐dimensional information in a single set. In this article not only basic properties of CIVq‐ROFSs are discussed but also averaging aggregation operator (AAO) and geometric aggregation operator (GAO) with some desirable properties and operations on CIVq‐ROFSs are discussed. The proposed operations are the extension of the operations of IVq‐ROFS, q‐ROFS, interval‐valued Pythagorean fuzzy, Pythagorean fuzzy (PF), interval‐valued intuitionistic fuzzy, intuitionistic fuzzy, complex q‐ROFS, complex PF, and complex intuitionistic fuzzy theories. Further, the Analytic hierarchy process (AHP) and technique for order preference by similarity to ideal solution (TOPSIS) method are also examine based on CIVq‐ROFS to explore the reliability and proficiency of the work. Moreover, we discussed the advantages of CIVq‐ROFS and showed that the concepts of IVCFS and q‐ROFS are the special cases of CIVq‐ROFS. Moreover, the flexibility of proposed averaging aggregation operator and geometric aggregation operator in a multi‐attribute decision making (MADM) problem are also discussed. Finally, a comparative study of CIVq‐ROFSs with pre‐existing work is discussed in detail.

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.

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 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.

Hesitant fuzzy set (HFS) is more flexible and general tool in comparison to fuzzy set theory. There is not yet reported an aggregation operator (AO) which can provide desirable generality, flexibility and compatibility in adjusting risk preferences while aggregating attribute values under hesitant fuzzy (HF) environment, although based on algebraic t-norm and t-conorm, Einstein t-norm and t-conorm, Hammacher t-norm and t-conorm, Dombi t-norm and t-conorm and Frank t-norm and t-conorm; weighted AOs have been developed earlier to attempt to meet above such eventualities. So, the primary objective of this paper is to develop some general, flexible as well as compatible AOs that can be exploited to solve MADM problems with HF information. From this perspective, at the very beginning, we develop new operations between HFEs by uniting the features of Archimedean and Dombi operations. Next, based on these operations, we develop HF Archimedean-Dombi weighted arithmetic and geometric AOs, HF Archimedean-Dombi ordered weighted arithmetic and geometric AOs and HF Archimedean-Dombi hybrid arithmetic and geometric AOs. We have shown that the existing HF-algebraic weighted AOs, HF-Einstein weighted AOs and HF-Hammacher weighted AOs are special cases of our developed AOs. We discuss in detail some intriguing properties of the proposed AOs. Next, we establish a procedure of MADM endowed by the proposed operators under HF environment. Then, we present a practical example concerning the personnel selection to gloss the decision steps of the proposed method. We also conduct a validity test to show that our proposed AOs are authentic and legal. Moreover, we exhibit a sensitivity investigation with diverse criteria weight sets to examine the stability of our proposed intriguing approach. Also, we draw attention toward a comparison between the existing decision-making methods with the proposed method to prove the superiority of our model.

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.

The notions of fuzzy set (FS) and intuitionistic fuzzy set (IFS) make a major contribution to dealing with practical situations in an indeterminate and imprecise framework, but there are some limitations. Pythagorean fuzzy set (PFS) is an extended form of the IFS, in which degree of truthness and degree of falsity meet the condition 0≤Θ˘2(x)+K2(x)≤1. Another extension of PFS is a q´-rung orthopair fuzzy set (q´-ROFS), in which truthness degree and falsity degree meet the condition 0≤Θ˘q´(x)+Kq´(x)≤1,(q´≥1), so they can characterize the scope of imprecise information in more comprehensive way. q´-ROFS theory is superior to FS, IFS, and PFS theory with distinguished characteristics. This study develops a few aggregation operators (AOs) for the fusion of q´-ROF information and introduces a new approach to decision-making based on the proposed operators. In the framework of this investigation, the idea of a generalized parameter is integrated into the q´-ROFS theory and different generalized q´-ROF geometric aggregation operators are presented. Subsequently, the AOs are extended to a “group-based generalized parameter”, with the perception of different specialists/decision makers. We developed q´-ROF geometric aggregation operator under generalized parameter and q´-ROF geometric aggregation operator under group-based generalized parameter. Increased water requirements, in parallel with water scarcity, force water utilities in developing countries to follow complex operating techniques for the distribution of the available amounts of water. Reducing water losses from water supply systems can help to bridge the gap between supply and demand. Finally, a decision-making approach based on the proposed operator is being built to solve the problems under the q´-ROF environment. An illustrative example related to water loss management has been given to show the validity of the developed method. Comparison analysis between the proposed and the existing operators have been performed in term of counter-intuitive cases for showing the liability and dominance of proposed techniques to the existing one is also considered.

Accumulation of q ˜ -rung picture fuzzy information plays an essential part in decision-making situations. q ˜ -rung picture fuzzy sets can handle the uncertain information more precisely and flexibly because of the presence of parameter q ˜ . Also the Frank t-norm and t-conorm operations perform suitably for the data accumulation with the operational parameter. In this paper, we introduce q ˜ -Rung picture fuzzy Frank weighted averaging operator and q ˜ -rung picture fuzzy Frank weighted geometric operator by extending q ˜ -rung orthopair fuzzy Frank arithmetic and geometric aggregation operators respectively. We establish an algorithm to address the tedious decision-making problems using these operators. Eventually, we discuss a multiple attribute decision-making problem to demonstrate the utility and efficacy of the proposed method. A comparison of existing methods is made to reveal the supremacy and benefits of our proposed method.