Linguistic information aggregation operator and its application in multi-attribute group decision making

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.

Novel approach to multi-attribute group decision-making based on interval-valued Pythagorean fuzzy power Maclaurin symmetric mean operator

Generalized trapezoidal fuzzy numbers (GTFNs) have been widely applied in uncertain decision-making problems. The similarity between GTFNs plays an important part in solving such problems, while there are some limitations in existing similarity measure methods. Thus, based on the cosine similarity, a novel similarity measure of GTFNs is developed which is combined with the concepts of geometric distance, center of gravity, area and perimeter after analyzing the limitations of previous methods. Then comparative analysis is conducted with existing similarity measures, and the results show that the novel similarity measure has better distinguishability and lower invalidity. Furthermore, a general process, which combines the new similarity measure of GTFNs with compromise methods, is developed to deal with multi-attribute group decision making (MAGDM) problem. Finally, we combine fuzzy VIKOR with the general process as illustrated example, which proves the superiority of the developed similarity measure in solving MAGDM problem.

Multiattribute group decision making based on intuitionistic 2-tuple linguistic information

Neutrosophic theories and methods are suitable for handling a variety of uncertain information, especially in complex decision-making situations. Nowadays, how to study multi-attribute group decision-making (MAGDM) problems in neutrosophic environments is a vital task for scholars and practitioners. Granular computing is a popular mathematical framework for uncertain problems, and it has been proved as a useful tool for solving MAGDM problems. In this chapter, a new neutrosophic multigranulation model for MAGDM is proposed, and some theoretical models and decision-making algorithms are presented. Finally, some case studies and comparative analysis are performed to show the merit of the presented models and algorithms. In general, this chapter is conducive to neutrosophic decision-making communities and intelligent decision-making methods.

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.

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.

The recruitment of university researchers can be considered a multi-attribute group decision-making (MAGDM) problem. MAGDM is a familiar issue with uncertainty and fuzziness in the decision-making field. Generalized hesitation fuzzy numbers (GHFNs) as a new expanded form of hesitation fuzzy numbers (HFNs) can better express the uncertain information in MAGDM. The TODIM is a very classical and widely used method to deal with the MAGDM issue. In this paper, we integrate cumulative prospect theory (CPT) into TODIM to consider not only decision makers’ subjective risk preferences but also their confidence level to obtain more reasonable choices under risk conditions. Therefore, we propose the GHF CPT-TODIM approach to tackle the MAGDM issue. Meanwhile, in the GHF environment, it is proposed to use the volatility of attribute information (entropy weighting method) to obtain the importance of attributes, obtain the unknown attribute weight, and enhance the rationality of weight information. Finally, the validity and usefulness of the technique are verified by applying the GHF CPT-TODIM technique to the recruitment of university researchers and comparing it with the existing GHF MAGDM method, which offers a new way to solve the MAGDM problem with GHFNs.

A sequential multiple attribute three-way group decision-making method to heterogeneous MAGDM problems with unknown weight information

Partitioned Heronian means based on linguistic intuitionistic fuzzy numbers for dealing with multi-attribute group decision making

Selecting an optimum technique for disposing of biomedical waste is a frequently observed obstacle in multi-attribute group decision-making (MAGDM) problems. The MAGDM is commonly applied to tackle decision-making states originated by obscurity and vagueness. The interval-valued q-rung orthopair fuzzy soft set is a novel variant of fuzzy sets. The main objective of this study is to introduce the interval-valued q-rung orthopair fuzzy soft Einstein-ordered weighted and Einstein hybrid weighted aggregation operators. Based on developed aggregation operators, a novel decision-making approach, the Evaluation based on the Distance from the Average Solution introduced to solve the MAGDM problem. The execution of the proposed approach demonstrates the significant impact of determining the most effective strategy to handle biomedical waste. Our proposed approach's practicality is confirmed by a case study focusing on selecting the most effective technique for Biomedical Waste (BMW) treatment. This study shows that autoclaving is the most effective method for the disposal of BMW. Comparative and sensitivity analysis confirms the consistency and effectiveness of our methodology. The comparative study indicates the effects of the proposed strategy are more feasible and realistic than the prevailing techniques.

Compromise ratio method for fuzzy multi-attribute group decision making

An extension of multi-attribute group decision making method based on quantum-like Bayesian network considering the interference of beliefs

Multi-granularity unbalanced hesitant fuzzy linguistic term set (MGUHFLTS) is an effective expression of linguistic information, which applied in multi-attribute group decision-making (MAGDM), meanwhile Dempster-Shafer evidence theory (DSET) is profound method of representing and aggregating uncertain information. In order to combine the advantages from both, a new MAGDM approach based on Dempster-Shafer with MGUHFLTSs is proposed. The initial MGUHFLTSs decision matrix is transformed to evidence matrix, and a novel weight determination model of MAGDM problem with MGUHFLTSs is established in this approach. In additional, in order to combine evidence with MGUHFLTSs, a new MAGDM combination algorithm is proposed by means of DSET combination rules, which reduces the loss of MGUHFLTSs information for. An example is applied with this method about evaluation on the development quality of open education. Finally, this paper proves the validity and superiority of the proposed method.

A generalized TODIM evaluation approach based on the novel score function and trust network under interval-valued hesitant fuzzy environment