Group decision making with incomplete interval‐valued q‐rung orthopair fuzzy preference relations

A novel group decision making method based on CoCoSo and interval-valued Q-rung orthopair fuzzy sets

Interval-valued q-rung orthopair fuzzy set (IVq-ROFS) is a powerful tool for dealing with uncertainty. In this paper, we first propose a new method for aggregating multiple IVq-ROFSs, which is easier to understand and implement in the multi-attribute group decision making process compared to current aggregation operators. Secondly, this paper introduces a new fuzzy entropy with parameters based on IVq-ROFS, which is highly flexible due to its adjustable parameters. Based on this, the IVq-ROFS-based attribute weight calculation method is proposed to obtain the objective weights of the attributes, which is more reasonable and objective than the existing methods. Then, for the dimensional differences between the three compromise scores in the original Combined Compromise Solution (CoCoSo) method, the enhanced compromise scores are proposed. These scores are obtained by normalizing the three dependent compromise scores, ensuring that they fall within the same range. Finally, a novel CoCoSo mothed on IVq-ROFS using the proposed fuzzy entropy and enhanced compromise scores is presented. The proposed method is highly adaptable and scalable, not limited to IVq-ROFS. The excellent performance and robustness of the proposed method are verified in sepsis diagnosis applications.

An integrated group decision-making method for the evaluation of hypertension follow-up systems using interval-valued q-rung orthopair fuzzy sets

It is imperative to comprehensively evaluate the function, cost, performance and other indices when purchasing a hypertension follow-up (HFU) system for community hospitals. To select the best software product from multiple alternatives, in this paper, we develop a novel integrated group decision-making (GDM) method for the quality evaluation of the system under the interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs). The design of our evaluation indices is based on the characteristics of the HFU system, which in turn represents the evaluation requirements of typical software applications and reflects the particularity of the system. A similarity is extended to measure the IVq-ROFNs, and a new score function is devised for distinguishing IVq-ROFNs to figure out the best IVq-ROFN. The weighted fairly aggregation (WFA) operator is then extended to the interval-valued q-rung orthopair WFA weighted average operator (IVq-ROFWFAWA) for aggregating information. The attribute weights are derived using the LINMAP model based on the similarity of IVq-ROFNs. We design a new expert weight deriving strategy, which makes each alternative have its own expert weight, and use the ARAS method to select the best alternative based on these weights. With these actions, a GDM algorithm that integrates the similarity, score function, IVq-ROFWFAWA operator, attribute weights, expert weights and ARAS is proposed. The applicability of the proposed method is demonstrated through a case study. Its effectiveness and feasibility are verified by comparing it to other state-of-the-art methods and operators.

Incomplete linguistic q-rung orthopair fuzzy preference relations and their application to multi-criteria decision making

With the development of social and economic research, the judgements that people deal with are full of fuzziness and vagueness. It is convenient to use the linguistic q-rung orthopair fuzzy numbers to offer the qualitative uncertain information. Consequently, in this paper, we mainly study linguistic q-rung orthopair fuzzy preference relations (Lq-ROFPRs) and apply them to a multi-criteria decision-making (MCDM) problem. The multiplicative consistency of Lq-ROFPRs is first introduced, then a consistency-based model is established to derive the normalized linguistic q-rung orthopair fuzzy priority weight vector. The concept of acceptably multiplicative consistency is further defined, and an optimization model is formulated to repair the unacceptably multiplicative consistent Lq-ROFPR. To cope with the incomplete Lq-ROFPR, another programming model is built to ascertain the missing values. The weights of criteria are determined by constructing a possibility degree matrix. Subsequently, an MCDM problem with incomplete Lq-ROFPRs is considered and a step-by-step algorithm is put forward. Finally, the proposed method is applied to three examples, and the advantages of this new approach are also demonstrated.

Incentive mechanism-based interval-valued q-rung orthopair fuzzy dynamic comprehensive evaluation method for measuring regional green development level

Interval-valued q-rung orthopair fuzzy number (IVq-ROFN) is a popular tool for modeling complex uncertain information and has gained successful applications in the field of comprehensive evaluation. However, most of the existing studies are based on the absolute values of evaluation data but fail to take incentive effects into account. Reasonable and appropriate incentive can guide the evaluated objects to better achieve the decision goals. Therefore, this study develops an incentive mechanism-based interval-valued q-rung orthopair fuzzy dynamic comprehensive evaluation method. Firstly, new interval-valued q-rung orthopair fuzzy measures including deviation measure and correlation coefficient are proposed for managing IVq-ROFNs data. To overcome the limitations of the existing aggregating operators that are not suitable for scenarios with need of many times of data aggregation, we introduce two new interval-valued q-rung orthopair fuzzy aggregating operators. Furthermore, a new interval-valued orthopair fuzzy CRITIC method is developed to objectively determine the importance of the evaluated criteria. More importantly, the horizontal incentive effects within a single period and the vertical incentive effects during multiple periods under IVq-ROFNs environments are proposed to reward (or punish) the evaluated objects in the evaluation process. The evaluated results are determined based on the full compensatory model and the multiplicative form model. The main advantage of the developed method is that the expectations of decision-makers and the dynamic characteristics during multiple periods are taken fully into account, which can make the evaluation results more reasonable and reliable. Finally, this developed comprehensive evaluation method is applied to evaluate the green development level of Jiangxi province within eleven cities from 2016 to 2020. We observe that the cities x 2, x 3, x 4, x 5, x 7, x 8 are rewarded within positive incentive values and the cities x 1, x 6, x 9, x 10, x 11 are punished within negative incentive values. Especially, the positive incentive value for the city x 3 is the biggest and the negative incentive value for the city x 9 is the biggest. The best city in term of GDL is x 3. The evaluated results with consideration of incentive effects are in line with the expectation of the decision-maker.