Multi-criteria decision support models under fuzzy credibility rough numbers and their application in green supply selection

As the increasing environmental issues, various companies have take initiatives to produce green products or to select green suppliers which maximize the business performance and minimize the environmental pollution. The real numbers data have imbiguity and uncertainty due to described by classical tools. Therefore, we consider a new type of fuzzy set, fuzzy credibility rough sets. In fuzzy credibility rough set has credibility membership of positive membership and they reduced the imbiguity in data information. In this paper we have defined a new set called fuzzy credibility rough set (FCRS), after that we defined Frank operational laws for FCRS information. Using these operational laws, we defined a series of aggregation operators that is fuzzy credibility Frank rough weigthed averaging aggregation operators, fuzzy credibility Frank rough ordered weigthed averaging aggregation operators, fuzzy credibility Frank rough hybrid weigthed averaging aggregation operators and its basic properties like boundedness, monotonicity and idempotency. As there is no work which is based on Frank norms aggregation operators under FCRS information. So, we defined a series of aggregation operators that can help us to collect the data for various green suppliers management. We developed a new set called fuzzy credibility rough set (FCRS). We developed a new Frank norms operational laws under FCRS information. We developed a series of aggregation operators. We developed and extend various steps of GRA, VIKOR and TOPSIS method under FCRS information. We explained the application of our proposed work to a real life decision making problem (green supplier management). All the proposed work is to applied to real life decision making problems (green supplier management) to find the best optimal result. Firstly we can collect the data from the decision makers using the proposed aggregation operators and then we applied all the steps of developed method to find the solution in case of green supplier management.

Extension of correlation coefficient based TOPSIS technique for interval-valued Pythagorean fuzzy soft set: A case study in extract, transform, and load techniques

Correlation is an essential statistical concept for analyzing two dissimilar variables' relationships. Although the correlation coefficient is a well-known indicator, it has not been applied to interval-valued Pythagorean fuzzy soft sets (IVPFSS) data. IVPFSS is a generalized form of interval-valued intuitionistic fuzzy soft sets and a refined extension of Pythagorean fuzzy soft sets. In this study, we propose the correlation coefficient (CC) and weighted correlation coefficient (WCC) for IVPFSS and examine their necessary properties. Based on the proposed correlation measures, we develop a prioritization technique for order preference by similarity to the ideal solution (TOPSIS). We use the Extract, Transform, and Load (ETL) software selection as an example to demonstrate the application of these measures and construct a prioritization technique for order preference by similarity to the ideal solution (TOPSIS) model. The method investigates the challenge of optimizing ETL software selection for business intelligence (BI). This study offers to illuminate the significance of using correlation measures to make decisions in uncertain and complex settings. The multi-attribute decision-making (MADM) approach is a powerful instrument with many applications. This expansion is predicted to conclude in a more reliable decision-making structure. Using a sensitivity analysis, we contributed empirical studies to determine the most significant decision processes. The proposed algorithm's productivity is more consistent than prevalent models in controlling the adequate conformations of the anticipated study. Therefore, this research is expected to contribute significantly to statistics and decision-making.

A new multi-attribute decision making approach based on new score function and hybrid weighted score measure in interval-valued Fermatean fuzzy environment

Interval-valued Fermatean fuzzy sets (IVFFSs) were introduced as a more effective mathematical tool for handling uncertain information in 2021. In this paper, firstly, a novel score function (SCF) is proposed based on IVFFNs that can distinguish between any two IVFFNs. And then, the novel SCF and hybrid weighted score measure were used to construct a new multi-attribute decision-making (MADM) method. Besides, three cases are used to demonstrate that our proposed method can overcome the disadvantages that the existing approaches cannot obtain the preference orderings of alternatives in some circumstances and involves the existence of division by zero error in the decision procedure. Compared with the two existing MADM methods, our proposed approach has the highest recognition index and the lowest error rate of division by zero. Our proposed method provides a better approach to dealing with the MADM problem in the interval-valued Fermatean fuzzy environment.

Cosine similarity measures between q-rung orthopair linguistic sets and their application to group decision making problems

The q-rung orthopair linguistic set (q-ROLS), a combined version of linguistic term sets and q-rung orthopair fuzzy set, is an efficient mathematical tool to accomplish the imprecise information while solving the decision-making problems. Under this environment, we propose additional operations and relations to deal with the decision information, and some properties are well proved. Furthermore, we propound some cosine similarity measures and weighted cosine similarity measures for q-ROLSs based on the traditional cosine similarity measures with a brief study of related properties. In the proposed similarity measures, various linguistic scale functions are utilized in order to take into account the semantics of linguistic terms. Besides this, we employ the stated q-rung orthopair linguistic similarity measures to multi-criteria group decision making problems, in which the weights of DMs are delineated by the projection of individual decisions on the ideal decision results. At last, a numerical example is used to demonstrate the practicality of the suggested technique, and its efficacy is validated by comparison with prevailing techniques. The suggested method’s sensitivity and stability analyses are also provided.

A Fuzzy Multi-Criteria Method for Sustainable Ferry Operator Selection: A Case Study

This study is motivated by the Zhuhai municipal government, which needs to select a sustainable ferry operator. Previous research has ignored the evaluation and selection of ferry operators. In addition, since ferry operator evaluation involves conflicting qualitative and quantitative criteria, and there may be uncertainty and ambiguity in the evaluation of criteria by experts, a fuzzy multi-criteria decision-making (MCDM) approach is required to address this challenge. To this end, this paper proposes an integrated MCDM framework model to evaluate and select the best ferry operator. First, a ferry operator evaluation index system with 15 sub-criteria is constructed according to literature and expert opinions; then the fuzzy analytic hierarchy process (FAHP) is used to determine the subjective weight of the criteria, and the entropy weight (EW) method is used to calculate the objective weight of the criteria. We use the linear weighting method to obtain the comprehensive weights of the criteria; finally, the fuzzy technique for order preference by similarity to ideal solution (FTOPSIS) method is adapted to determine the best ranking of the alternatives. This paper takes the Wanshan Islands in Zhuhai as a real case study to verify the proposed FAHP-EW-FTOPSIS method. The results show that the proposed method can be effectively applied to the evaluation and selection of ferry operators. Sensitivity analysis of criteria weights demonstrates the effectiveness and robustness of the proposed framework model. Key findings based on the research provide management insights that can benefit relevant stakeholders. This is the first paper to study the evaluation and selection of ferry operators. Hence, the evaluation index system and integrated framework model proposed in this paper can make important contributions to the evaluation of ferry operators.