DEMATEL serves as a tool for addressing multi-criteria decision-making problems, primarily by identifying critical factors that exert the most significant influence on a specific system. To enhance its capabilities in handling contextual decision problems, DEMATEL has been further developed through integration with various other MCDM methods. The inherent reliance on direct input from experts for initial decision information in DEMATEL raises concerns about the potential limitations imposed by experts' domain knowledge and bounded rationalities. The effectiveness of decision-making can be compromised if the initial information provided by experts is deemed unreliable, leading to debatable outcomes. To address these challenges, this study proposes the incorporation of a BONFERRONI mean aggregation operator within a Pythagorean neutrosophic environment, illustrated through a numerical example applied to DEMATEL. This integration is intended to fortify decision accuracy by introducing a more enhanced decision framework by developing a new normalized weighted BONFERRONI mean operator for Pythagorean neutrosophic set aggregation (PN-NWBM). By integrating this operator, this study aims to alleviate the impact of unreliable initial information and enhance the overall reliability of decision outcomes thereby contributing to its improvement in decision making. Through the implementation of the BONFERRONI mean aggregation operator, the study anticipates achieving a more comprehensive and accurate representation of decision factors as illustrated in the numerical example. This research includes a comparative and sensitivity analysis to thoroughly examine the implications and effectiveness of the proposed integration.

In various studies, to evaluate and measure the poverty, based on the poverty line, the poor are divided into the poor and non-poor and based on the data of the poor households, different indeces of poverty are calculated. Since the rate of poverty varies, the effect of each poor individual on the society varies as well. In this study, the size of poverty in Iran is measured by Fuzzy Membership Function. In the current study, using the raw data, the household income of the Iranian Sensus Beauro, from 1385 to 1397 is calculated using the index of age poverty by Gini coefficient and Bonferonie standard, in classic and fuzzy modes of poverty size. The results show that using the fuzzy logic has a significant effect on poverty size so that in the classic mode, it is significantly less than that of the fuzzy mode. The results also suggest that in both the classic and the fuzzy ways, using the Bonferonie standard instead of Gini Coefficient causes the rise of poverty.

Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events. In this paper we prove an inclusion-exclusion principle for IF-states based on a method which can also be used to prove Grzegorzewski's inclusion-exclusion principle for probabilities on IF-events. Finally, we give some applications of this principle by extending some results regarding the classical probabilities to the case of the IF-states.

Objective: Income INEQUALITY affects consumption structure via changes in the composition of expenditure basket. Shocks, fluctuations, disparities, and dispersions of income INEQUALITY, is expected to be transmitted to consumption expenditures. These shocks might induce inequalities in consumption expenditures. This paper tries to measure the amount of such consumption expenditures inequalities that are derived from income INEQUALITY.Method: To measure the consumption expenditures INEQUALITY and income INEQUALITY, the variance of logs is employed. For this purpose, Iranian urban households' data of the period of 1982 to 2007 is used. To analyze relations between variables, panel data methodology is applied. Findings: All fluctuations of income distribution do not translate in consumption expenditure distribution. Conclusion: The distribution of households' consumption expenditure in comparison to the distribution of income is less subjected to fluctuations and variations.

The BONFERRONI mean (BM) has the advantages that it can capture the interrelationship among the input arguments, and the Harmonic mean is a conservative average lying between the max and min operators. The 2-dimension uncertain linguistic variables add a subjective evaluation on the reliability of the evaluation results given by decision makers, so they can better express fuzzy information. In this paper, in order to combine the advantages of them, we first propose the 2-dimensional uncertain linguistic weighted BONFERRONI mean (2DULWBM) operator. However, it cannot consider the case when the given arguments are too high or too low. So we further proposed the 2-dimensional uncertain linguistic improved weighted BONFERRONI harmonic mean (2DULIWBHM) operator, which combine the 2DULWBM with Harmonic Mean. Furthermore, we study some desirable properties and some special cases of them. Further, we develop a new method to deal with some multi-attribute group decision making (MAGDM) problems under 2-dimension uncertain linguistic environment based on the proposed operators. Finally, an illustrative example is given to testify the validity of the developed method by comparing with the other existing methods.

The q-Rung Orthopair Fuzzy Soft Set (q-ROFSS) theory is a significant extension of Pythagorean fuzzy soft set and intuitionistic fuzzy soft set theories for dealing with the imprecision and uncertainty in data. The purpose of this study is to improve and apply this theory in decision-making. To achieve this purpose, we firstly propose some BONFERRONI Mean (BM) and Weighted BONFERRONI Mean (WBM) aggregation operators for aggregating the data. Some desired properties are presented in detail and the existing aggregation operators are used as distinct cases of our proposed operators. Further, a decision-making analysis is presented based on our proposed operations and applied to decision-making in COVID-19 diagnosis. The preferred way is discussed to protect maximum human lives from COVID-19. A numerical example is given to support the claim. The experimental results demonstrate the proposed operators have an ability to make a precise decision with imprecision and uncertain information which will find a broad application in the decision-making area.