A method to multi-attribute decision making problems by using heronian mean operators based on linear diophantine uncertain linguistic settings

In the real decision process, an important problem is how to express the attribute value more efficiently and accurately. In the real world, because of the complexity of decision-making problems and the fuzziness of decision-making environments, it is not enough to express attribute values of alternatives by exact values. For this managing with such sorts of issues, the principle of Linear Diophantine uncertain linguistic set is a valuable and capable technique to manage awkward and inconsistent information in everyday life problems. In this manuscript, we propose the original idea of Linear Diophantine uncertain linguistic set and elaborated their essential laws. Additionally, to determine the association among any numbers of attributes, we elaborated the Linear Diophantine uncertain linguistic arithmetic Heronian mean operator, Linear Diophantine uncertain linguistic weighted arithmetic Heronian mean operator, Linear Diophantine uncertain linguistic geometric Heronian mean operator, Linear Diophantine uncertain linguistic weighted geometric Heronian mean operator, and their properties are also discovered. By using these operators, we utilize the multi-attribute decision-making procedure by using elaborated operators. To determine the consistency and validity of the elaborated operators, we illustrate some examples by using explored operators. Finally, the superiority and comparative analysis of the elaborated operators with some existing operators are also determined and justified with the help of a graphical point of view.

Water Quality Index (WQI) of Shitalakshya River Near Haripur Power Station, Narayanganj, Bangladesh

The present investigation is aimed at understanding the water quality parameters and the findings of a water quality index (WQI) to assess the characteristics of the Shitalakshya River near Haripur power station, Narayanganj for five different years (2013-2018) considering monsoon, pre-monsoon, post-monsoon seasonal variations. In this study, three different methods were used to evaluate the WQI named as; Weighted Arithmetic Index Method, Canadian Council of Ministers of the Environment (CCME) WQI Method and National Sanitation Foundation (NSF) Method. Essential parameters i.e. dissolved oxygen, pH, chloride, turbidity, color, biochemical oxygen demand, total dissolved solids, Silica, Iron, electrical conductivity, Phosphate were considered for calculating the WQI. According to Weighted Arithmetic Index Method, the WQI value varied from 80 to 286 for the last five years. From the National Sanitation Foundation Method, the WQI value was found within 36 to 56 for the study duration. The WQI value was varied from 3 to 16 according to the Canadian Council of Ministers of the Environment Water Quality Index Method. Based on WQI values, the Shitalakhya river water was being classified as poor water for the above-mentioned different years. Among the different parameters, mostly turbidity, electrical conductivity, TSS, Iron were the parameters that caused the situation worst. Journal of Engineering Science 12(3), 2021, 45-55

Intuitionistic fuzzy-valued neutrosophic multi-sets and numerical applications to classification

A single-valued neutrosophic multi-set is characterized by a sequence of truth membership degrees, a sequence of indeterminacy membership degrees and a sequence of falsity membership degrees. Nature of a single-valued neutrosophic multi-set allows us to consider multiple information in the truth, indeterminacy and falsity memberships which is pretty useful in multi-criteria group decision making. In this paper, we consider sequences of intuitionistic fuzzy values instead of numbers to define the concept of intuitionistic fuzzy-valued neutrosophic multi-set. In this manner, such a set gives more powerful information. We also present some set theoretic operations and a partial order for intuitionistic fuzzy-valued neutrosophic sets and provide some algebraic operations between intuitionistic fuzzy-valued neutrosophic values. Then, we develop two types of weighted aggregation operators with the help of intuitionistic fuzzy t-norms and t-conorms. By considering some well-known additive generators of ordinary t-norms, we give the Algebraic weighted arithmetic and geometric aggregation operators and the Einstein weighted arithmetic and geometric aggregation operators that are the particular cases of the weighted aggregation operators defined via general t-norms and t-conorms. We also define a simplified neutrosophic valued similarity measure and we use a score function for simplified neutrosophic values to rank similarities of intuitionistic fuzzy-valued neutrosophic multi-values. Finally, we give an algorithm to solve classification problems using intuitionistic fuzzy-valued neutrosophic multi-values and proposed aggregation operators and we apply the theoretical part of the paper to a real classification problem.

Interval basic uncertain information and related aggregations in decision making

The recently proposed basic uncertain information can directly present numerical uncertainties for given real values, but it cannot handle given interval values which themselves also have uncertainties. Against this background, this work proposes the concept of interval basic uncertain information which serves as a generalization of basic uncertain information and involves two types of uncertainties. We analyze some basic operations, weighted arithmetic mean and preference transformation for interval basic uncertain information. The Rule-based decisions and the comprehensive certainty of interval basic uncertain information are also discussed. An illustrative example of multi-source multi-criteria evaluation under interval basic uncertain information environment is presented.

Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management

For the multi-criteria group decision-making problem where the criterion value is a normal interval number and the weight information is incomplete, the normal interval number and its compromise expected value, compromise mean square error, algorithm, weighted arithmetic average of normal interval number (ININWAA) Operator, the ordered weighted average (ININOWA) operator of normal interval numbers and the mixed weighted average (ININHA) operator of normal interval numbers, and a multi-criteria group with incomplete information based on normal interval numbers is proposed. Decision-making methods. This method uses ININWAA operator and INNHA operator to integrate criterion values, uses the compromise mean square error of criterion values, establishes an optimisation model to solve the optimal criterion weights and uses the expectation variance criterion to determine the order of the schemes. The case analysis shows the effectiveness and feasibility of this method.

Bounds for the Differences between Arithmetic and Geometric Means and Their Applications to Inequalities

Refining and reversing weighted arithmetic-geometric mean inequalities have been studied in many papers. In this paper, we provide some bounds for the differences between the weighted arithmetic and geometric means , using known inequalities. We improve the results given by Furuichi-Ghaemi-Gharakhanlu and Sababheh-Choi. We also give some bounds on entropies, applying the results in a different approach. In Section 4, we explore certain convex or concave functions, which are symmetric functions on the axis t=1/2.

Integrating water quality index, GIS and multivariate statistical techniques towards a better understanding of drinking water quality

Groundwater is considered as an imperative component of the accessible water assets across the world. Due to urbanization, industrialization and intensive farming practices, the groundwater resources have been exposed to large-scale depletion and quality degradation. The prime objective of this study was to evaluate the groundwater quality for drinking purposes in Mewat district of Haryana, India. For this purpose, twenty-five groundwater samples were collected from hand pumps and tube wells spread over the entire district. Samples were analyzed for pH, electrical conductivity (EC), total dissolved solids (TDS), total hardness (TH), turbidity, total alkalinity (TA), cations and anions in the laboratory using the standard methods. Two different water quality indices (weighted arithmetic water quality index and entropy weighted water quality index) were computed to characterize the groundwater quality of the study area. Ordinary Kriging technique was applied to generate spatial distribution map of the WQIs. Four semivariogram models, i.e. circular, spherical, exponential and Gaussian were used and found to be the best fit for analyzing the spatial variability in terms of weighted arithmetic index (GWQI) and entropy weighted water quality index (EWQI). Hierarchical cluster analysis (HCA), principal component analysis (PCA) and discriminant analysis (DA) were applied to provide additional scientific insights into the information content of the groundwater quality data available for this study. The interpretation of WQI analysis based on GWQI and EWQI reveals that 64% of the samples belong to the “poor” to “very poor” bracket. The result for the semivariogram modeling also shows that Gaussian model obtains the best fit for both EWQI and GWQI dataset. HCA classified 25 sampling locations into three main clusters of similar groundwater characteristics. DA validated these clusters and identified a total of three significant variables (pH, EC and Cl) by adopting stepwise method. The application of PCA resulted in three factors explaining 69.81% of the total variance. These factors reveal how processes like rock water interaction, urban waste discharge and mineral dissolution affect the groundwater quality.

Economic Security in Post-Soviet Countries: Level of Ensuring and Development Trends

At the national level of economic security studies, a special place has alway s b e lon ged t o t he estimating side of the issue. Estimations of state economic security serve as input data for the determinat ion of directions and ways of further security provision. At the same time, such estimations should be considered not only as a result of a certain methodology application in a certain co un try b ut a lso i n t h e c o nte xt o f comparing the economic security estimations across a set of countries. The aim of the article is to determin e the level of ensuring economic security in post-Soviet countries and recognize patterns, ri sk s, a n d t h rea ts that affect the future development of state economic security. For comparative analysis of economic security, Ukraine, Azerbaijan, Kazakhstan, Moldova, Georgia, and period 2016-2020 have been selected. The methodological basis of the study included the followingmethods: comparative economic studies, methods of summation, arithmetic mean, weighted arithmetic, geometric mean, rating; international index systems we re used as a basis for comparative analysis. Using the suggested methodology of estimation allowed obta ini ng results that characterize level real economic security, is lower than average. None of the analyzed countri es has managed to maintain an acceptable level of economic security. The determined levels allow u s t o st a te that the economic systems of the analyzed post-Soviet countries demonstrat e h i gh p erc ep ti ve ne ss t o t h e actualization of various threats. And this perceptiveness, in its turn, leads to various negative changes in t h e economic systems of these countries. The high perceptiveness of the economic systems in the analyze d p o st-Soviet countries to the actualization of various threats can be explained by the c h an gin g q u ali ty o f t he ir economic potential, low levels of their innovativeness, and also the lack of proper condi ti ons t o a p ply t h e innovations

The optimal emergency decision-making method with incomplete probabilistic information

Emergencies often occur irregularly, such as infectious diseases, earthquakes, wars, floods, the diffusion and leakage of chemically toxic and harmful substances, etc. These emergencies can bring huge disasters to people, even worse, the time left for people to make critical decisions is usually very limited. When an emergency occurs, the most important thing for people is to make reasonable decisions as soon as possible to deal with the current problems, otherwise, the situation may deteriorate further. The paper proposes an emergency decision-making algorithm under the constraints of the limited time and incomplete information, the research is mainly carried out from the following aspects, firstly, we use the data structure of the hesitant fuzzy probabilistic linguistic set to collect the basic data after careful comparison, which has three advantages, (1) considering the hesitation in the decision-making process, each evaluation information is allowed to contain multiple values instead of just one value; (2) each evaluation value is followed by a probability value, which further describes the details of the evaluation information; (3) the data structure allows some probability information to be unknown, which effectively expands the application scope of the algorithm. Secondly, the maximization gap model is proposed to calculate unknown parameters, the model can distinguish alternatives with small differences. Thirdly, all the evaluation information will be aggregated by the dynamic hesitant probability fuzzy weighted arithmetic operator. Subsequently, an instance is given to illustrate the effectiveness and the accuracy of the algorithm proposed in the paper. Finally, the advantages of the proposed algorithm are further demonstrated by comparing it with other outstanding algorithms. The main contribution of the paper is that we propose the maximization gap model to obtain the unknown parameters, which can effectively and accurately distinguish alternatives with small differences.