Arithmetic operations of intuitionistic Z numbers using horizontal membership functions

An intuitionistic Z-number (IZN) is an integration of an intuitionistic fuzzy number with a Z-number. The IZN composes of two components; restriction and reliability components, which are represented by the membership and non-membership degrees to indicate the hesitancy. The objective of this paper is to propose new arithmetic operations of IZN using the horizontal membership functions, which are closely related the concept of the relative distance measure. For that reason, the addition, subtraction, multiplication and division on normal trapezoidal IZNs are considered. The proposed operations preserve the arithmetic operations over real numbers and the original IZN-based information, avoiding any significant loss of information. The implementation of the bandwidth method in deriving the operations has reduced the computational complexity on IZN. In the future, aggregation operators of IZN can be derived using the proposed arithmetic operations

Synergic ranking of fuzzy Z-numbers based on vectorial distance and spread for application in decision-making

Decision science has a wide range of applications in daily life. Decision information is usually incomplete and partially reliable. In the fuzzy set theory, Z-numbers are introduced to handle this situation because they contain the restriction and reliability components, which complement the impaired information. The ranking of Z-numbers is a challenging task since they are composed of pairs of fuzzy numbers. In this research, the vectorial distance and spread of Z-numbers were proposed synergically, in which the vectorial distance measures how much the fuzzy numbers are apart from the origin, which was set as a relative point, and their spreads over a horizontal axis. Furthermore, a ranking method based on the convex compound was proposed to combine the restriction and reliability components of Z-numbers. The proposed ranking method was validated using several empirical examples and a comparative analysis was conducted. The application of the proposed ranking method in decision-making was illustrated via the development of the Analytic Hierarchy Process-Weighted Aggregated Sum Product Assessment (AHP-WASPAS) model to solve the prioritization of public services for the implementation of Industry 4.0 tools. Sensitivity analysis was also conducted to evaluate the performance of the proposed model and the results showed that the proposed model has improved its consistency from 66.67% of the existing model to 83.33%. This research leads to a future direction of the application of ranking based on the vectorial distance and spread in multi-criteria decision-making methods, which use Z-numbers as linguistic values

Synergic ranking of fuzzy Z-numbers based on vectorial distance and spread for application in decision-making

Decision science has a wide range of applications in daily life. Decision information is usually incomplete and partially reliable. In the fuzzy set theory, Z-numbers are introduced to handle this situation because they contain the restriction and reliability components, which complement the impaired information. The ranking of Z-numbers is a challenging task since they are composed of pairs of fuzzy numbers. In this research, the vectorial distance and spread of Z-numbers were proposed synergically, in which the vectorial distance measures how much the fuzzy numbers are apart from the origin, which was set as a relative point, and their spreads over a horizontal axis. Furthermore, a ranking method based on the convex compound was proposed to combine the restriction and reliability components of Z-numbers. The proposed ranking method was validated using several empirical examples and a comparative analysis was conducted. The application of the proposed ranking method in decision-making was illustrated via the development of the Analytic Hierarchy Process-Weighted Aggregated Sum Product Assessment (AHP-WASPAS) model to solve the prioritization of public services for the implementation of Industry 4.0 tools. Sensitivity analysis was also conducted to evaluate the performance of the proposed model and the results showed that the proposed model has improved its consistency from 66.67% of the existing model to 83.33%. This research leads to a future direction of the application of ranking based on the vectorial distance and spread in multi-criteria decision-making methods, which use Z-numbers as linguistic values

Application of Intuitionistic Z-Numbers in Supplier Selection

Intuitionistic fuzzy numbers incorporate the membership and nonmembership degrees. In contrast, Z-numbers consist of restriction components, with the existence of a reliability component describing the degree of certainty for the restriction. The combination of intuitionistic fuzzy numbers and Z-numbers produce a new type of fuzzy numbers, namely intuitionistic Z-numbers (IZN). The strength of IZN is their capability of better handling the uncertainty compared to Zadeh's Z-numbers since both components of Z-numbers are characterized by the membership and non-membership functions, exhibiting the degree of the hesitancy of decision-makers. This paper presents the application of such numbers in fuzzy multi-criteria decision-making problems. A decision-making model is proposed using the trapezoidal intuitionistic fuzzy power ordered weighted average as the aggregation function and the ranking function to rank the alternatives. The proposed model is then implemented in a supplier selection problem. The obtained ranking is compared to the existing models based on Znumbers. The results show that the ranking order is slightly different from the existing models. Sensitivity analysis is performed to validate the obtained ranking. The sensitivity analysis result shows that the best supplier is obtained using the proposed model with 80% to 100% consistency despite the drastic change of criteria weights. Intuitionistic Z-numbers play a very important role in describing the uncertainty in the decision makers’ opinions in solving decision-making problems

The application of z-numbers in fuzzy decision making: The state of the art

A Z-number is very powerful in describing imperfect information, in which fuzzy numbers are paired such that the partially reliable information is properly processed. During a decision-making process, human beings always use natural language to describe their preferences, and the decision information is usually imprecise and partially reliable. The nature of the Z-number, which is composed of the restriction and reliability components, has made it a powerful tool for depicting certain decision information. Its strengths and advantages have attracted many researchers worldwide to further study and extend its theory and applications. The current research trend on Z-numbers has shown an increasing interest among researchers in the fuzzy set theory, especially its application to decision making. This paper reviews the application of Z-numbers in decision making, in which previous decision-making models based on Z-numbers are analyzed to identify their strengths and contributions. The decision making based on Z-numbers improves the reliability of the decision information and makes it more meaningful. Another scope that is closely related to decision making, namely, the ranking of Z-numbers, is also reviewed. Then, the evaluative analysis of the Z-numbers is conducted to evaluate the performance of Z-numbers in decision making. Future directions and recommendations on the applications of Z-numbers in decision making are provided at the end of this review

Defuzzification of intuitionistic Z-Numbers for fuzzy multi criteria decision making

Z-numbers and intuitionistic fuzzy numbers are both important as they consider the reliability of the judgement, membership and non-membership functions of the numbers. The combination of these two numbers produce intuitionistic Z-numbers which need to be defuzzified before aggregation of multiple experts’ opinions could be done in the decision making problems. This paper presents the generalised intuitionistic Z-numbers and proposes a centroid-based defuzzification of such numbers, namely intuitive multiple centroid. The proposed defuzzification is used in the decision making model and applied to the supplier selection problem. The ranking of supplier alternatives is evaluated using the ranking function based on centroid. In the present paper, the ranking is improved since the intuitionistic fuzzy numbers (IFN) are integrated within the evaluations which were initially in form of Z-numbers, considering their membership and non-membership grades. The ranking of the proposed model gives almost similar ranking to the existing model, with simplified but detailed defuzzification method

Risk factors and in-hospital outcome of acute ST segment elevation myocardial infarction in young Bangladeshi adults

BackgroundSouth Asians have a higher overall incidence rate and younger age of onset for acute myocardial infarction (AMI) compared to Western populations. However, limited information is available on the association of preventable risk factors and outcomes of AMI among young individuals in Bangladesh. The aim of this study was to determine the risk factors and in-hospital outcome of AMI among young (age &le;40 years) adults in Bangladesh.MethodsWe conducted a prospective observational study among consecutive 50 patients aged &le;40 years and 50 patients aged &gt;40 years with acute ST Segment Elevation Myocardial Infarction (STEMI) and followed-up in-hospital at the National Institute of Cardiovascular Diseases (NICVD). Clinical characteristics, biochemical findings, diet, echocardiography and in-hospital outcomes were compared between the two groups. Multivariate logistic regression was performed to assess the association between risk factors and in-hospital outcome in young patients adjusting for other confounding variables.ResultsThe mean age of the young and older patient groups was 36.5&thinsp;&plusmn;&thinsp;4.6 years and 57.0&thinsp;&plusmn;&thinsp;9.1 years respectively. Male sex (OR 3.4, 95 % CI 1.2&thinsp;&minus;&thinsp;9.75), smoking (OR 2.4, 95 % CI 1.04&thinsp;&minus;&thinsp;5,62), family history of MI (OR 2.4, 95 % CI 1.11&thinsp;&minus;&thinsp;5,54), homocysteine (OR 1.2, 95 % CI 1.08&thinsp;&minus;&thinsp;1.36), eating rice &ge;2 times daily (OR 3.5, 95 % CI 1.15&thinsp;&minus;&thinsp;10.6) and eating beef (OR 4.5, 95 % CI 1.83&thinsp;&minus;&thinsp;11.3) were significantly associated with the risk of AMI in the young group compared to older group. In multivariate analysis, older patients had significantly greater chance of developing heart failure (OR 7.5, 95 % CI 1.51 to 37.31), re-infarction (OR 7.0, 95 % CI 1.08&thinsp;&minus;&thinsp;45.72), arrhythmia (OR 15.3, 95 % CI 2.69&thinsp;&minus;&thinsp;87.77) and cardiogenic shock (OR 69.0, 95 % CI 5.81&thinsp;&minus;&thinsp;85.52) than the younger group.ConclusionYounger AMI patients have a different risk profile and better in-hospital outcomes compared to the older patients. Control of preventable risk factors such as smoking, unhealthy diet, obesity and dyslipidemia should be reinforced at an early age in Bangladesh.<br /

Extensions of Hermite-Hadamard type inequality for co-ordinated (alpha,m)-convex functions

In this paper, the classes of (,m) convex functions in real and complex co-ordinated space have been introduced. Some new Hermite-Hadamard type inequalities have been obtained for these classes of functions

Analytic Hierarchy Process Based on the Magnitude of Z-Numbers

The Analytic Hierarchy Process (AHP) is a powerful multi-criteria and multi-alternative decision-making model, which assists decision-makers in giving preferences using pairwise comparison matrices. The development of the AHP using fuzzy numbers has received attention from many researchers due to the ability of fuzzy numbers to handle vagueness and uncertainty. The integration of the AHP with fuzzy Z-numbers has improved the model since the reliability of the decision-makers is considered, in which the judgment is followed by a degree of certainty or sureness. Most of the existing decision-making models based on Z-numbers transform the Z-numbers into regular fuzzy numbers by integrating the reliability parts into the restriction parts, causing a significant loss of information. Hence, this study develops the AHP based on the magnitude of Z-numbers, which is used to represent the criteria weights. A numerical example of criteria ranking for the prioritization of public services for digitalization is implemented to illustrate the proposed AHP model

Comparative investigation of the free radical scavenging potential and anticancer property of Diospyros blancoi (Ebenaceae)

Objective: To investigate the comparative effects of Diospyros blancoi (Ebenaceae) leaves (DBL), root bark (DBRB) and stem bark (DBSB) on free radicals and cancer. Methods: The polyphenol contents, antioxidant and free radical scavenging properties were determined using standard spectrophotometric methods. Cytotoxicity and anticancer activities were performed on brine shrimp nauplii and Ehrlich ascite carcinoma cells, respectively. Results: Among the extracts, DBSB showed the highest total antioxidant capacity and reducing capacity on ferrous ion. Based on 1,1-diphenyl-2-picrylhydrazyl and hydroxyl radical scavenging activities, DBSB showed (95.760 ± 0.343)% and (67.460 ± 2.641)% scavenging with IC50 of (3.10 ± 0.17) and (50.00 ± 3.11) μg/mL, respectively. The IC50 values of standard butylated hydroxytoluene and catechin (CA) for 1,1-diphenyl-2-picrylhydrazyl and hydroxyl radicals were (8.50 ± 0.25) and (75.00 ± 0.14) μg/mL, respectively suggesting that DBSB had a significant (P  DBRB > CA > DBL. Also, the phenolic [(139.91 ± 3.924) mg gallic acid equivalent/g] and flavonoid contents [(412.00 ± 16.70) mg catechin equivalent/g)] of DBSB were higher than that of other extracts. In addition, the DBSB showed the moderate cytotoxic and anticancer properties. Conclusions: Our results indicate that Diospyros blancoi stem bark had the significant highest antioxidant and free radical scavenging properties as well as moderate anticancer activity. Hence, we assume that the anticancer activity of this plant can be, at least in part, attributed to its content in phenolic compounds as well as its significant free radical scavenging properties