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On the basis of prioritized aggregated operator and prioritized ordered weighted average (POWA) operator, in this paper, the authors further present interval neutrosophic prioritized ordered weighted aggregation (INPOWA) operator with respect to interval neutrosophic numbers (INNs). Firstly, the definition, operational laws, characteristics, expectation and comparative method of INNs are introduced. Then, the INPOWA operator is developed, and some properties of the operator are analyzed. Furthermore, based on the INPOWA operator and the comparative formula of the INNs, an approach to decision making with INNs is established. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector. Besides, it is a universal operator since it can contain other general operators by assigning some special parameter values. However, the MM can only process the crisp numbers. Inspired by the MM' advantages, the aim of this paper is to extend MM to process the intuitionistic fuzzy numbers (IFNs) and then to solve the multi-attribute group decision making (MAGDM) problems. Firstly, we develop some intuitionistic fuzzy Muirhead mean (IFMM) operators by extending MM to intuitionistic fuzzy information. Then, we prove some properties and discuss some special cases with respect to the parameter vector. Moreover, we present two new methods to deal with MAGDM problems with the intuitionistic fuzzy information based on the proposed MM operators. Finally, we verify the validity and reliability of our methods by using an application example, and analyze the advantages of our methods by comparing with other existing methods.

Pipeline transportation of oil and gas is widespread. To improve inspection and maintenance, a pipeline inspection robot was developed in our study. We employed a threaded nut mechanism with a preload spring and diameter-adjustment methods. A torque output formula was derived. At maximum (340 mm) and minimum (260 mm) diameters, angles α and β were given. A pipeline obstacle model was established with a maximum crossing height of 7.5 mm. Simulation and experiments showed that the robot could cross up to 7.8 mm, performed well, and operated stably, which met our expectations.

Linguistic neutrosophic numbers (LNNs) can easily describe the incomplete and indeterminate information by the truth, indeterminacy, and falsity linguistic variables (LVs), and the Hamy mean (HM) operator is a good tool to deal with multiple attribute group decision making (MAGDM) problems because it can capture the interrelationship among the multi-input arguments. Motivated by these ideas, we develop linguistic neutrosophic HM (LNHM) operator and weighted linguistic neutrosophic HM (WLNHM) operator. Some desirable properties and special cases of two operators are discussed in detail. Furthermore, considering the situation in which the decision makers (DMs) can't give the suitable weight of each attribute directly from various reasons, we propose the concept of entropy for linguistic neutrosophic set (LNS) to obtain the attribute weight vector objectively, and then the method for MAGDM problems with LNNs is proposed, and some examples are used to illustrate the effectiveness and superiority of the proposed method by comparing with the existing methods.

In this study, a novel picosecond laser ring-cut drilling method was employed to drill holes in alumina ceramics. The morphology, dimensions, taper angle, and heat-affected zone (HAZ) of the resultant micro-holes were systematically characterized under various laser processing parameters. The crystal structure, microstructure, and elemental composition of micro-holes processed under specific parameters were characterized. The results showed that the micro-hole entrance and exit dimensions and HAZ area increased with increasing spot-scanning number. However, the micro-hole taper angle initially decreased before stabilizing with an increasing spot-scanning number. Furthermore, the micro-hole entrance and exit dimensions and HAZ area gradually decreased with increasing spot-scanning speed. Conversely, the micro-hole taper angle increased with increasing spot-scanning speed. Additionally, the micro-hole entrance and exit dimensions and HAZ area gradually increased with increasing average power. However, the micro-hole taper angle gradually decreased with increasing average power. Under processing parameters of spot-scanning number N = 90, scanning speed v = 600 mm/s, and average power P = 24 W, the micro-holes exhibited a taper angle α of 4.32° and a HAZ width of approximately 0.207 mm2. In contrast to the large bright grains on the original substrate, fine grains were observed around the machining area. Compared to the original substrate surface, the percentage of oxygen atoms decreased, whereas the percentage of aluminum atoms increased at the micro-hole edge and HAZ surface. The results of this study have potential applications in the field of ceramic manufacturing.

In this paper we deal with the martingales in variable Lebesgue space over a probability space. We first prove several basic inequalities for conditional expectation operators and give several norm convergence conditions for martingales in variable Lebesgue space. The main aim of this paper is to investigate the boundedness of weak-type and strong-type Doob’s maximal operators in martingale Lebesgue space with a variable exponent. In particular, we present two kinds of weak-type Doob’s maximal inequalities and some necessary and sufficient conditions for strong-type Doob’s maximal inequalities. Finally, we provide two counterexamples to show that the strong-type inequality does not hold in general variable Lebesgue spaces with p > 1.

In this paper, we proposed a single-valued neutrosophic normalized weighted Bonferroni mean (SVNNWBM) operator on the basis of Bonferroni mean, the weighted Bonferroni mean (WBM), and the normalized WBM. Firstly, the definition, operational laws, characteristics, and comparing method of single-valued neutrosophic numbers (SVNNs) are introduced. Then, the SVNNWBM operator is developed, and some properties and special cases of this operator are analyzed. Furthermore, an approach is developed to solve the multiple attribute decision-making problems with SVNNs based on the SVNNWBM operator. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

q -rung picture fuzzy sets can handle complex fuzzy and impression information by changing a parameter q based on the different hesitation degree, and Yager operator is a useful aggregation technology that can control the uncertainty of valuating data from some experts and thus get intensive information in the process of decision-making. Thus, in this paper, we develop specific types of operators, namely, q -rung picture fuzzy Yager weighted average, q -rung picture fuzzy Yager ordered weighted average, q -rung picture fuzzy Yager hybrid weighted average, q -rung picture fuzzy Yager weighted geometric, q -rung picture fuzzy Yager ordered weighted geometric and q -rung picture fuzzy Yager hybrid weighted geometric operators. We propose q -rung picture fuzzy Yager aggregation operators to handle multiple attribute decision-making problems in a modernize way. Moreover, we discuss the effect of parameter on the decision-making results. To demonstrate the superiority and advantage of our proposed method, a comparison with existing methods is presented.

Supply and distribution management of blood products is a challenging task due to their short lifespan. The problem is even more sophisticated considering uncertain demand for these products. This paper addresses integrated inventory-routing of blood in a supply chain network consisting of a single supplier and a group of blood centers. Transshipment among blood centers is allowed to decrease the cost of excess inventory and shortage of goods. A mathematical model is developed that decides on the optimal quantity of supplied blood, delivery plan, inventory level, and quantity of products transshipped between blood centers with the objective of minimizing total costs. In addition, a robust optimization approach is adopted to deal with uncertainty in demand. Since the proposed model is NP-hard, a heuristic solution algorithm is developed that improves solution quality by determining the most efficient change in vehicle routes in each search stage. The efficiency of the proposed algorithm is examined in a set of numerical experiments and using data from a real case of supply and distribution management of blood platelets. The results indicated that allowing transshipment reduces the need for supply capacity at the supplier, product shortage, inventory level, and the total cost.

The notions of complex q-rung orthopair fuzzy sets (Cq-ROFSs) and linguistic sets (LSs) are two different concepts to deal with uncertain information in multi-attribute group decision-making (MAGDM) problems. The Heronain mean (HM) and geometric Heronain mean (GHM) operators are an effective tool used to aggregate some q-rung orthopair linguistic fuzzy numbers (q-ROLFNs) into a single element. The purpose of this manuscript is to propose a new concept called complex q-rung orthopair linguistic sets (Cq-ROLSs) to cope with complex uncertain information in real decision-making problems. Then the fundamental laws and their examples of the Cq-ROLSs are also given. Furthermore, the notions of complex q-rung orthopair linguistic Heronian mean (Cq-ROLHM) operator, complex q-rung orthopair linguistic weighted Heronian mean (Cq-ROLWHM) operator, complex q-rung orthopair linguistic geometric Heronian mean (Cq-ROLGHM) operator, complex q-rung orthopair linguistic weighted geometric Heronian mean (Cq-ROLWGHM) operator are proposed and their basic properties are also discussed. Moreover, we develop a novel approach to MAGDM using proposed operators and a numerical example is used to describe the flexibility and explicitly of the initiated operators. In last, the comparison between proposed method and existing work is also discussed in detail.