Linguistic term sets combining with different types of fuzzy sets to settle decision making problems have been a hot area of decision making research. Linguistic Pythagorean fuzzy sets (LPFSs) and soft sets have strong ability to model uncertainty of decision-making. However, there are still few studies about LPFSs at present and these studies have some deficiencies. Aiming at these problems, we do the following things. Firstly, we give the definition of linguistic Pythagorean fuzzy soft sets (LPFSSs), redefine the entropy for LPFSs and introduce a novel linguistic Pythagorean fuzzy entropy which is more simple and valid. Then we give another way to represent linguistic Pythagorean fuzzy numbers (LPFNs) which can better reflect the characteristics of LPFSs. Based on that, we give the definition of distance measures for LPFSs and propose a series of distance measures for LPFNs and LPFSs. Finally, we improve the TOPSIS method with the proposed entropy and distance measure under LPFSSs environment and then apply the method in two cases. Compared with other methods, it’s shown that our method has better distinguishability in evaluation results and can deal with group decision-making problems under LPFSSs environment.

A decision-making environment is full of uncertainty and complexity. Existing tools include fuzzy sets, soft sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets (PFSs) and so on. Compared with intuitionistic fuzzy sets (IFSs), PFSs proposed by Yager have advantages in handling vagueness in the real world and possess good symmetry. The entropy measure is the most widespread form of uncertainty measure. In this paper, we improve the technique for order preference by similarity to an ideal solution (TOPSIS) method to better deal with multiple-attribute group decision making (MAGDM) problems based on Pythagorean fuzzy soft sets (PFSSs). To better determine the weights of attributes, we firstly define a novel Pythagorean fuzzy soft entropy which is more reasonable and valid. Meanwhile the entropy has good symmetry. Entropy for PFSSs which is used to determine the subjective weights of attributes is also defined. Then we introduce a measure to calculate integrated weights by combining objective weights and subjective weights. Based on the integrated weights, the TOPSIS method is generalized and improved to solve the MAGDM problem. A distance measure taking into account the characteristics of Pythagorean fuzzy numbers (PFNs) is used to calculate distance between alternatives and ideal solutions. Finally, the proposed MAGDM method is applied in the case of selecting a missile position. Compared with other methods, it is shown that the proposed method can rank alternatives more reasonably and have higher distinguishability.

The driving cycle is a speed-to-time curve, a fundamental technique in the automotive industry, and also a basis to set standards for fuel consumption and emissions of vehicles. A driving cycle is developed based on firsthand driving data collected from fieldwork. First, bad data in the original dataset are preprocessed, the time-series standard smoothing algorithm is used to smoothen the data, and Lagranges interpolation is used to realize data interpolation. Next, the rules for kinematic fragment extraction are set to divide the data into kinematic fragments. Last, an evaluation system of kinematic fragment feature parameters is built. On that basis, the K-means clustering method is used to cluster the dimensionally reduced data, and the adaptive mutation particle swarm optimization (AMPSO) algorithm is employed to select the optimal fragments from candidate fragments to develop a driving cycle. The experiment result shows that the developed driving cycle can represent the kinematic features of the experiment car and provides a basis for the development of a driving cycle for Fuzhou.

Intelligent wars can take place not only in the physical domain and information domain but also in the cognitive domain. The cognitive domain will become the key domain to win in the future intelligent war. A Lanchester equation considering cognitive domain is proposed to fit the development tendency intelligent wars in this paper. One party is considered to obtain the exponential enhancement advantage on combat forces in combat if it can gain an advantage in the cognitive domain over the other party according to the systemic advantage function. The operational effectiveness of the cognitive domain in war is considered to consist of a series of indicators. Hesitant fuzzy sets and linguistic term sets are powerful tools when evaluating indicators, hence the indicators are scored by experts using hesitant fuzzy linguistic terms sets here. A unique hesitant fuzzy hybrid arithmetical averaging operator is used to aggregate the evaluation.