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.

Evaluation of Transfer Efficiency between Subway and Bus Based on the Interval Number Ranking Method by Employing Probability Reliability: Taking Ningbo for Example

In recent years, the construction and operation of urban subways have been gradually increasing in developing countries. In the next step, more attention should be paid to the transfer efficiency between subway and bus so as to improve the travel efficiency of more urban residents. This paper uses the probability credibility interval number ranking method to evaluate the bus transfer efficiency. Firstly, this study obtains the dynamic transfer time data by matching individual smart card and subway/bus global positioning system (GPS) records, which is used to evaluate the transfer efficiency of corresponding subway stations. Then, we establish a probability density function to represent the characteristic information of transfer time. Accordingly, the probability reliability model of the order relation of interval numbers can be constructed. In the end, the method is applied to evaluate the transfer efficiency between subway and bus stations in Ningbo. Compared to the traditional interval number ranking method, the evaluation result shows that this method can get a more objective transfer efficiency order relation. The reason is that this method can not only consider the random feature of transfer time but also make use of the data distribution characteristics. This method could be applied to obtain the stations with relatively low transfer efficiency and the feedback can be used for bus line operation and station layout improvement.

Fast Diameter Computation within Split Graphs

When can we compute the diameter of a graph in quasi linear time? We address this question for the class of {\em split graphs}, that we observe to be the hardest instances for deciding whether the diameter is at most two. We stress that although the diameter of a non-complete split graph can only be either $2$ or $3$, under the Strong Exponential-Time Hypothesis (SETH) we cannot compute the diameter of an $n$-vertex $m$-edge split graph in less than quadratic time -- in the size $n+m$ of the input. Therefore it is worth to study the complexity of diameter computation on {\em subclasses} of split graphs, in order to better understand the complexity border. Specifically, we consider the split graphs with bounded {\em clique-interval number} and their complements, with the former being a natural variation of the concept of interval number for split graphs that we introduce in this paper. We first discuss the relations between the clique-interval number and other graph invariants such as the classic interval number of graphs, the treewidth, the {\em VC-dimension} and the {\em stabbing number} of a related hypergraph. Then, in part based on these above relations, we almost completely settle the complexity of diameter computation on these subclasses of split graphs: - For the $k$-clique-interval split graphs, we can compute their diameter in truly subquadratic time if $k={\cal O}(1)$, and even in quasi linear time if $k=o(\log{n})$ and in addition a corresponding ordering of the vertices in the clique is given. However, under SETH this cannot be done in truly subquadratic time for any $k = \omega(\log{n})$. - For the {\em complements} of $k$-clique-interval split graphs, we can compute their diameter in truly subquadratic time if $k={\cal O}(1)$, and even in time ${\cal O}(km)$ if a corresponding ordering of the vertices in the stable set is given. Again this latter result is optimal under SETH up to polylogarithmic factors. Our findings raise the question whether a $k$-clique interval ordering can always be computed in quasi linear time. We prove that it is the case for $k=1$ and for some subclasses such as bounded-treewidth split graphs, threshold graphs and comparability split graphs. Finally, we prove that some important subclasses of split graphs -- including the ones mentioned above -- have a bounded clique-interval number.

Observational Spatial Memory in North Island Robins (Petroica Longpies)

<p>Observational spatial memory is employed by members of food-hoarding species to pilfer caches created by other individuals more effectively. North Island robins (Petroica australis) experience high levels of reciprocal cache pilferage within mate pairs. These circumstances were hypothesised to produce conditions under which advanced pilferage strategies such as observational spatial memory may evolve. Here I tested the ability of North Island robins to use observational spatial memory to discriminate between varying prey rewards. Three experiments were conducted which differed in the maximum number of prey items offered as a reward. Additional variables of retention interval, number of cache sites and a variable reward were included to assess how the birds’ memory was affected by small-scale factors. Results showed that North Island robins performed above chance expectations in most treatment combinations, indicating that they were able to utilize observational spatial memory. They were equally able to discriminate between different combinations of prey numbers that were hidden in 2, 3 and 4 caches sites from between 0, 10 and 60 seconds. Overall results indicate that North Island robins can solve complex numerical problems involving more than two parameters and up to one minute long retention intervals without training.</p>

Observational Spatial Memory in North Island Robins (Petroica Longpies)

<p>Observational spatial memory is employed by members of food-hoarding species to pilfer caches created by other individuals more effectively. North Island robins (Petroica australis) experience high levels of reciprocal cache pilferage within mate pairs. These circumstances were hypothesised to produce conditions under which advanced pilferage strategies such as observational spatial memory may evolve. Here I tested the ability of North Island robins to use observational spatial memory to discriminate between varying prey rewards. Three experiments were conducted which differed in the maximum number of prey items offered as a reward. Additional variables of retention interval, number of cache sites and a variable reward were included to assess how the birds’ memory was affected by small-scale factors. Results showed that North Island robins performed above chance expectations in most treatment combinations, indicating that they were able to utilize observational spatial memory. They were equally able to discriminate between different combinations of prey numbers that were hidden in 2, 3 and 4 caches sites from between 0, 10 and 60 seconds. Overall results indicate that North Island robins can solve complex numerical problems involving more than two parameters and up to one minute long retention intervals without training.</p>

Solving Discounting Problem Using Piece-Wise Quadratic Fuzzy Numbers

The discounting problem is one of the important aspects in investment, portfolio selection, purchasing with credit, and many other financial operations. In this paper, a discounting problem using piecewise quadratic fuzzy numbers is proposed. The implementation of piecewise quadratic fuzzy numbers is described based on such operations. Fuzzy arithmetic and interval number arithmetic are used for computation. The close interval approximation of piecewise quadratic fuzzy numbers is used for solving the proposed discounting problem. This research article addresses the discounted investment for Year 1, Year 2, and Year 3. Additionally, the authors determine the cumulative discounted investment for different values of the parameter α ranging from 0 to 1. A discounting problem using piecewise quadratic fuzzy numbers is solved as a numerical example to illustrate the proposed procedure.

Interval TOPSIS with a novel interval number comprehensive weight for threat evaluation on uncertain information

Threat evaluation (TE) is essential in battlefield situation awareness and military decision-making. The current processing methods for uncertain information are not effective enough for their excessive subjectivity and difficulty to obtain detailed information about enemy weapons. In order to optimize TE on uncertain information, an approach based on interval Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) and the interval SD-G1 (SD standard deviation) method is proposed in this article. By interval SD-G1 method, interval number comprehensive weights can be calculated by combining subjective and objective weights. Specifically, the subjective weight is calculated by interval G1 method, which is an extension of G1 method into interval numbers. And the objective weight is calculated by interval SD method, which is an extension of SD method with the mean and SD of the interval array defined in this paper. Sample evaluation results show that with the interval SD-G1 method, weights of target threat attributes can be better calculated, and the approach combining interval TOPSIS and interval SD-G1 can lead to more reasonable results. Additionally, the mean and SD of interval arrays can provide a reference for other fields such as interval analysis and decision-making.

A Portfolio Selection Model Based on the Interval Number

Traditional portfolio theory uses probability theory to analyze the uncertainty of financial market. The assets’ return in a portfolio is regarded as a random variable which follows a certain probability distribution. However, it is difficult to estimate the assets return in the real financial market, so the interval distribution of asset return can be estimated according to the relevant suggestions of experts and decision makers, that is, the interval number is used to describe the distribution of asset return. Therefore, this paper establishes a portfolio selection model based on the interval number. In this model, the semiabsolute deviation risk function is used to measure the portfolio’s risk, and the solution of the model is obtained by using the order relation of the interval number. At the same time, a satisfactory solution of the model is obtained by using the concept of acceptability of the interval number. Finally, an example is given to illustrate the practicability of the model.