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Enayattabr et al. (Journal of Intelligent and Fuzzy Systems 37 (2019) 6865– 6877) claimed that till now no one has proposed an approach to solve interval-valued trapezoidal fuzzy all-pairs shortest path problems (all-pairs shortest path problems in which distance between every two nodes is represented by an interval-valued trapezoidal fuzzy number). Also, to fill this gap, Enayattabr et al. proposed an approach to solve interval-valued trapezoidal fuzzy all-pairs shortest path problems. In this paper, an interval-valued trapezoidal fuzzy shortest path problem is considered to point out that Enayattabr et al.’s approach fails to find correct shortest distance between two fixed nodes. Hence, it is inappropriate to use Enayattabr et al.’s approach in its present from. Also, the required modifications are suggested to resolve this inappropriateness of Enayattabr et al.’s approach.

Solving the shortest path problem is very difficult in situations such as emergency rescue after a typhoon: road-damage caused by a typhoon causes the weight of the rescue path to be uncertain and impossible to represent using single, precise numbers. In such uncertain environments, neutrosophic numbers can express the edge distance more effectively: membership in a neutrosophic set has different degrees of truth, indeterminacy, and falsity. This paper proposes a shortest path solution method for interval-valued neutrosophic graphs using the particle swarm optimization algorithm. Furthermore, by comparing the proposed algorithm with the Dijkstra, Bellman, and ant colony algorithms, potential shortcomings and advantages of the proposed method are deeply explored, and its effectiveness is verified. Sensitivity analysis performed using a 2020 typhoon as a case study is presented, as well as an investigation on the efficiency of the algorithm under different parameter settings to determine the most reasonable settings. Particle swarm optimization is a promising method for dealing with neutrosophic graphs and thus with uncertain real-world situations.

There are different conditions where SPP play a vital role. However, there are various conditions, where we have to face with uncertain parameters such as variation of cost, time and so on. So to remove this uncertainty, Yang et al. [1] “[Journal of Intelligent & Fuzzy Systems, 32(1), 197-205”] have proposed the fuzzy reliable shortest path problem under mixed fuzzy environment and claimed that it is better to use their proposed method as compared to the existing method i.e., “[Hassanzadeh et al.; A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths, Mathematical and Computer Modeling, 57(2013) 84-99” [2]]. The aim of this note is, to highlight the shortcoming that is carried out in Yang et al. [1] article. They have used some mathematical incorrect assumptions under the mixed fuzzy domain, which is not true in a fuzzy environment.

Environment monitoring is one of the typical application scenarios of the wireless sensor networks. As an energy limited system, most of the energy consumption is for the data transmission. As a well-known principle, the difference among the physical parameters of adjacent nodes is approximate a constant. Eliminating these data to be transmitted will lead to remarkable energy saving. A correlative pattern based data aggregation mechanism following this principle is proposed in this paper, which is named the Correlative Pattern based Data Aggregation (CPDA). CPDA mines the correlations of every adjacent nodes pair, and generates a correlation graph of the network, then builds an aggregation routing tree for each connected component of correlation graph based on the shortest path methodology. Following the CPDA algorithm, a node’s sensed data will be suppressed when the data and the children’s match the restriction that is defined by CPDA. When the aggregated data arrive at the Sink node, all the data can be recovered. The recovery error will be limited within a specified small error threshold based on the reversed mechanism. The simulations based on the data set of Berkeley lab show that CPDA has excellent performance in aggregation degree and average error. Further more, a real established temperature sensing experiment also gives the same conclusion.

Growing popularity of social networking not only brings the convenience of information sharing but also concerns of privacy breaches. Information on social networks can be modeled as un-weighted or weighted graph data. To preserve privacy, k-anonymity on relational, set-valued, and graph data have been studied extensively in recent years. In this work, we consider the edge weight anonymity problem. In particular, to protect the weight privacy of the shortest path between two vertices on a weighted graph, we present a new concept called k-anonymous path privacy. A published social network graph with k-anonymous path privacy has at least k indistinguishable shortest paths between the source and destination vertices. Three greedy-based modification algorithms, based on modifying different types of edges, to achieve k-anonymous path privacy are proposed. Experimental results showing the feasibility and characteristics of the proposed approach are presented. The proposed techniques clearly provide different options to achieve the same level of privacy under different requirements.