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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.

In the current health care scenario, security is the major concern in IoT-WSN with more devices or nodes. Attack or anomaly detection in the IoT infrastructure is increasing distress in the field of medical IoT. With the enormous usage of IoT infrastructure in every province, threats and attacks in these infrastructures are also mounting commensurately. This paper intends to develop a security mechanism to detect and prevent the black hole and selective forwarding attack from medical IoT-WSN. The proposed secure strategy is developed in five stages: First is selecting the cluster heads, second is generating k-routing paths, third is security against black hole attack, fourth is security against the selective forwarding attack, and the last is optimal shortest route path selection. Initially, a topology is developed for finding the cluster heads and discovering the best route. In the next phase, the black hole attacks are detected and prevented by the bait process. For detecting the selective forwarding attacks, the packet validation is done by checking the transmitted packet and the received packet. For promoting the packet security, Elliptic Curve Cryptography (ECC)-based hashing function is deployed. As the main contribution of this paper, optimal shortest route path is determined by the proposed hybrid algorithm with the integration of Deer Hunting Optimization Algorithm (DHOA), and DragonFly Algorithm (DA) termed Dragonfly-based DHOA (D-DHOA) by concerting the parameters like trust, distance, delay or latency and packet loss ratio in the objective model. Hence, the entire phases will be very active in detecting and preventing the two fundamental attacks like a black hole and selective forwarding from IoT-WSN in the health care sector.

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.

Neighbourhood singleton arc consistency (NSAC) is a type of singleton arc consistency (SAC) in which the subprob- lem formed by variables adjacent to a variable with a singleton domain is made arc consistent. This paper describes two exten- sions to neighbourhood SAC. The first is a generalization from NSAC to k-NSAC, where k is the maximum length of the shortest path between the singleton variable and any variable in the subgraph. The second is an extension of k-NSAC to problems with n-ary constraints, which retains the basic definition of a k-neighbourhood subgraph. To establish such consistencies a suite of algorithms is considered based on various SAC algorithms including SAC-1, SACQ, SAC-SDS, and SAC-3. In analyzing these different algorithms it was found useful to distinguish between "light-weight" and "heavy-weight" SAC algorithms, based on the complexity of data structures and procedures needed to carry out the task of establishing (N)SAC. Under this classification, SAC-1 and SACQ are light-weight; the other two (and SAC-2) are heavy-weight. It was found that only light-weight algorithms can be readily and effectively transformed into efficient NSAC algorithms. In contrast, because of their specialized procedures, it was necessary to modify heavy-weight algorithms significantly, which also compromised performance. Extensive experimental analysis shows that with a spectrum of neighbourhood consistencies and attendant algorithms, one can finesse the fundamental tradeoff between efficiency and effectiveness across a greater range of problems than with SAC and NSAC algorithms alone. This work serves to enlarge the scope of SAC-based consistency maintenance as well as defining the various niches that light-weight and heavy-weight algorithms are best suited for.