User Association in Cell-less 5G Networks Exploiting Particle Swarm Optimisation

In heterogeneous networks (HetNets), users can by default associate with the macro base stations (BSs) while the small cell BSs are underloaded. Biasing user association is a simple and realistic approach to balance the load in HetNets, as well as creating a cell-less architecture where a user does not connect to the closest base station. Most of the existing research focuses on the static biasing scheme which is not the optimal strategy to improve the system performance. In this paper, the biasing factors are generated dynamically by the algorithm of particle swarm optimisation (PSO) with the objective of balancing the load and maximising the cell spectral efficiency (CSE). This work studies two different interference cases: the first case is when each tier uses different radio resources (typical when multiple radio access technologies are used) and a user receives interference only from same-tier base stations, whereas the second interference case is when all tiers use the same radio resources and a user receives interference from the same-tier and other tier BSs. The simulation results show that the dynamic biasing using PSO outperforms the static biasing in terms of balancing the load and maximising the CSE

AN ADAPTIVE LOCALIZATION SYSTEM USING PARTICLE SWARM OPTIMIZATION IN A CIRCULAR DISTRIBUTION FORM

Tracking the user location in indoor environment becomes substantial issue in recent research High accuracy and fast convergence are very important issues for a good localization system. One of the techniques that are used in localization systems is particle swarm optimization (PSO). This technique is a stochastic optimization based on the movement and velocity of particles. In this paper, we introduce an algorithm using PSO for indoor localization system. The proposed algorithm uses PSO to generate several particles that have circular distribution around one access point (AP). The PSO generates particles where the distance from each particle to the AP is the same distance from the AP to the target. The particle which achieves correct distances (distances from each AP to target) is selected as the target. Four PSO variants, namely standard PSO (SPSO), linearly decreasing inertia weight PSO (LDIW PSO), self-organizing hierarchical PSO with time acceleration coefficients (HPSO-TVAC), and constriction factor PSO (CFPSO) are used to find the minimum distance error. The simulation results show the proposed method using HPSO-TVAC variant achieves very low distance error of 0.19 mete

On supra R-open sets and some applications on topological spaces

In the present paper a new class of generalized supra open sets called supra R-open set is introduced. The relationships between some generalized supra open sets and this class are investigated and illustrated with enough examples. Also, new types of supra continuous maps, supra open maps, supra closed maps, and supra homeomorphism maps are studied depending on the concept of supra R-open sets. Finally, new separation axioms are dened and their several properties are studied

SUPRA HOMEOMORPHISM IN SUPRA TOPOLOGICAL ORDERED SPACES

The purpose of this paper is to introduce the concepts of x-supra continuous (open, closed, homeomorphism) maps in supra topological ordered spaces for x ∈ {I,D,B}. We study the relationship among these types with the help of examples and investigate the equivalent conditions for each concept. In particular, we present the sufficient conditions for maps to preserve some of separation axioms

A Comprehensive study on (α,β)-multi-granulation bipolar fuzzy rough sets under bipolar fuzzy preference relation

The rough set (RS) and multi-granulation RS (MGRS) theories have been successfully extended to accommodate preference analysis by substituting the equivalence relation (ER) with the dominance relation (DR). On the other hand, the bipolar fuzzy sets (BFSs) are effective tools for handling bipolarity and fuzziness of the data. In this study, with the description of the background of risk decision-making problems in reality, we present $(\alpha, \beta)$-optimistic multi-granulation bipolar fuzzified preference rough sets ($(\alpha, \beta)^o$-MG-BFPRSs) and $(\alpha, \beta)$-pessimistic multi-granulation bipolar fuzzified preference rough sets ($(\alpha, \beta)^p$-MG-BFPRSs) using bipolar fuzzy preference relation (BFPR). Subsequently, the relevant properties and results of both $(\alpha, \beta)^o$-MG-BFPRSs and $(\alpha, \beta)^p$-MG-BFPRSs are investigated in detail. At the same time, a relationship among the $(\alpha, \beta)$-BFPRSs, $(\alpha, \beta)^o$-MG-BFPRSs and $(\alpha, \beta)^p$-MG-BFPRSs is given

Novel categories of spaces in the frame of fuzzy soft topologies

In the present paper, we introduce and discuss a new set of separation properties in fuzzy soft topological spaces called $FS\delta$-separation and $FS\delta$-regularity axioms by using fuzzy soft $\delta$-open sets and the quasi-coincident relation. We provide a comprehensive study of their properties with some supporting examples. Our analysis includes more characterizations, results, and theorems related to these notions, which contributes to a deeper understanding of fuzzy soft separability properties. We show that the $FS\delta$-separation and $FS\delta$-regularity axioms are harmonic and heredity property. Additionally, we examine the connections between $FS{\delta }^*$-compactness and $FS\delta$-separation axioms and explore the relationships between them. Overall, this work offers a new perspective on the theory of separation properties in fuzzy soft topological spaces, as well as provides a robust foundation for further research in the transmission of properties from fuzzy soft topologies to fuzzy and soft topologies and vice-versa by swapping between the membership function and characteristic function in the case of fuzzy topology and the set of parameters and a singleton set in the case of soft topology

TPPSO: A Novel Two-Phase Particle Swarm Optimization

Particle swarm optimization (PSO) is a stout and rapid searching algorithm that has been used in various applications. Nevertheless, its major drawback is the stagnation problem that arises in the later phases of the search process. To solve this problem, a proper balance between investigation and manipulation throughout the search process should be maintained. This article proposes a new PSO variant named two-phases PSO (TPPSO). The concept of TPPSO is to split the search process into two phases. The first phase performs the original PSO operations with linearly decreasing inertia weight, and its objective is to focus on exploration. The second phase focuses on exploitation by generating two random positions in each iteration that are close to the global best position. The two generated positions are compared with the global best position sequentially. If a generated position performs better than the global best position, then it replaces the global best position. To prove the effectiveness of the proposed algorithm, sixteen popular unimodal, multimodal, shifted, and rotated benchmarking functions have been used to compare its performance with other existing well-known PSO variants and non-PSO algorithms. Simulation results show that TPPSO outperforms the other modified and hybrid PSO variants regarding solution quality, convergence speed, and robustness. The convergence speed of TPPSO is extremely fast, making it a suitable optimizer for real-world optimization problems

Bipolar Soft Sets: Relations between Them and Ordinary Points and Their Applications

Bipolar soft set is formulated by two soft sets; one of them provides us the positive information and the other provides us the negative information. The philosophy of bipolarity is that human judgment is based on two sides, positive and negative, and we choose the one which is stronger. In this paper, we introduce novel belong and nonbelong relations between a bipolar soft set and an ordinary point. These relations are considered as one of the unique characteristics of bipolar soft sets which are somewhat expression of the degrees of membership and nonmembership of an element. We discuss essential properties and derive the sufficient conditions of some equivalence of these relations. We also define the concept of soft mappings between two classes of bipolar soft sets and study the behaviors of an ordinary point under these soft mappings with respect to all relations introduced herein. Then, we apply bipolar soft sets to build an optimal choice application. We give an algorithm of this application and show the method for implementing this algorithm by an illustrative example. In conclusion, it can be noted that the relations defined herein give another viewpoint to explore the concepts of bipolar soft topology, in particular, soft separation axioms and soft covers

(2,1)-Fuzzy sets: properties, weighted aggregated operators and their applications to multi-criteria decision-making methods

Abstract Orthopair fuzzy sets are fuzzy sets in which every element is represented by a pair of values in the unit interval, one of which refers to membership and the other refers to non-membership. The different types of orthopair fuzzy sets given in the literature are distinguished according to the proposed constrain for membership and non-membership grades. The aim of writing this manuscript is to familiarize a new class of orthopair fuzzy sets called “(2,1)-Fuzzy sets” which are good enough to control some real-life situations. We compare (2,1)-Fuzzy sets with IFSs and some of their celebrated extensions. Then, we put forward the fundamental set of operations for (2,1)-Fuzzy sets and investigate main properties. Also, we define score and accuracy functions which we apply to rank (2,1)-Fuzzy sets. Moreover, we reformulate aggregation operators to be used with (2,1)-Fuzzy sets. Finally, we develop the successful technique “aggregation operators” to handle multi-criteria decision-making (MCDM) problems in the environment of (2,1)-Fuzzy sets. To show the effectiveness and usability of the proposed technique in MCDM problems, an illustrative example is provided

Generalized Frame for Orthopair Fuzzy Sets: (<i>m</i>,<i>n</i>)-Fuzzy Sets and Their Applications to Multi-Criteria Decision-Making Methods

Orthopairs (pairs of disjoint sets) have points in common with many approaches to managing vaguness/uncertainty such as fuzzy sets, rough sets, soft sets, etc. Indeed, they are successfully employed to address partial knowledge, consensus, and borderline cases. One of the generalized versions of orthopairs is intuitionistic fuzzy sets which is a well-known theory for researchers interested in fuzzy set theory. To extend the area of application of fuzzy set theory and address more empirical situations, the limitation that the grades of membership and non-membership must be calibrated with the same power should be canceled. To this end, we dedicate this manuscript to introducing a generalized frame for orthopair fuzzy sets called “(m,n)-Fuzzy sets”, which will be an efficient tool to deal with issues that require different importances for the degrees of membership and non-membership and cannot be addressed by the fuzzification tools existing in the published literature. We first establish its fundamental set of operations and investigate its abstract properties that can then be transmitted to the various models they are in connection with. Then, to rank (m,n)-Fuzzy sets, we define the functions of score and accuracy, and formulate aggregation operators to be used with (m,n)-Fuzzy sets. Ultimately, we develop the successful technique “aggregation operators” to handle multi-criteria decision-making problems in the environment of (m,n)-Fuzzy sets. The proposed technique has been illustrated and analyzed via a numerical example