Fuzzy minimum spanning tree with interval type 2 fuzzy arc length: formulation and a new genetic algorithm

A Review: Machine Learning for Combinatorial Optimization Problems in Energy Areas

Combinatorial optimization problems (COPs) are a class of NP-hard problems with great practical significance. Traditional approaches for COPs suffer from high computational time and reliance on expert knowledge, and machine learning (ML) methods, as powerful tools have been used to overcome these problems. In this review, the COPs in energy areas with a series of modern ML approaches, i.e., the interdisciplinary areas of COPs, ML and energy areas, are mainly investigated. Recent works on solving COPs using ML are sorted out firstly by methods which include supervised learning (SL), deep learning (DL), reinforcement learning (RL) and recently proposed game theoretic methods, and then problems where the timeline of the improvements for some fundamental COPs is the layout. Practical applications of ML methods in the energy areas, including the petroleum supply chain, steel-making, electric power system and wind power, are summarized for the first time, and challenges in this field are analyzed.

Particle swarm optimization for the shortest path problem

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.

GLDS method for multiple attribute group decision making under 2-Tuple linguistic neutrosophic environment

In this article, the gained and lost dominance score (GLDS) method is extended into the 2-tuple linguistic neutrosophic environment, which also combined the power aggregation operator with the evaluation information to deal with the multi-attribute group decision-making problem. Since the power aggregation operator can eliminate the effects of extreme evaluating data from some experts with prejudice, this paper further proposes the 2-tuple linguistic neutrosophic numbers power-weighted average operator and 2-tuple linguistic neutrosophic numbers power-weighted geometric operator to aggregate the decision makers’ evaluation. Moreover, a model based on the score function and distance measure of 2-tuple linguistic neutrosophic numbers (2TLNNs) is developed to get the criteria weights. Combing the GLDS method with 2-tuple linguistic neutrosophic numbers and developing a 2TLNN-GLDS method for multiple attribute group decision making, it can express complex fuzzy information more conveniently in a qualitative environment and also consider the dominance relations between alternatives which can get more effective results in real decision-making problems. Finally, an applicable example of selecting the optimal low-carbon logistics park site is given. The comparing results show that the proposed method outperforms the other existing methods, as it can get more reasonable results than others and it is more convenient and effective to express uncertain information in solving realistic decision-making problems.

An algorithmic approach for finding the fuzzy constrained shortest paths in a fuzzy graph

Shortest path problem (SPP) is a fundamental and well-known combinatorial optimization problem in the area of graph theory. In real-life scenarios, the arc weighs in a shortest path of a network/graph have the several parameters which are very hard to define exactly (i.e., capacity, cost, demand, traffic frequency, time, etc.). We can incorporate the fuzziness into a graph to handle this type of uncertain situation. In this manuscript, we propose the idea of constrained SPP (CSPP) in fuzzy environment. CSPP has an useful real-life application in online cab booking system. The main motivation of this study is to determine a path with minimal cost where traveling time within two locations does not more than predetermined time. We can not predicate the exact time and cost of the path due to uncertain traffic scenarios and another unexpected reasons; still, the geometrical distance between the locations is fixed. Here, we use trapezoidal fuzzy number to describe the edge weight of a fuzzy network/graph for CSPP. We define this CSPP as fuzzy CSPP (FCSPP). The utility of FCSPP is described in several real-life scenarios. We propose a mathematical formulation for the FCSPP and an algorithm is proposed for solving the FCSPP. We describe an application of our proposed algorithm on an online cab booking system.

p-ideals of BCI-algebras based on neutrosophic N -structures

In this paper, neutrosophic N -structures are applied to p-ideals of BCI-algebras. In fact, we introduce the notion of neutrosophic N -p-ideal in BCI-algebras, and investigate several properties. Further, we present characterizations of neutrosophic N -p-ideal. Moreover, we consider relations between a neutrosophic N -ideal and a neutrosophic N -p-ideal. Also, we provide conditions for a neutrosophic N -ideal to be a neutrosophic N -p-ideal. Furthermore, it is proved that the neutrosophic N -structure Q N G over Q is a neutrosophic N p -ideal of Q ⇔ G is a p-ideal of Q where G is a non-empty subset of a BCI-algebras Q.

Representation of competitions by complex neutrosophic information

The concept of generalized complex neutrosophic graph of type 1 is an extended approach of generalized neutrosophic graph of type 1. It is an effective model to handle inconsistent information of periodic nature. In this research article, we discuss certain notions, including isomorphism, competition graph, minimal graph and competition number corresponding to generalized complex neutrosophic graphs. Further, we describe these concepts by several examples and present some of their properties. Moreover, we analyze that a competition graph corresponding to a generalized complex neutrosophic graph can be represented by an adjacency matrix with suitable real life examples. Also, we enumerate the utility of generalized complex neutrosophic competition graphs for computing the strength of competition between the objects. Finally, we highlight the significance of our proposed model by comparative analysis with the already existing models.

Extension of competition graphs under complex fuzzy environment

A complex fuzzy set (CFS) is a remarkable generalization of the fuzzy set in which membership function is restricted to take the values from the unit circle in the complex plane. A CFS is an efficient model to deal with uncertainties of human judgement in more comprehensive and logical way due to the presence of phase term. In this research article, we introduce the concept of competition graphs under complex fuzzy environment. Further, we present complex fuzzy k-competition graphs and p-competition complex fuzzy graphs. Moreover, we consider m-step complex fuzzy competition graphs, complex fuzzy neighborhood graphs (CFNGs), complex fuzzy economic competition graphs (CFECGs) and m-step complex fuzzy economic competition graphs with interesting properties. In addition, we describe an application in ecosystem of our proposed model. We also provide comparison of proposed competition graphs with existing graphs.

New expected impact functions and algorithms for modeling games under soft sets

Soft set is the power tool to deal with uncertainty in a parametric manner. In applications of soft set, one of the most important steps is to define mappings on soft sets. In this study, we model theory of game under theory of soft set which is an effective tool for handling uncertainties events and problems that may exist in a game. To this end, we first define some expected impact functions of players in soft games. Then, we propose three new decision making algorithms to solve the 2.2 × p, 2 . n × p and m . 2 × p soft matrix games, which cannot be settled by the relevant soft methods such as saddle points, lover and upper values, dominated strategies and Nash equilibrium. The proposed soft game algorithms are illustrated by examples.

Stability and monotony dependence of second-order fuzzy functional systems in partially ordered metric spaces

 In this paper, we consider Cauchy problems for second order fuzzy functional differential equations (DEs) with generalized Hukuhara (gH) derivatives. We study the solvability of the problem by using Perov fixed point theorem in ordered partial metric spaces. The data monotony, continuity, diferentiability dependence of mild solutions with respect to parameters are investigated via weak Picard operators. Moreover, the stability of mild solutions is addressed in sense of Ulam-Hyers stability related to the technique of coefficient matrix converges to zero. Some examples are presented to demonstrate for theoretical results.

Enhanced synchronization-inspired clustering for high-dimensional data

The synchronization-inspired clustering algorithm (Sync) is a novel and outstanding clustering algorithm, which can accurately cluster datasets with any shape, density and distribution. However, the high-dimensional dataset with high dimensionality, high noise, and high redundancy brings some new challenges for the synchronization-inspired clustering algorithm, resulting in a significant increase in clustering time and a decrease in clustering accuracy. To address these challenges, an enhanced synchronization-inspired clustering algorithm, namely SyncHigh, is developed in this paper to quickly and accurately cluster the high-dimensional datasets. First, a PCA-based (Principal Component Analysis) dimension purification strategy is designed to find the principal components in all attributes. Second, a density-based data merge strategy is constructed to reduce the number of objects participating in the synchronization-inspired clustering algorithm, thereby speeding up clustering time. Third, the Kuramoto Model is enhanced to deal with mass differences between objects caused by the density-based data merge strategy. Finally, extensive experimental results on synthetic and real-world datasets show the effectiveness and efficiency of our SyncHigh algorithm.

Modified Vogel’s approximation method for transportation problem under uncertain environment

The fuzzy transportation problem is a very popular, well-known optimization problem in the area of fuzzy set and system. In most of the cases, researchers use type 1 fuzzy set as the cost of the transportation problem. Type 1 fuzzy number is unable to handle the uncertainty due to the description of human perception. Interval type 2 fuzzy set is an extended version of type 1 fuzzy set which can handle this ambiguity. In this paper, the interval type 2 fuzzy set is used in a fuzzy transportation problem to represent the transportation cost, demand, and supply. We define this transportation problem as interval type 2 fuzzy transportation problems. The utility of this type of fuzzy set as costs in transportation problem and its application in different real-world scenarios are described in this paper. Here, we have modified the classical Vogel’s approximation method for solved this fuzzy transportation problem. To the best of our information, there exists no algorithm based on Vogel’s approximation method in the literature for fuzzy transportation problem with interval type 2 fuzzy set as transportation cost, demand, and supply. We have used two Numerical examples to describe the efficiency of the proposed algorithm.

An EDAS Method for Multiple Attribute Group Decision-Making under Intuitionistic Fuzzy Environment and Its Application for Evaluating Green Building Energy-Saving Design Projects

Multiple attribute group decision-making (MAGDM) methods have a significant influence on decision-making in a variety of strategic fields, including science, business and real-life studies. The problem of evaluation in green building energy-saving design projects could be regarded as a type of MAGDM problem. The evaluation based on distance from average solution (EDAS) method is one of the MAGDM methods, which simplifies the traditional decision-making process. Symmetry among some attributes that are known and unknown as well as between pure attribute sets and fuzzy attribute membership sets can be an effective way to solve MAGDM problems. In this paper, the classical EDAS method is extended to intuitionistic fuzzy environments to solve some MAGDM issues. First, some concepts of intuitionistic fuzzy sets (IFSs) are briefly reviewed. Then, by integrating the EDAS method with IFSs, we establish an IF-EDAS method to solve the MAGDM issues and present all calculating procedures in detail. Finally, we provide an empirical application for evaluating green building energy-saving design projects to demonstrate this novel method. Some comparative analyses are also made to show the merits of the method.

A Comparative Assessment of Graphic and 0–10 Rating Scales Used to Measure Entrepreneurial Competences

This article presents an empirical comparative assessment of the measurement quality of two instruments commonly used to measure fuzzy characteristics in computer-assisted questionnaires: a graphic scale (a line production scale using a slider bar) and an endecanary scale (a 0–10 rating scale using radio buttons). Data are analyzed by means of multitrait–multimethod models estimated as structural equation models with a mean and covariance structure. For the first time in such research, the results include bias, valid variance, method variance, and random error variance. The data are taken from a program that assesses entrepreneurial competences in undergraduate Economics and Business students by means of questionnaires administered on desktop computers. Neither of the measurement instruments was found to be biased with respect to the other, meaning that their scores are comparable. While both instruments achieve valid and reliable measurements, the reliability and validity are higher for the endecanary scale. This study contributes to the still scarce literature on fuzzy measurement instruments and on the comparability and relative merits of graphic and discrete rating scales on computer-assisted questionnaires.

Algebraic Operations on Spatiotemporal Data Based on RDF

In the context of the Semantic Web, the Resource Description Framework (RDF), a language proposed by W3C, has been used for conceptual description, data modeling, and data querying. The algebraic approach has been proven to be an effective way to process queries, and algebraic operations in RDF have been investigated extensively. However, the study of spatiotemporal RDF algebra has just started and still needs further attention. This paper aims to explore an algebraic operational framework to represent the content of spatiotemporal data and support RDF graphs. To accomplish our study, we defined a spatiotemporal data model based on RDF. On this basis, the spatiotemporal semantics and the spatiotemporal algebraic operations were investigated. We defined five types of graph algebras, and, in particular, the filter operation can filter the spatiotemporal graphs using a graph pattern. Besides this, we put forward a spatiotemporal RDF syntax specification to help users browse, query, and reason with spatiotemporal RDF graphs. The syntax specification illustrates the filter rules, which contribute to capturing the spatiotemporal RDF semantics and provide a number of advanced functions for building data queries.

Updating the Reduct in Fuzzy β-Covering via Matrix Approaches While Adding and Deleting Some Objects of the Universe

Since fuzzy β -covering was proposed, few papers have focused on how to calculate the reduct in fuzzy β -covering and how to update the reduct while adding and deleting some objects of the universe. Here, we propose a matrix-based approach for computing the reduct in a fuzzy β -covering and updating it dynamically using a matrix. First, matrix forms for computing the reduct in a fuzzy β -covering are proposed. Second, properties of the matrix-based approaches are studied while adding and deleting objects. Then, matrix-based algorithms for updating the reduct in a fuzzy β -covering are proposed. Finally, the efficiency and validity of the designed algorithms are verified by experiments.

Coordinated Formation Design of Multi-Robot Systems Via an Adaptive-Gain Super-Twisting Sliding Mode Method

This paper presents a super-twisting-based sliding mode control method for the formation problem of multi-robot systems. The multiple robots contain plenty of uncertainties and disturbances. Such a control method has two adaptive gains that can contribute to the robustness and improve the response of the formation maneuvers despite these uncertainties and disturbances. Based on the leader-follower frame, this control method was investigated. The closed-loop formation stability is theoretically guaranteed in the sense of Lyapunov. From the aspect of practice, the control method was carried out by a multi-robot system to achieve some desired formation patterns. Some numerical results were demonstrated to verify the feasibility of the control method. Some comparisons were also illustrated to support the superiority and effectiveness of the presented sliding mode control method.