Fuzzy Quantities Research Articles

Performance Analysis of Fully Intuitionistic Fuzzy Multi-Objective Multi-Item Solid Fractional Transportation Model

An investigation is conducted in this paper into a performance analysis of fully intuitionistic fuzzy multi-objective multi-item solid fractional transport model (FIF-MMSFTM). It is to be anticipated that the parameters of the conveyance model will be imprecise by virtue of numerous uncontrollable factors. The model under consideration incorporates intuitionistic fuzzy (IF) quantities of shipments, costs and profit coefficients, supplies, demands, and transport. The FIF-MMSFTM that has been devised is transformed into a linear form through a series of operations. The accuracy function and ordering relations of IF sets are then used to reduce the linearized model to a concise multi-objective multi-item solid transportation model (MMSTM). Furthermore, an examination is conducted on several theorems that illustrate the correlation between the FIF-MMSFTM and its corresponding crisp model, which is founded upon linear, hyperbolic, and parabolic membership functions. A numerical example was furnished to showcase the efficacy and feasibility of the suggested methodology. The numerical data acquired indicates that the linear, hyperbolic, and parabolic models require fewer computational resources to achieve the optimal solution. The parabolic model has the greatest number of iterations, in contrast to the hyperbolic model which has the fewest. Additionally, the elapsed run time for the three models is a negligible amount of time: 0.2, 0.15, and 1.37 s, respectively. In conclusion, suggestions for future research are provided.

OWA-based multi-criteria decision making based on fuzzy methods

AbstractOne of the most important challenges in Multi-Attribute Decision Making (MADM) problems is how can the optimal weights of the criteria can be determined properly by the decision maker. In the relevant research literature, various methods based on the requirements and assumptions of the problem were introduced to determine the weights of the criteria. In this regard, in particular, the Yager’s OWA operator is one of the most significant and widely used approaches to evaluate the weights of criteria. But there is a drawback, that is, the results of Yager’s OWA operator depend only on the level of decision-maker’s risk and the number of the criteria. Therefore, in this paper, using a multi-objective decision making approach, we try to express this MADM challenge in the form of a generalization of the Yager’s OWA operators and Ahn’s method. One of the advantages of this generalization is that the proposed method uses all the information in the decision matrix compared to the methods proposed by Yager’s OWA operators and the Ahn’s method. The proposed approach is also able to enter various types of preferences considered by the decision maker for the criteria calculations as crisp or fuzzy quantities. Numerical examples and real dataset analysis based on a survey of students’ opinions on teaching activities are provided.

Application of algebraic operations on fuzzy numbers

The main difficulty in working with fuzzy quantities is that, even in the case of the simplest relevance functions, as a result of elementary operations carried out on them, relevance functions of a complex form requiring a large number of parameters are formed. Therefore, the article analyzes the approximation of the current relevance functions and the results of operations performed on them by triangular, exponential, and trapezoidal functions of a certain class depending on a set number of parameters. In this case, there is an opportunity to build relatively simple basic operations that do not exceed the class of selected functions.

Investigation of a Fuzzy Production Inventory Model with Carbon Emission using Sign Distance Method

Reducing costs associated with inventory is the primary goal of conventional inventory models like the models of economic order quantity and economic production quantity. However, these models fall short of addressing defective goods or revising them. Imperfections in the manufacturing process result in flawed products alongside the final goods. To convert these flawed components into finished goods, rework is necessary. In manufacturing and reworking process produces carbon emissions which are harmful for the earth. To determine the optimal quantity for a single product manufactured in a single-stage manufacturing system that yields partially defective products that are reworked in the same cycle, is determined in real-life situations, where the inventory characteristics and objectives are not exact. Such a type of uncertainty may be characterized by fuzzy numbers. A pentagonal fuzzy number has been used to define the cost parameters. Due to fuzzy parameters, the model becomes a fuzzy quantity, and it is defuzzied by the sign distance method. this article formulates a model of manufacturing inventories with planned backorders. Furthermore, a closed form for the inventory’s system total cost is determined, and a range of actual values for defective products for which an appropriate method exists is also provided. A proper mathematical model is created to accomplish the goal, and the manufacturing lot size that reduces the overall cost is determined. The ideal amount of a production batch to reduce total cost is established in to attain this goal using an appropriate mathematical model. While formulating and solving the relevant model, the necessary and sufficient conditions for a single globally optimal solution have been determined. Examples used as visualizations are given and confirmed by data.

Local Path Planning via Improved Fuzzy and Q(λ)-learning Algorithms for the Mobile Robot

<p>With the complexity of the robot operating environment increases, there becoming higher demands on the optimal path planning for robots. Most of the path planning is performed in known environments and static models. However, there are still challenges for robots to perform path planning in complex unknown or dynamic environments, which will suffer from deadlock problems and obstacle avoidance failures. Reinforcement learning (RL) can help fuzzy algorithm to optimize the strategy. However, the difficulty of designing the rewards in RL makes the algorithm require a large number of samples to learn the strategy, resulting in computational complexity. To solve these problems, a new local path planning based on the improved fuzzy and Q(λ)-learning algorithms is proposed, aiming to plan the shortest path and avoid obstacles. For solving the problems of breaking through and avoiding obstacles, a fuzzy controller is designed. The distance of nearest obstacle in front of the mobile robot and the distance between the obstacles in the two breakout directions are regarded as the two inputs for this controller. And the two fuzzy quantities of the mobile robot’s running angle and the safe step length are outputted. In the path planning, the Q(λ)-learning algorithm are used to optimize the weights of the running angle and the safe step, obtaining a more accurate robot position and speeding up path planning efficiency. Furthermore, to solve the overlap problems among the starting point, end point, and obstacles, a safer running environment is designed considering radiuses of these objects. Besides, the mobile robot breakout scheme and sustainable obstacle avoidance scheme are designed to solve the deadlock problem and “large obstacle” avoidance problem, respectively. Simulation results in the sparse and complex operating environment show that our proposed algorithm can plan a relatively optimal and safe path, improving the success rate of path planning.</p> <p> </p>

Fuzzy response to SH guided-wave scattering by semicircular depressions on the boundary of a ribbon-shaped elastic plate

In this paper, the fuzzy scattering problem with semicircular depressions on the boundary of a band-shaped elastic plate with steady SH guided wave incident is studied and an analytical solution is given. First, the SH guided wave is constructed by the guided wave expansion method, and then the scattered wave satisfying the free condition of the boundary stress of the strip domain is constructed by the cumulative mirror method. Finally, a definite solution equation is obtained based on the fact that the shear stress at the edge of the semi-circular recessed hole is zero. In this paper, the ambiguity of the number of waves and the width of the bands is taken into account. In order to avoid the irreversibility of interval algorithm and the difficulty of solving non-linear equations, the membership function of fuzzy quantity is segmented to make the membership degree and fuzzy quantity correspond respectively. A deterministic problem that translates into piecewise processing. Two numerical examples are given to examine the changes in fuzzy response of different numbers of fuzzy waves and fuzzy thicknesses to the dynamic stress concentration factor of the hoop at the collapse limit.

Improving empirical models of complex technological objects under conditions of uncertainty

This paper proposes a method for improving empirical models of complex technological objects with insufficient information about the input and output values of an object's parameters. It has been established that most methods for constructing empirical models require knowledge of the statistical characteristics of the input and output values of an object. When modeling complex non-reproducible stochastic processes that evolve over time, information about the parameters and structure of an object is usually not available. A method has been proposed where input and output values are treated as fuzzy quantities with a triangular membership function. Since at some points in the region, the triangular membership function is undifferentiated, it is inconvenient to use it in its typical form to solve the problem of optimal control. Therefore, it is proposed to approximate it with the Gaussian membership function. It is shown that such an approximation is reduced to finding one parameter, which is determined by the least squares method. Its value practically does not depend on the magnitude of the uncertainty interval while the value characterizing the accuracy of approximation is a monotonously increasing function that has a linear character. This makes it possible to define the main operations on fuzzy numbers and derive an empirical model for the case of a polynomial "base" model. The resulting model is linear in its parameters, so a genetic algorithm can be used to find them. It is shown that genetic algorithms can be used in the construction of empirical polynomial models when input parameters are interpreted as fuzzy numbers. Thus, it can be argued that when constructing an empirical model of an object that is affected by external disturbances that cannot be measured, it is advisable to approximate all input quantities with a triangular Gaussian membership function

Extension principles for picture fuzzy sets

Picture fuzzy set (PFS), is a newly developed apparatus to treaty with uncertainties in problems where the opinions are yes, no, neutral, and refusal types. Extension principle is one of the key tools for describing uncertainties. It provides a general method for existing classical mathematical concepts to address fuzzy quantities. It has numerous applications in various arena of our real life. However, there are less works on extension principle for picture fuzzy sets. In this article, new extension principles namely minimal extension principle and average extension principle are proposed for picture fuzzy sets. Various properties of the minimal extension principle and the average extension principle for PFSs are also established. We also prove some properties of Zadeh’s extension principle for PFSs. Finally, arithmetic operations for PFSs based on the average extension principle are developed with numerical illustrations.

A hybrid combined algorithm based on intelligent water drops and electromagnetism-like algorithms for fuzzy TSP1

This paper presents a new combined algorithm for the fuzzy Travelling Salesman Problem (FTSP) based on a composition of the Intelligent Water Drops (IWD) and the Electromagnetism-like (EM) algorithms. In a FTSP, the time consumed distance between cities i and j can be described by vague knowledge, such as fuzzy quantity. The main goal of FTSP is to achieve the minimum distance of Hamilton circuit of G graph, where the Hamilton circuit is a closed route of cities (i.e., nodes) of G that have been visited only once. The proposed algorithm transfers the generated responses by the IWD to the EM, where the best answer is selected. Importantly, the computed results from both algotithm are compared and the best is accumulated. In other words, in each iteration, the best result is collected by comparison between the current and previous hierarchies until the halt condition is fulfilled. Finally, the results of the genetic algorithm (GA), IWD and EM algorithms are compared, so that the efficiency of the proposed combined IWD-EM algorithm is determined.

An Efficient Hybrid Conjugate Gradient Algorithm for Solving Intuitionistic Fuzzy Nonlinear Equations

This paper presents an iterative algorithm for solving intuitionistic fuzzy nonlinear equations (IFNEs). The proposed method is based on the classical conjugate gradient (CG) search direction. An interesting feature of the new algorithm is that it considers problems based on the special triangular intuitionistic fuzzy number. For this purpose, intuitionistic fuzzy quantities are transformed into membership and non-membership parametric forms, and a line search procedure is employed to compute the step length. Preliminary results from numerical experiments are presented to demonstrate the performance of the method. It is observed that the proposed hybrid CG method is highly effective and promising. KEYWORDS Hybrid CG, intuitionistic fuzzy nonlinear equation, parametric form, step length, inexact line search

An Application Model for Linear Programming with an Evolutionary Ranking Function

One of the most important methodologies in operations research (OR) is the linear programming problem (LPP). Many real-world problems can be turned into linear programming models (LPM), making this model an essential tool for today's financial, hotel, and industrial applications, among others. Fuzzy linear programming (FLP) issues are important in fuzzy modeling because they can express uncertainty in the real world. There are several ways to tackle fuzzy linear programming problems now available. An efficient method for FLP has been proposed in this research to find the best answer. This method is simple in structure and is based on crisp linear programming. To solve the fuzzy linear programming problem (FLPP), a new ranking function (RF) with the trapezoidal fuzzy number (TFN) is devised in this study. The fuzzy quantities are de-fuzzified by applying the proposed ranking function (RF) transformation to crisp value linear programming problems (LPP) in the objective function (OF). Then the simplex method (SM) is used to determine the best solution (BS). To demonstrate our findings, we provide a numerical example (NE).

Derivative-free Newton's method for solving intuitionistic fuzzy nonlinear equations with an application

In this paper, we present a derivative-free Newton’s method that avoids computing the derivative by generating an approximation of the derivative for the intuitionistic fuzzy nonlinear equation. We first consider transforming the intuitionistic fuzzy quantities into their equivalent membership and non-membership parametric forms and insert the approximation from the forward difference method applied to F'(x_k) = 0 in Newton’s method to avoid computing the Jacobian matrix. Numerical experiments were carried out, which shows that the approach is a good option for computing Jacobian and is an efficient one.

Optimisation of an FEOQ model for deteriorating items with reliability influence demand

The classical (crisp) inventory control model with reliability influence demand and partially backlogged items is to be considered. The primary motive of efficient inventory management is to provide a suitable customer service thereby keeping a low inventory cost for the model. The cost factor is to consider a fuzzy random variable. Here the ordering cost and reliability of the production process are the decision variables. Thus the aim of this paper is to minimise the cost of the inventory system. This model has been developed for both crisp and fuzzy systems. Due to fuzzy parameters, the model becomes a fuzzy quantity and it is fuzzily by sign distance method. The facts used in this research work have been exemplified by the use of an appropriate numerical example.

Fuzzy Stochastic Differential Equations Driven by a Fuzzy Brownian Motion

In our previous work, we study fuzzy Itô integrals driven by a fuzzy Brownian motion. In this article, we continue this study. The purpose of this paper is to study the weak uniqueness of fuzzy stochastic differential equations taking into account fuzzy Brownian motion. For instance, we construct the fuzzy stochastic differential equation driven by a fuzzy Brownian motion. To define and prove our results, we use the fuzzification, the alpha cut method and the Hausdorff distance between two fuzzy quantities. Some results are to our credit in this article like the instance, we construct the fuzzy stochastic differrential equation driven by fuzzy Brownian motion. Furthermore, we develop fuzzy Itô calculus driven by a fuzzy Brownian motion. Our result complement existing ones in that the fuzzy version of Brownian motion is taken into account.

Fuzzy system F-CalcRank for calculating functions of fuzzy arguments and ranking of fuzzy numbers

Assessing functions of fuzzy arguments and ranking of fuzzy quantities are two key steps in fuzzy modeling and Fuzzy Multicriteria Decision Analysis (FMCDA). Approximate calculations along with the use of centroid index as a defuzzification based ranking methods are a generally accepted approach to applications in the fuzzy environment. This paper presents a novel fuzzy system, F-CalcRank, which is integration of two coupled fuzzy systems: F-Calc (Fuzzy Calculator) and F-Ranking (Fuzzy Ranking). F-Calc allows assessing functions of fuzzy numbers with the use of different approaches: approximate calculations, standard fuzzy arithmetic, and transformation methods. The input values to F-Calc are fuzzy numbers with the following membership functions: triangular and trapezoidal, Gaussian, bell shape, sigmoid, and piece-wise linear continuous or upper semicontinuous membership functions of any complexity, as well as fuzzy linguistic terms of a given term set. F-Ranking system is intended for ranking of a given set of fuzzy numbers, including those, which are inputs and/or outputs of the F-Calc system. F-Ranking includes six ranking methods: three defuzzification based and three pairwise comparison ones. The structure of F-CalcRank as well as input and output information and the user interfaces of both F-Calc and F-Ranking systems, which can also be used independently, are presented. Examples of computing functions of fuzzy arguments and ranking of fuzzy numbers using implemented methods as well as exploring a real case study in agro-ecology with the use of a math model in fuzzy environment are considered. These examples stress the features and novelty of F-CalcRank system as well as presented applied research. The computer modules created within F-CalcRank are a basis for different FMCDA models developed by the authors. F-CalcRank system is intended for university education, research and various applications in engineering and technology.

From MCDA to fuzzy MCDA: Presumption of model adequacy or is every fuzzification of an mCDA method justified?

A fuzzy extension of a Multi-Criteria Decision Analysis (MCDA) method implies a choice of an approach to estimating corresponding functions of fuzzy variables and a method for ordering alternatives based on ranking of fuzzy quantities. The objective of this paper is the development and comparison of Fuzzy MCDA (FMCDA) models, which represent different approaches to fuzzy extensions of an ordinary MCDA method. To do so, different approaches to assessing functions of fuzzy numbers are considered along with several methods for ranking of fuzzy numbers. Distinctions in ranking alternatives, including the number and significance of distinctions based on a granulation of the output information, are explored for different FMCDA models by using Monte Carlo simulating input scenarios of fuzzy multi-criteria problems. In addition, both intra-distinctions and inter-distinctions are explored. According to the results, distinctions in ranking alternatives by different FMCDA models may be considered as significant both for ranking and choice multi-criteria problematiques. This research is of fundamental and applied importance and has no analogues.

Some properties of integration of real-valued function over a fuzzy interval

One of the most fundamental concepts in fuzzy set theory is the extension principle. It gives a generic way of dealing with fuzzy quantities by extending non-fuzzy mathematical concepts. There are a few examples, including the concept of fuzzy distance between fuzzy sets. The extension approach is then methodically applied to real algebra, with considerable development of fuzzy number operations. These operations are computationally appealing and generalized interval analysis. Although the set of real fuzzy numbers with extended addition or multiplication is no longer a group, it retains many structural qualities. The extension concept is demonstrated to be particularly beneficial for defining set-theoretic operations for higher fuzzy sets. We need some definitions related to our properties before we can create the properties of integration of a crisp real-valued function over a fuzzy interval. It is our goal in this article to develop and demonstrate certain characteristics of a real-valued function over a fuzzy interval in order to broaden the scope of the notion of integration of a real-valued function over a fuzzy interval. Some of these characteristics are linked to the operations of extended addition and extended subtraction, while others are not.

Explainable Fuzzy Utility Mining on Sequences

Fuzzy systems have good modeling capabilities in several data science scenarios and can provide human-explainable intelligence models with explainability and interpretability. To obtain a human-explainable data intelligence model for decision making, in this article, we investigate explainable fuzzy-theoretic utility mining on multisequences. Meanwhile, a more normative formulation of the problem of fuzzy utility mining on sequences is formulated. By exploring fuzzy set theory for utility mining, we propose a novel method termed pattern growth fuzzy utility mining (PGFUM) for mining fuzzy high-utility sequences with linguistic meaning. In the case of sequence data, PGFUM reflects the fuzzy quantity and utility regions of sequences. To improve the efficiency and feasibility of PGFUM, we develop two compressed data structures with explainable fuzziness. Furthermore, one existing and two new upper bounds on the explainable fuzzy utility of candidates are adopted in three proposed pruning strategies to substantially reduce the search space and, thus, expedite the mining process. It is demonstrated that PGFUM achieves not only human-explainable mining results that contain the original nature of revealable intelligibility, but also high efficiency in terms of runtime and memory cost.

Real-Time Application Optimization Control Algorithm for Energy Management Strategy of the Hybrid Power System Based on Artificial Intelligence

In recent years, due to the strengthening of our country’s comprehensive strength, the rapid development of science and technology and artificial intelligence has also attracted people’s attention. Artificial intelligence is a highly applicable subject, which has very good applications in power systems. In the experiment, the open circuit voltage method and the ampere-hour integration method are used to estimate the SOC of the lithium battery and the particle swarm energy management algorithm is used to allocate the output power of the fuel cell and the lithium battery. The particle swarm algorithm module calls the dual source hybrid power system module through the sim function to convert the actual value input in the system into a fuzzy quantity suitable for fuzzy control. The energy management strategy based on particle swarm optimization and fuzzy control was tested based on working conditions under the comprehensive test bench. Finally, the matching of the hybrid system is analyzed from the structure, component parameters, control strategy, and driving cycle of the vehicle. The experimental data show that the total fuel consumption of the three sets of experiments is averaged to get a fuel consumption rate of 26.3 m3/100 km for the hybrid city bus under the optimized energy management strategy. The results show that the real-time energy management strategy based on particle swarm algorithm can significantly improve the real-time performance of traditional instantaneous energy management strategies while reducing fuel consumption.

Computer-Based Fuzzy Numerical Method for Solving Engineering and Real-World Applications

The nonlinear equation is a fundamentally important area of study in mathematics, and the numerical solutions of the nonlinear equations are also an important part of it. Fuzzy sets introduced by Zedeh are an extension of classical sets, which have several applications in engineering, medicine, economics, finance, artificial intelligence, decision-making, and so on. The most special types of fuzzy sets are fuzzy numbers. The important fuzzy numbers are trapezoidal fuzzy and triangular fuzzy numbers, which have several applications. In this research article, we propose an efficient numerical iterative method for estimating roots of fuzzy nonlinear equations, which are based on the special type of fuzzy number called triangular fuzzy number. Convergence analysis proves that the order of convergence of the numerical method is three. Some real-life applications are considered as numerical test problems from engineering, which contain fuzzy quantities in the parametric form. Engineering models include fractional conversion of nitrogen-hydrogen feed into ammonia and Van der Waal’s equation for calculating the volume and pressure of a gas and motion of the object under constant force of gravity. Numerical illustrations are given to show the dominance efficiency of the newly constructed iterative schemes as compared to existing methods in the literature.