Imprecise Problems Research Articles

Bilateral fuzzy sets and their three-way decisions: a new perspective of fuzzy logic

Fuzzy sets provide an effective method for dealing with uncertain and imprecise problems. For data of intermediate fuzzy distribution, membership degrees of objects whose attribute values are larger or smaller than the normal value would be the same and carried out the same decision. However, objects with different values mean that the information they contain is different for the decision-making problem. The decision process of calculating membership degrees in fuzzy set will lose the information of data itself. Therefore, bilateral fuzzy sets and their three-way decisions are proposed. First, the deviation degree is proposed in order to distinguish these objects. Compared with the membership degree, the deviation degree extends the mapping range from [0, 1] to [- 1, 1]. For six typical membership functions, their corresponding deviation functions are discussed and deduced. Second, the concept of bilateral fuzzy sets is proposed and the corresponding operation rules are analyzed and proved. Then, three-way decisions and approximations based on bilateral fuzzy sets are constructed. Next, for the optimization of threshold, principle of least cost is extended to the three-way decisions model based on bilateral fuzzy sets, and theoretical derivation is carried out. Finally, based on probability statistics, the principle based on confidence interval is proposed, which provides a new perspective for threshold calculation.

Intelligent English Translation Model Based on Improved GLR Algorithm

An intelligent English translation model based on the improved GLR algorithm is proposed to solve the imprecise problem of traditional methods. This algorithm is used to create a body of tagged sentences from tens of thousands of English and Chinese words, so that the sentences can be searched. In addition, the knowledge structure translated into English is designed to prepare the knowledge structure based on information collection, processing and production. To use the knowledge of English translation, the English text is written according to the plan, design and negative features are extracted. The clinical trial was based on the standard knowledge of English translation and the trial data was recorded. According to the test results, the accuracy of English translation is 75.1% before modification and 99.1% after using smart text. Syntax and sentence-based knowledge systems have weak nodal point distributions, but the nodal point distributions are compact in the first, fourth, and fifth trials. Conclusion: The English translation knowledge model is highly accurate and can meet the needs of English translation.

Fractal Design of Indoor and Outdoor Forms of Architectural Space Based on a Three-Dimensional Box Dimension Algorithm

The three-dimensional organic growth features of buildings have been given more and more attention according to the unique view representation regulations of the indoor construction industry, in order to optimize the usage and allocation efficiency of building space. To explore the configuration structure of building function space, the three-dimensional box dimension algorithm is used to measure the fractal dimension of the indoor and outdoor form of building space, and the two-dimensional and three-dimensional fractal characteristics of building space are compared and analyzed; the method of the second derivative is utilized for the automatic recognition of fractal scale-free areas, aiming at the imprecise problem of the artificial judgment of scale-free areas in earlier fractal research of interior and outdoor forms of architectural space. The experimental results show that the second derivative method can effectively and automatically identify the scale-free region. The coefficients of linear fitting are above 0.990, and the indoor and outdoor forms of architectural space have clear fractal characteristics. After applying the method, the three-dimensional fractal dimension grows, indicating that the interior and outdoor form usage of architectural space in this area is generally effective and compact.

Multifunctional Radar Cognitive Jamming Decision Based on Dueling Double Deep Q-Network

To solve the inefficient and imprecise problem using the Deep Q-network (DQN) algorithm for the radar jamming decision, this paper proposes a multifunctional radar jamming decision optimization method based on the Dueling Double Deep Q-network (D3QN). First, we use a value function reflecting the radar state’s change, and an advantage function related to radar state S and jamming action A to improve the cognitive jamming level for unknown radar modes. Then, using the dueling networks for jamming strategy selection and effectiveness evaluation can further improve decision accuracy. Finally, we propose a prioritized experience replay mechanism during network training to shorten the decision-making time. The experimental results show that our proposed method completes decision tasks 2.1 times more efficiently than the DQN and improves decision accuracy by approximately 10% over DQN.

On the neutrosophic soft set with rough set theory.

Rough set is a very powerful invention to the whole world for dealing with uncertain, incomplete and imprecise problems. Also soft set theory and neutrosophic set theory are advance mathematical tools to handle these uncertain, incomplete, inconsistent information in a better way. The purpose of this article is to expand the scope of rough set, soft set and neutrosophic set theory. We have introduced the concept of neutrosophic soft set with roughness without using full soft set. Some definitions, properties and examples have been established on neutrosophic soft rough set. Moreover, dispensable and equalities are written on roughness with neutrosophic soft set.

Multi-level Qualitative Reasoning Logic

Qualitative reasoning is a very efficient method that people often use to solve problems. Recently, the literature about qualitative reasoning as a causal analysis and decision-making tool has been emerging. However, the existing qualitative reasoning methods are mainly used for the modeling of imprecise problems. There are not many studies on formalization tools of qualitative “inference”. This paper proposes a logical system for qualitative reasoning (QRL). The main research contents include: the grammar and semantic structure of QRL are given; the meaning of formula logic truth value in QRL and its assignment rules are discussed; and the reliability and completeness of QRL are proved. Compared with fuzzy logic, probability logic and other uncertain reasoning methods, the advantage of QRL method is that it can use axiomatic reasoning method, and does not need to construct membership functions and collect a large number of samples.

A Hybrid PSO-GA Algorithm for Traveling Salesman Problems in Different Environments

In this study particle swarm optimization (PSO) is modified and hybridised with genetic algorithm (GA) using one’s output as the other's input to solve Traveling Salesman Problem(TSP). Here multiple velocity update rules are introduced to modify the PSO and at the time of the movement of a solution, one rule is selected depending on its performances using roulette wheel selection process. Each velocity update rule and the corresponding solution update rule are defined using swap sequence (SS) and swap operation (SO). K-Opt operation is applied in a regular interval of iterations for the movement of any stagnant solution. GA is applied on the final output swarm of the PSO to search the optimal path of the large size TSPs. Roulette wheel selection process, multi-point cyclic crossover and the K-opt operation for the mutation are used in the GA phase. The algorithm is tested in crisp environment using different size benchmark test problems available in the TSPLIB. In the crisp environment the algorithm gives approximately 100% success rate for the test problems up to considerably large sizes. Efficiency of the algorithm is tested with some other existing algorithms in the literature using Friedman test. Some approaches are incorporated with this algorithm for finding solutions of the TSPs in imprecise (fuzzy/rough) environment. Imprecise problems are generated from the crisp problems randomly, solved and obtained results are discussed. It is observed that the performance of the proposed algorithm is better compared to the some other algorithms in the existing literature with respect to the accuracy and the consistency for the symmetric TSPs as well as the Asymmetric TSPs.

Synergistic Effect Evaluation of Main and Auxiliary Industry of Power Grid Based on the Information Fusion Technology from the Perspective of Sustainable Development of Enterprises

With the development of the diversified economic union, the power grid enterprises’ auxiliary industries are continuing to grow and develop faster. However, in the process of development, power grid enterprises are still faced with the problem of low efficiency of the management of main and auxiliary and resource allocation and utilization. Thus, the synergistic development evaluation for power grid enterprises’ main and auxiliary industries has a strong practical significance. It can help the managers to find the short board of each industry and search for the exploration direction for improvement to promote the sustainable development of the main and auxiliary industries comprehensively. It can also provide the reference for improving the management level of power grid enterprises. Information fusion technology, as a process of information processing for decision making, can make use of multi-source information synergistically to get a more objective and more essential understanding of the same thing or the same goal. It has been applied to many fields in a mature way. Based on the characteristics of each industry, this paper constructs a synergistic effect evaluation index system of the main and auxiliary industries from the aspects of management foundation, resource integration, operational efficiency and effectiveness. The variable precision fuzzy rough set (VPFRS) is introduced to screen the index system, eliminate redundant indexes, retain key indexes and improve the efficiency and accuracy of evaluation effectively. Meanwhile, based on the characteristic of dealing with the imprecise problem of the vague set, this paper establishes the evaluation model based on information fusion technology of the variable precision fuzzy rough set and vague set (VPFRS-Vague). In order to verify the validity of the model, five typical companies belonging to power grid enterprises are selected as examples for analysis to prove the validity and applicability of the evaluation method.

Implementation of Biologically Motivated Optimization Approach for Tumor Categorization

Tumour prediction and classification is regarded as a complex task that needs attention. Moreover, medical experts lack expertise in this section. Hence, an intelligent clinical system model is the time of the hour. Recently, biologically motivated techniques are emerging to be an efficient computing method to solve imprecise and complex problems. Nature forms an immense source of motivation in finding solutions to sophisticated problems IT sector since it is highly robust and dynamic. The result obtained is highly optimised and balanced solution. This is the basic idea of such nature motivated techniques. In our research, we have analysed and implemented some important bio-inspired optimisation techniques to categorise different kinds of tumour. Multilayer perceptron is the classifier used in the process. We have later evaluated our results with some critical metrics like RMSE, Kappa coefficient, accuracy and many others to determine the effectiveness of our system model developed. It is observed that using bio-inspired computation approach enhances the efficiency of tumour classification. The results are depicted in this paper.

A novel hybrid algorithm for generalized traveling salesman problems in different environments

A swap sequence-based particle swarm optimization (SSPSO) technique and genetic algorithm (GA) are used in tandem to develop a hybrid algorithm to solve generalized traveling salesman problem. Local search algorithm K-Opt is occasionally used to move any stagnant solution. Here, SSPSO is used to find the sequence of groups of a solution in which a tour to be made and cities from different groups of the sequence are selected using GA. The K-Opt algorithm (for K=3) is used periodically for a predefined number of iterations to improve the quality of the solutions. The algorithm is capable of solving the problem in crisp as well as in imprecise environment. For this purpose, a general fitness evaluation rule for the solutions is proposed. The efficiency of the algorithm is tested in crisp environment using different size benchmark problems available in TSPLIB. In crisp environment, the algorithm gives 100% success rate for problems up to considerably large sizes. Imprecise problems are generated from crisp problems randomly using a rule and are solved using the proposed approach. The obtained results are discussed. Moreover it is observed that the proposed algorithm finds multiple optimal paths, when they exist, both for the crisp problems and their fuzzy variations.

Regression Analysis of a Kind of Trapezoidal Fuzzy Numbers Based on a Shape Preserving Operator

Fuzzy regression provides more approaches for us to deal with imprecise or vague problems. Traditional fuzzy regression is established on triangular fuzzy numbers, which can be represented by trapezoidal numbers. The independent variables, coefficients of independent variables and dependent variable in the regression model are fuzzy numbers in different times and TW, the shape preserving operator, is the only T-norm which induces a shape preserving multiplication of LL-type of fuzzy numbers. So, in this paper, we propose a new fuzzy regression model based on LL-type of trapezoidal fuzzy numbers and TW. Firstly, we introduce the basic fuzzy set theories, the basic arithmetic propositions of the shape preserving operator and a new distance measure between trapezoidal numbers. Secondly, we investigate the specific model algorithms for FIFCFO model (fuzzy input-fuzzy coefficient-fuzzy output model) and introduce three advantages of fit criteria, Error Index, Similarity Measure and Distance Criterion. Thirdly, we use a design set and two reference sets to make a comparison between our proposed model and the reference models and determine their goodness with the above three criteria. Finally, we draw the conclusion that our proposed model is reasonable and has better prediction accuracy, but short of robust, comparing to the reference models by the three goodness of fit criteria. So, we can expand our traditional fuzzy regression model to our proposed new model.

Domination in Fuzzy Soft Graphs

Fuzzy soft set are introduced by author Molodtsov, which is solve imprecise problems in the field of engineering, social science, economic, medical secience and environment. This paper addresses the study of domination in fuzzy soft graphs. By using the concept of strength of a path, strength of connectedness and strong arc, domination set is established. The necessary and sufficient condition for the minimum domination set of FSG is investigated. Further some properties of independent domination number of FSG are obtained and the proposed concepts are described with suitable examples. Finally, we state and prove some results related to these concepts.

Injective module based on rough set theory

It is important to handle real-life problems algebraically, but as most of the real-life problems as well as the applications are imprecise(i.e. vague, inexact, or uncertain), it makes harder to analyze algebraically, while Rough Set Theory (RST) has the capability to deal imprecise problems. To solve imprecise problems algebraically, we investigated injective module based on RST.

Fuzzy pricing of geometric Asian options and its algorithm

Owing to the fluctuations of the financial market, input data in the options pricing formula cannot be expected to be precise. This paper discusses the problem of pricing geometric Asian options under the fuzzy environment. We present the fuzzy price of the geometric Asian option under the assumption that the underlying stock price, the risk-free interest rate and the volatility are all fuzzy numbers. This assumption makes the financial investors to pick any geometric Asian option price with an acceptable belief degree. In order to obtain the belief degree, the interpolation search algorithm has been proposed. Some numerical examples are presented to illustrate the rationality and practicability of the model and the algorithm. Finally, an empirical study is performed based on the real data. The empirical study results indicate that the proposed fuzzy pricing model of geometric Asian option is a useful tool for modeling the imprecise problem in the real world.

Novel Motion Modes for 2-D Locomotion of a Microrobot

This paper proposes novel motion modes for a microrobot which enable several driving options during its 2-D locomotion. The robot motion based on conventional methods shows stick-slip phenomena which produce imprecise jerking movement. We solved the imprecise control problem by using the concept of kinetic friction force. Furthermore, we introduced several motion modes that can generate smooth motion under different environments and presented the pros and cons of each motion mode. A motion mode is properly selected depending on the environment or application purpose, and it can exhibit high performance in the execution of the task. The proposed method using a suitable mode of operation of the microrobot has the potential to be applied in various medical fields.

A Webpage Ranking Algorithm Based on Collaborative Recommendation

In view of the present personalized ranking of search results user interest model construction difficult, relevant calculation imprecise problems, proposes a combination of user interest model and collaborative recommendation algorithm for personalized ranking method. The method from the user search history, including the submit query, click the relevant webpage information to train users interest model, then using collaborative recommendation algorithm to obtain with common interests and neighbor users, on the basis of these neighbors on the webpage and webpage recommendation level associated with the users to sort the search results. Experimental results show that: the algorithm the average minimum precision than general sorting algorithm was increased by about 0.1, with an increase in the number of neighbors of the user, minimum accuracy increased. Compared with other ranking algorithms, using collaborative recommendation algorithm is helpful for improving webpage with the user interest relevance precision, thereby improving the sorting efficiency, help to improve the search experience of the user.

On Possibility Interval-Valued Fuzzy Soft Sets

Soft set theory, initiated by Molodtsov, can be used as a new mathematical tool for dealing with imprecise, vague, and uncertain problems. In this paper, the concepts of two types of possibil­ity interval-valued fuzzy soft sets are proposed. Their operations and basic properties are studied which are subset, equal, relative complement, union, intersection, restricted union, extended intersection, “AND”, “OR” and De Morgan Laws. Furthermore, an application of the new approach in decision making based on possibility interval-valued fuzzy soft set is illustrated.

An infrared image impulse noise suppression algorithm based on fuzzy logic

In this paper we propose a novel impulse noise suppression algorithm for infrared images based on fuzzy logic. The traditional impulse noise filter algorithms, such as median filter and its modified versions, will cause the loss of dim targets and detail information along with the impulse noise. The proposed algorithm includes two steps, noise detection and removal. First, we introduce fuzzy algorithm to deal with the fuzzy and imprecise problem to obtain the membership function, which describes the extent of the noise pollution and is used to detect noisy pixels; Second, consider that the gray-levels of non-noisy pixels change continuously, we use a weighted-interpolation algorithm in order to improve the preservation of the detail information and dim targets. Experiment results demonstrate that the proposed algorithm, with highly practical value, not only performs excellently on impulse noise filtering while preserves the detail information and dim targets, but also requires no prior knowledge.

A fuzzy simulation via contractive mapping genetic algorithm approach to an imprecise production inventory model under volume flexibility

In this paper, an economic production quantity model for multi-item with storage space and budget constraints in a volume flexible manufacturing system is developed. Here it is assumed that the demand rate is constant up to a certain level of stock and after that it depends on stock itself. The unit production cost is taken to be a function of the finite production rate involving labour cost and wear and tear expenditure. Here, the inventory costs, selling price, storage space and available budget are defined imprecisely. Using necessary measure theory, the imprecise problem is reduced to deterministic problem. Here, necessity measure approach has been used for triangle fuzzy number and parabolic fuzzy number. Finally the crisp nonlinear optimization problem is solved by Fuzzy simulation, Contractive Mapping Genetic Algorithm and Generalized Reduced Gradient technique. The model is illustrated numerically and the results are compared.

Posynomial Parametric Geometric Programming with Interval Valued Coefficient

The article presents solution procedure of geometric programming with imprecise coefficients. We have considered problems with imprecise data as a form of an interval in nature. Many authors have solved the imprecise problem by geometric programming technique in a different way. In this paper, we introduce parametric functional form of an interval number and then solve the problem by geometric programming technique. The advantage of the present approach is that we get optimal solution of the objective function directly without solving equivalent transformed problems. Numerical examples are presented to support of the proposed approach.