Fuzzy Rough Number Research Articles

A mathematical model for solving fuzzy integer linear programming problems with fully rough intervals

A suggested algorithm to solve triangular fuzzy rough integer linear programming (TFRILP) problems with α-level is introduced in this paper in order to find rough value optimal solutions and decision rough integer variables, where all parameters and decision variables in the constraints and the objective function are triangular fuzzy rough numbers. In real-life situations, the parameters of a linear programming problem model may not be defined precisely, because of the current market globalization and some other uncontrollable factors. In order to solve this problem, a proper methodology is adopted to solve the TFRILP problems by the slice-sum method with the branch-and-bound technique, through which two fuzzy integers linear programming (FILP) problems with triangular fuzzy interval coefficients and variables were constructed. One of these problems is an FILP problem, where all of its coefficients are the upper approximation interval and represent rather satisfactory solutions; the other is an FILP problem, where all of its coefficients are the lower approximation interval and represent completely satisfactory solutions. Moreover, α-level at α = 0.5 is adopted to find some other rough value optimal solutions and decision rough integer variables. Integer programming is used, since a lot of the linear programming problems require that the decision variables be integers. In addition, the motivation behind this study is to enable the decision makers to make the right decision considering the proposed solutions, while dealing with the uncertain and imprecise data. A flowchart is also provided to illustrate the problem-solving steps. Finally, two numerical examples are given to clarify the obtained results.

Evaluation and selection of third party logistics provider under sustainability perspectives: an interval valued fuzzy-rough approach

In today’s world, industries are facing massive pressure to integrate sustainability issues for efficient and successful supply chain management (SCM). Hence, worldwide it has become critically important to make economic operational balance satisfying environment protection norms and social welfare perspectives. Consequently, the industries are investigating their SCM structures in association with a third party logistics (3PL) service provider adopting the triple bottom line framework for improving the overall supply chain performance. Therefore, selection of the right 3PL provider for the sustainable alliance is supremely important for broader perspective of greater business value. Thus, the main objective of this research work is the selection of most appropriate 3PL provider for a food manufacturing company (FMC) after systematic evaluation of six different feasible logistic providers serving over a decade in India. Selection of optimal alternative 3PL provider is very complex and challenging because of the qualitative description of service provider performances and the inherent uncertainty due to subjectivity. The concept of interval-valued fuzzy-rough number (IVFRN) offers perfect treatment of such uncertainty. In this paper, we develop a multi criteria decision making (MCDM) model combining the factor relationship (FARE) and multi-attributive border approximation area comparison (MABAC) models based on IVFRN. The proposed model is tested and validated on a case study where the optimal selection of 3PL providers is performed for an Indian FMC. Based on the results obtained in sensitivity analysis, it was shown that the proposed IVFRN based FARE-MABAC model produces stable/consistent solutions. Through the research presented in this paper, it is shown that the new hybrid MCDM method is a useful and reliable tool for rational decision-making.

Fuzzy Multi-objective Programming Approach for Constrained Matrix Games with Payoffs of Fuzzy Rough Numbers

Imprecise constrained matrix games (such as fuzzy constrained matrix games, interval-valued constrained matrix games, and rough constrained matrix games) have attracted considerable research interest. This article is concerned with developing an effective fuzzy multi-objective programming algorithm to solve constraint matrix games with payoffs of fuzzy rough numbers (FRNs). For simplicity, we refer to this problem as fuzzy rough constrained matrix games. To the best of our knowledge, there are no previous studies that solve the fuzzy rough constrained matrix games. In the proposed algorithm, it is proven that a constrained matrix game with fuzzy rough payoffs has a fuzzy rough-type game value. Moreover, this article constructs four multi-objective linear programming problems. These problems are used to obtain the lower and upper bounds of the fuzzy rough game value and the corresponding optimal strategies of each player in any fuzzy rough constrained matrix games. Finally, a real example of the market share game problem demonstrates the effectiveness and reasonableness of the proposed algorithm. Additionally, the results of the numerical example are compared with the GAMS software results. The significant contribution of this article is that it deals with constraint matrix games using two types of uncertainties, and, thus, the process of decision-making is more flexible.

An extended MABAC method for multi-criteria group decision making based on intuitionistic fuzzy rough numbers

Considering multi-criteria group decision-making (MCGDM) problems under uncertain environment, this paper presents a novel concept of intuitionistic fuzzy rough numbers (IFRNs), which is fused by intuitionistic fuzzy numbers (IFNs) and rough numbers (RNs), and proposes a new approach for MCGDM based on IFRNs. The proposed approach can aggregate group information and obtain the final decision results in an objective and effective way. First, we propose the constructing process of IFRNs and discuss the arithmetic operations, ranking rules, aggregation operators, as well as some corresponding properties. Then the novel concept of IFRN is used to aggregate intuitionistic fuzzy information given by decision group. Based on the aggregated IFRNs, the MABAC model is extended from two perspectives, obtaining an IFN-based MABAC model and an IFRN-based MABAC model respectively. Finally an empirical example of supplier selection for medical devices is utilized to show the application of proposed models, and comparisons with five traditional models, of which three refer to information aggregating and two refer to alternatives selecting, are made to validate the effectiveness and superiority of proposed methods.

Application of interval valued fuzzy-rough numbers in multi-criteria decision making: The IVFRN-MAIRCA model

This paper presents a new approach for the treatment of uncertainty and imprecision based on interval-valued fuzzy-rough numbers (IVFRNs). IVFRNs make a decision making possible using only the internal knowledge from the data, using objective indeterminacy without the need to rely on models of any assumption. Namely, instead of subjectively entering external uncertainties, the structure of the given data is used. Taking into account the given assumptions, we developed an original multi-criteria model based upon the IVFR approach. In the multi-criteria model the traditional MAIRCA (Multi-Attribute Ideal-Real Comparative Analysis) method was modified. The model was tested and validated on a case study, considering selection of the optimal landing operations point for overcoming water obstacles. The sensitivity analysis of the IVFRN MAIRCA model was carried out through 24 scenarios which showed that our results are of a high stability degree.

Hybrid Model of IVFRN-BWM and Robust Goal Programming in Agile and Flexible Supply Chain, a Case Study: Automobile Industry

The main purpose of this paper is the allocation of orders to suppliers in an agile and flexible manner suitable to the automobile industry. In this paper, parts supplied by a single source were eliminated from the set of parts. Using mathematical modeling and through the interval-valued fuzzy-rough numbers best worst method (IVFRN-BWM), we try to achieve the results that can meet the proposed model’s needs and provide the ideal results by introducing new modes. This paper addressed some new aspects of the subject and achieved robust results by considering five objective functions. These five functions are as follows: minimization of production line disruptions due to the performance of suppliers, minimization of the complaints of production line about supplied parts, minimization of defective parts received from suppliers (PPM), maximization of on-time delivery services, and minimization of overall costs of supplied parts. Reviewing the literature, the originality of this study are as follows: 1) identifying the structure of a supply chain (SC) in general and particularly in an automobile industry SC; 2) investigating the modeling techniques of the existing SC models for coordinating all the members of a product SC; 3) building a hybrid model of IVFRN-BWM and a robust goal programming agile and flexible supply chain in an uncertain situation; and 4) identifying the suitable scenarios/cases for testing the proposed models to validate the models. This paper can help decision makers and managers to opt for the best suppliers and also allocate the right numbers of parts to those supplier(s) based on a real situation of each firm.

Modification of the Best–Worst and MABAC methods: A novel approach based on interval-valued fuzzy-rough numbers

Abstract This paper presents a new approach for the treatment of uncertainty which is based on interval-valued fuzzy-rough numbers (IVFRN). It is shown that by integrating the rough approach with the traditional fuzzy approach, the subjectivity that exists when defining the borders of fuzzy sets is eliminated. IVFRN make decision making possible using only the internal knowledge in the operative data available to the decision makers. In this way objective uncertainties are used and there is no need to rely on models of assumptions. Instead of different external parameters in the application of IVFRN, the structure of the given data is used. On this basis an original multi-criteria model was developed based on an IVFRN approach. In this multi-criteria model the traditional steps of the BWM (Best–Worst method) and MABAC (Multi-Attributive Border Approximation area Comparison) methods are modified. The model was tested and validated on a study of the optimal selection of fire fighting helicopters. Testing demonstrated that the model based on IVFRN enabled more objective expert evaluation of the criteria in comparison with traditional fuzzy and rough approaches. A sensitivity analysis of the IVFRN BWM-MABAC model was carried out by means of 57 scenarios, the results of which showed a high degree of stability. The results of the IVFRN model were validated by comparing them with the results of the fuzzy and rough extension of the MABAC, COPRAS and VIKOR models.

A Kind of Fuzzy Set for Rough Fuzzy Sorting Method

Fuzzy set sorting method is studied in this prepare. Firstly, a sorting method of Fuzzy number is proposed under the condition of rough fuzzy number. Use rough fuzzy number to approach fuzzy set by rough set and fuzzy set; it is an approximate expression of fuzzy set. Secondly, prove partial order structures above method and give an example for fuzzy set sorting method, showing the whole process for the sorting method. Lastly, summarize the sorting method that is convenient, concise and easy to apply. It is enrich and supplement for fuzzy sorting method.

Multi-item production inventory model with fuzzy rough coefficients via geometric programming approach

Inventory Management and production planning are essential tasks for every company in the industry. Therefore, the development of a large set of Economic Order Quantity (EOQ) models is needed. In this paper, a Fuzzy Rough (Fu-Ro) multi-item Economic Production Quantity (EPQ) model is developed with constant demand, infinite production rate having flexibility and reliability consideration in production process and demand dependent unit production cost and shortages under the restrictions on storage area. Some of the inventory parameters are considered as trapezoidal fuzzy rough numbers and the model is formulated following cost minimization principle. Then by geometric programming (GP) technique we solve the problem. The model is illustrated through numerical example.

Rough Fuzzy Distance of the Rough Fuzzy Number

Rough sets theory and fuzzy sets theory research the unperfect problem in information systems. the combination of them formed Rough fuzzy sets and Rough Fuzzy number. in this paper, defines the Rough fuzzy distance of the Rough fuzzy number. Then it discusses the nature of Rough fuzzy distance. Key words: Rough fuzzy number; Distance; Rough fuzzy Distance