A New Metatheorem and Subdirect Product Theorem for L-SubgroupsAjmal, Naseem; Jahan, Iffat
2018 Fuzzy Information and Engineering
doi: 10.1080/16168658.2018.1517971
This paper is a continuation of the work of Tom Head ‘Metatheorem for deriving fuzzy theorems from crisp versions’. The concept of natural extension is introduced which is then applied in the development of a new metatheorem in L-setting, where L is a complete chain. The application of this theorem is demonstrated through the notions of generated L-subgroups and commutator L-subgroups. Moreover, a new subdirect product theorem is developed wherein it is demonstrated that for a group G, the L-subgroup lattice can be represented as a subdirect product of copies of its associated lattice of crisp subgroups. The significance of this theorem is exhibited by applying it to a characterization of generalized cyclic groups in terms of the distributivity of the lattice of L-subgroups of a group.
Rough Genetic Algorithm for Constrained Solid TSP with Interval Valued Costs and TimesMaity, Samir; Roy, Arindam; Maiti, Manoranjan
2018 Fuzzy Information and Engineering
doi: 10.1080/16168658.2018.1517972
This paper presents new rough set based genetic algorithms (RSGAs) to solve constrained solid travelling salesman problems (CSTSPs) with restricted conveyances (CSTSPwR) having uncertain costs and times as interval values. To grow the impreciseness in soft computing (SC), the proposed RSGAs, a rough set based age-dependent selection technique and an age-oriented min-point crossover are used along with three types of probability, p-dependent random mutations. A number of benchmark problems from standard data set, TSPLIB are tested against the proposed algorithms and existing simple GA (SGA). CSTSPwRs are formulated as constrained linear programming problems and solved by both proposed RSGAs and SGA. These are illustrated numerically by some empirical data and the results from the above methods are compared. Statistical significance of the proposed algorithms are demonstrated through statistical analysis using standard deviation. Moreover, the non-parametric test, Friedman test, is performed with the proposed algorithms. In addition, a post hoc paired comparison is applied and the out performance of the RSGAs.
A Rough Approximation of Fuzzy Soft Set-Based Decision-Making Approach in Supplier Selection ProblemChatterjee, A.; Mukherjee, S.; Kar, S.
2018 Fuzzy Information and Engineering
doi: 10.1080/16168658.2018.1517973
Nowadays, supplier selection process, a multicriteria decision-making problem, has become one of the most indispensable parts for every purchasing sector for the improvement of performances of business operations. Most of the literatures in this field have considered only the opinion of decision-makers. But in fact, each company has its own opinion about the suppliers. The purpose of this paper is to select the best supplier by integrating the opinions of both decision- makers and company's stake holders. In this literature, these opinions are taken as fuzzy soft sets. These two fuzzy soft sets are then integrated by the rough approximation theory. The attributes in this literature are taken in the form of linguistic variable. At the end of this paper, a case study is given to illustrate the proposed method for selecting the best supplier.
Stability Analysis of General Takagi-Sugeno Fuzzy Two-Term ControllersRaj, Ritu; Mohan, B. M.
2018 Fuzzy Information and Engineering
doi: 10.1080/16168658.2018.1517974
This paper deals with general fuzzy two-term controllers of Takagi-Sugeno (TS) type. Analytical structures and properties of general fuzzy PI/PD controllers are investigated with a modified rule base. The rule base contains three rules which effectively reduce the number of tuning parameters of the controllers. The fuzzy two-term controller uses at least three triangular or trapezoidal fuzzy sets on each input variable, algebraic product/minimum t-norm, bounded sum/maximum t-co-norm, and Centre of Gravity (CoG) defuzzification strategy. Four new models of TS type fuzzy controllers are proposed. The general fuzzy PI/PD controller with modified TS rule base is analogous to a variable gain (nonlinear) PI/PD controller. The gain either varies or remains constant in different regions of the input plane. The gain variations of the controller and the stability analysis of closed-loop control system with any one of the proposed models in the loop have been investigated. The applicability of the proposed controllers is shown with the help of examples.
Type-2 Hesitant Fuzzy SetsFeng, Liu; Chuan-qiang, Fan; Wei-he, Xie
2018 Fuzzy Information and Engineering
doi: 10.1080/16168658.2018.1517977
By using type-2 fuzzy sets and hesitant fuzzy sets, type-2 hesitant fuzzy sets are defined and their mathematical structure and characteristics are given. The relations of the structures of type-2 hesitant fuzzy sets and hesitant fuzzy sets are further studied. Consequently, we prove that type-2 hesitant fuzzy sets are the generalization of hesitant fuzzy sets. Type-2 hesitant fuzzy sets may deal with the problem that hesitant fuzzy sets can't have repeated memberships. Otherwise, a part of the special type-2 hesitant fuzzy sets can be changed into discrete type-2 fuzzy sets, but their operations have many differences. On dealing with the fact problems, type-2 hesitant fuzzy sets are the better methods to solve the problems and can be easy to get better results.
Type-II Fuzzy Multi-Product, Multi-Level, Multi-Period Location–Allocation, Production–Distribution Problem in Supply Chains: Modelling and Optimisation ApproachJ.-Sharahi, Sarah; Khalili-Damghani, Kaveh; Abtahi, Amir-Reza; Rashidi-Komijan, Alireza
2018 Fuzzy Information and Engineering
doi: 10.1080/16168658.2018.1517978
In this study, the application of type-II fuzzy sets is addressed to design a multi-product, multi-level, multi-period supply chain networks. The proposed model provides integrated approach to make optimal decisions such as location–allocation, production, procurement and distribution subject to operational and tactical constraints. In the context of fuzzy linear programming, this study involves type-II fuzzy numbers for the right-hand side of constraints regarding three sources of uncertainty: demand, manufacturing and supply. According to fuzzy components considered, a type-II fuzzy mixed-integer linear programming is converted into an equivalent auxiliary crisp model using linear fuzzy type-reducer models. The final models are linear and the global optimum solutions can be achieved using commercial OR softwares. The contributions of this study are three folds: (1) introducing a new integrated supply chain network design problem; (2) considering a solution procedure based on type-II fuzzy sets and (3) presenting a linear fuzzy type-II reducer. Finally, the proposed model and solution approach are illustrated through a numerical example to demonstrate the significance.
Improved Image Fusion of Colored and Grayscale Medical Images Based on Intuitionistic Fuzzy SetsKumar, Marut; Kaur, Amandeep; Amita,
2018 Fuzzy Information and Engineering
doi: 10.1080/16168658.2018.1517980
Image fusion is the process of combining the properties of two images into one single image that will show the features of both the images. There are various methods available in the literature to fuse the images. In this paper, an intuitionistic fuzzy logic-based image fusion approach has been implemented for medical images that firstly suppresses the noise and enhances the input images, and merges them efficiently in Hue-Saturation-Intensity domain. Here, enhancement is included because these input images are not always well contrasted and may contain some noise due to the inherent properties of the modalities used for capturing the images. The intuitionistic fuzzy sets are incorporated to handle uncertainties that are often due to vagueness and ambiguity. The results certify that this method significantly improves the output fused image than the image obtained by existing technique both visually and metrically.