Kajla Basu

Solution of a class of Intuitionistic Fuzzy Assignment Problem by using similarity measures

In this paper, we set mathematical models of the assignment problem with restriction on person cost depending on efficiency/qualification and restriction on job cost where both the costs are considered as intuitionistic fuzzy numbers. Restriction of qualification is in the form of the maximum intuitionistic fuzzy cost which can be offered to a person depending on his/her efficiency/qualification. Further restrictions on the intuitionistic fuzzy cost which can be spent for doing a particular job makes the problem of Intuitionistic Fuzzy Assignment Problem with Restrictions (IFAPR) more realistic than the problems found in the literature so far. Consideration of Intuitionistic Fuzzy Numbers (IFNs) for representing the costs makes the problem more general in the sense that it considers both the degree of acceptance and the degree of rejection. A heuristic method has been constructed for showing the existence of the solution so that both the constraints are satisfied. The methodology for solving the problem consists of two algorithms. The concept of relative degree of similarity measures to the Positive Ideal Intuitionistic Fuzzy Solution (PIIFS) has been applied under Atanassovs intuitionistic fuzzy environment. A well established intuitionistic fuzzy ranking method has been used here for comparing the IFNs using their score functions and the accuracy degrees. Mathematical model of the problem has been established. Numerical examples show the effectiveness of this method.

Improved similarity measure in neutrosophic environment and its application in finding minimum spanning tree

Minimum spanning tree finds its huge application in network designing, approximation algorithms for NP-hard problems, clustering problems and many more. Many research works have been done to find minimum spanning tree due to its various applications. But, till date very few research works are available in finding minimum spanning tree in neutrosophic environment. This paper contributes significantly by defining the weight of each network edge using single valued neutro- sophic set (SVNS) and introduce a new approach using similarity measure to find minimum spanning tree in neutrosophic environment. Use of SVNS makes the problem realistic as it can describe the uncertainty, indeterminacy and hesitancy of the real world in a better way. We introduce two new and simple similarity measures to overcome some disadvantages of existing Jaccard, Dice and Cosine similarity measures of SVNSs for ranking the alternatives. Further from the similarity measures we have developed two formulas for the entropy measure proving a fundamental relation between similarity measure and entropy measure. The new entropy measures define the uncertainty more explicitly in comparison to other entropy measure existing in the literature which has been established using an example.

Solution of a Multi-Objective and Multi-Index Real-Life Transportation Problem Using Different Fuzzy Membership Functions

The paper presents the application of an exponential membership function to fuzzy programming technique for solving a multi-objective and multi-index real-life transportation problem. It focusses on the minimization of the transportation cost, deterioration rate and underused capacity of the transported raw materials like coal, iron ore, etc. from different sources to different destination sites at Durgapur Steel Plant, Durgapur, West Bengal, India, by different transportation modes like train, trucks, etc. A special type of non-linear (exponential) membership function is assigned to each objective function. Thus, the paper presents fuzzy programming approach with an exponential function to a real-life transportation problem and develops a non-dominated compromise solution. In addition, the interval-valued numbers used in supply and demand parameters represent the uncertainties in a real-life problems. The optimization models have a wide use in real-life multi-objective transportation problems. The use of fuzzy programming technique has been successfully concluded for the focussed transportation problem taking a linear and a hyperbolic membership function. But the numerical illustration shows that exponential membership function gives a better and comparable result for the problem.

Applications of fuzzy classification in insurance industry: A fuzzy logic based approaches

In this paper an attempt has been made to implement the problem of investing money in insurance sector,so as achieve high return with the help of fuzzy classification. We provide a better understanding of fuzzy classification.

Multi-item 4D-TPs under budget constraint using rough interval

Abstract Multi-item four dimensional transportation problems (MI4D-TPs) are formulated with budget constraint under rough and fuzzy interval environments. Here unit selling prices, unit purchasing costs, unit transportation costs, fixed charges, sources, demands, capacities of conveyances and total budget are represented by rough intervals for rough model and fuzzy numbers for fuzzy model. In this paper, four dimensional transportation problems (4D-TPs) under rough interval environment are transformed to deterministic ones by three different methods – (i) upper and lower approximation intervals, (ii) Expected Value Technique and (iii) rough chance-constraint programming technique. The fuzzy 4D-TP is made deterministic using possibility measures. Reduced problems are solved by generalized reduced gradient (GRG) method using LINGO 12.0 software. The models are illustrated with numerical examples and natures of the solutions i.e. complete and rather satisfactory solutions are presented. As particular cases, the results of solid transportation problems (3D-TPs) and conventional transportation problems (2D-TPs) are obtained. Importance of consideration of routes in MI4D-TPs is pointed out. As a particular case, the results of an earlier investigation are derived. Sensitivity of profit in the rough model through Expected Value Technique is presented against the arithmetic combination parameter. Percentage of increase of profit against the expectation parameter is furnished.

Solution of a class of generalized assignment problem

The paper presents the solution of a multi objective multi-index generalized assignment problem using Fuzzy Programming Technique which is a new concept. It emphasizes on minimization of the job cost and time at different sites where the jobs are being performed using different machines (medium). Multi objective assignment problem or multi objective generalized assignment problem have been solved in different ways by different mathematicians. But they have considered only two indices (jobs and alternatives). Here we have considered more than two indices and so it becomes a multi-index generalized assignment problem which makes it superior to the previous methods. This type of problem has not been solved earlier by our proposed method. Moreover in this paper Fuzzy Programming Technique has been used considering linear, exponential and hyperbolic (non-linear) membership functions for getting optimal solutions. Finally a real life application has been presented.

A new fuzzy programming technique approach to solve fuzzy transportation problem

The paper presents an application of a new method - Modified Fuzzy Programming Technique(MFTP) for the Fuzzy optimal solution to the Single Objective FuzzyTransportation Problem(SOFTP) with Fuzzy parameters in terms of Triangular Fuzzy Numbers without defuzzifying the problem. Numerical illustrations are solved to show the better results and comparisons are also provided to show the same. The problem is formulated where parameters of cost objective functions, supply and demand are taken as Triangular Fuzzy Numbers. The proposed method is applied for the first time to solve the SOFTP. First, the SOFTP is converted into a Multi-Objective Transportation Problem and then solved by the MFTP.

Enhancement of Gross Enrollment Ratio of Higher Education of West Bengal through e-Learning: A Fuzzy Delphi Forecasting Approach

E-learning has now revolutionized the way of learning process across the world. Following the conventional systems of learning, the Gross Enrollment Ratio (GER) of West Bengal is not at all optimistic. To enhance the enrollments and diminish the drop outs in higher education in West Bengal, e-learning can be a better way out. In this paper an attempt has been made to forecast the increase in higher education enrollments and decrease in drop outs in higher education. Through Fuzzy Delphi Forecasting techniques views are collected from experts regarding the increase of higher education enrollments and decrease of drop outs through web enabled learning systems in comparison to the traditional learning systems.

Decision Making In Assignment Problem With Multiple Attributes Under Intuitionistic Fuzzy Environment

In this paper we develop a methodology to solve the multiple attribute assignment problems where the attributes are considered to be Intuitionistic Fuzzy Sets (IFS). We apply the concept of similarity measures of IFS to solve the Intuitionistic Fuzzy Multi‐Attribute Assignment Problem (IFMAAP). The weights of the attributes are determined from expert opinion. An illustrative example is solved to verify the developed approach and to demonstrate its practicality.

A Study towards Building An Optimal Graph Theory Based Model For The Design of Tourism Website

Effective tourism website is a key to attract tourists from different parts of the world. Here we identify the factors of improving the effectiveness of website by considering it as a graph, where web pages including homepage are the nodes and hyperlinks are the edges between the nodes. In this model, the design constraints for building a tourism website are taken into consideration. Our objectives are to build a framework of an effective tourism website providing adequate level of information, service and also to enable the users to reach to the desired page by spending minimal loading time. In this paper an information hierarchy specifying the upper limit of outgoing link of a page has also been proposed. Following the hierarchy, the web developer can prepare an effective tourism website. Here loading time depends on page size and network traffic. We have assumed network traffic as uniform and the loading time is directly proportional with page size. This approach is done by quantifying the link structu...