From the beginning, the assessment of membership function in fuzzy mathematics is a demanding task. The extraction of the membership function is ambience dependent and thus complication exists in the process of evaluation. In this assessment, the main work deals with the derivation of fuzzy membership function where numerical data is available. The numerical interpolation and defuzzification technique are used here. Many types of fuzzy number have been used to find out the membership function. In this paper, we mainly used triangular fuzzy number to construct the membership function. A case study is furnished to emphasise the advantage of adopting the method.
As competition is growing high on this globalized world, the companies are imposing more and more importance on the process of supplier selection. After the foundation of fuzzy logic, the problem of supplier selection has been treated from the viewpoint of uncertainty. The present work reviews and classifies different approaches towards this problem. A new fuzzy preference degree between two triangular fuzzy numbers is introduced and a new approach is prescribed to solve the problem using this preference degree. The weights of the Decision Makers are considered and a methodology is proposed to determine the weights. Moreover, a unique process of classifying the suppliers in different groups is proposed. The methodologies are exemplified by a suitable case study.
In recent years, extensive research jobs have been developed on the definition, measurement and analyzing of poverty. Poverty is a multidimensional phenomenon, thus a number of challenges appears measuring it. The fuzzy set theoretic approach has been used to measure the poverty and to classify the difference between poor and non-poor households. This paper aims at proposing a new methodology to measure the poverty index in fuzzy environment via a two-step membership function. The concept of one poverty line is chalked out first and then a general method is developed to split the poverty index. Linguistic variables are used for the attributes to find the membership values of the households against the attributes and to grade the attributes. The effectiveness and usefulness of the proposed method is numerically illustrated through a case study for rural household people living in remote rural areas of India.
In this paper two problems on the evaluation process of the education system are talked about. The methodologies to solve the problems are based on soft computing techniques. Fuzzy sets have been used to model and solve the problem of identifying the 'educational importance factor' of each academic year and grey numbers have been used to obtain the students' answer script evaluation process. The algorithmic approaches are supported by suitable examples.
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.
In most researches on fuzzy sets and its application, it is found that the consideration of membership function is predetermined and mostly linear in nature. Extraction and evaluation of non-linear fuzzy membership function that can update itself with in different paradigms is still a matter of great concern to researchers. Here, we discuss 33 different membership function evaluation methodologies published between 1971 and 2016. In a approach to solve the problem, this paper presents a novel algorithm based non-linear fuzzy membership function evaluation scheme with the help of regression analysis and algebra. Three different case studies are done to check the applicability and tractability of the method. A comparative analysis with recent literature justifies the robustness of the proposed method.
In fuzzy mathematics, evaluation of membership function is still a problem, as the methods for this purpose do not hold well in all aspects. The purpose of this work is to assemble and to draw an overview of them. In addition, this work consists of a new approach, which may lead to a new way. The approach is from numerical point of view with the help of statistics. There are two methods, namely (i) modified Newton's divided difference method and (ii) modified Lagrange's interpolation method
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