Membership function

About: Membership function is a research topic. Over the lifetime, 15795 publications have been published within this topic receiving 418366 citations.

Application of fuzzy goal programming technique to land use planning in agricultural system

Abstract: This paper presents how fuzzy goal programming can be efficiently used for modelling and solving land-use planning problems in agricultural systems for optimal production of several seasonal crops in a planning year. In the model formulation of the problem, utilization of total cultivable land, supply of productive resources, aspiration levels of various production of crops as well as the total expected profit from the farm are fuzzily described. In the decision-making situation, minimization of the under-deviational variables of the membership goals with highest membership value (unity) as their achievement levels defined for the membership functions of the fuzzy goals of the problem on the basis of the priorities of importance of achieving the aspired levels of the fuzzy goals to the extent possible is considered. As a study region, the District Nadia, West Bengal, India is taken into account. To expound the potential use of the approach, the model solution is compared with the existing cropping plan of the District as well as a solution of the problem obtained by using the additive fuzzy goal programming model studied by Tiwari et al. (Fuzzy sets and systems 24(1987)27.) previously.

A probabilistic fuzzy logic system for modeling and control

Abstract: In this paper, a probabilistic fuzzy logic system (PFLS) is proposed for the modeling and control problems. Similar to the ordinary fuzzy logic system (FLS), the PFLS consists of the fuzzification, inference engine and defuzzification operation to process the fuzzy information. Different to the FLS, it uses the probabilistic modeling method to improve the stochastic modeling capability. By using a three-dimensional membership function (MF), the PFLS is able to handle the effect of random noise and stochastic uncertainties existing in the process. A unique defuzzification method is proposed to simplify the complex operation. Finally, the proposed PFLS is applied to a function approximation problem and a robotic system. It shows a better performance than an ordinary FLS in stochastic circumstance.

Combination of Rough and Fuzzy Sets Based on α-Level Sets

Abstract: A fuzzy set can be represented by a family of crisp sets using its α-level sets, whereas a rough set can be represented by three crisp sets. Based on such representations, this paper examines some fundamental issues involved in the combination of rough-set and fuzzy-set models. The rough-fuzzy-set and fuzzy-rough-set models are analyzed, with emphasis on their structures in terms of crisp sets. A rough fuzzy set is a pair of fuzzy sets resulting from the approximation of a fuzzy set in a crisp approximation space, and a fuzzy rough set is a pair of fuzzy sets resulting from the approximation of a crisp set in a fuzzy approximation space. The approximation of a fuzzy set in a fuzzy approximation space leads to a more general framework. The results may be interpreted in three different ways.

Improved extensions of the TOPSIS for group decisionmaking under fuzzy environment

Abstract: Chen [2] extended the TOPSIS to a fuzzy environment. In his work, a vertex method was proposed to measure the distance between two given triangular fuzzy numbers. He further applied the vertex method to measure the distance between the weighted normalized fuzzy ratings and the fuzzy positive (negative}-ideal solutions to complete the fuzzy TOPSIS model. Despite the merits of his work, this application is not reasonable. Because the weighted normalized fuzzy ratings are truly not triangular fuzzy numbers. To overcome the above shortcomings, we suggest an improved fuzzy TOPSIS model, where membership functions for the weighted normalized fuzzy ratings are presented. A simple method is also proposed for ranking fuzzy numbers with mean of relative areas. This ranking method is further applied to establish the proposed model. Illustrative examples demonstrate the merits of the proposed ranking method and the feasibility of the improved fuzzy TOPSIS model, respectively.