Membership function

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

On correlation measures of intuitionistic fuzzy sets

Abstract: The intuitionistic fuzzy set, developed by Atanassov [I], is a useful tool to deal with vagueness and uncertainty. Correlation analysis of intuitionistic fuzzy sets is an important research topic in the intuitionistic fuzzy set theory and has great practical potential in a variety of areas, such as engineering, decision making, medical diagnosis, pattern recognition, etc. In this paper, we propose a new method for deriving the correlation coefficients of intuitionistic fuzzy sets, which has some advantages over the existing methods. Furthermore, we extend the developed method to the interval-valued intuitionistic fuzzy set theory, and show its application in medical diagnosis.

Relations between fuzzy time intervals

Abstract: Time intervals like "tonight", which are usually not very precise, can be modeled as fuzzy sets. But this causes the problem that the relations between points and intervals and between two intervals, which are usually very trivial, become very complex when the intervals are fuzzy sets. Moreover, there are many different possibilities to define such relations. In this paper a very flexible operator-based approach to point-interval and interval-interval relations is proposed, where the intervals are fuzzy time intervals over the real numbers. The relations yield non-trivial fuzzy values even if the intervals are crisp. As an example for an application, consider a database with, say, a cinema timetable, and you query the timetable give me all performances ending before midnight. The usual "before" relation will exclude the performances ending a second after midnight. With the fuzzy before relation you can get instead of a sharp drop to 0 at midnight decreasing fuzzy values after midnight, and these can be used to order the results of the query. The intervals and relations are implemented in the Fu-TIRe library (Fuzzy Time intervals and Relations). FuTIRe is an open source C++ library.

On the importance of interval sets in type-2 fuzzy logic systems

Abstract: Type-2 fuzzy logic systems (FLSs) allow uncertainties that occur in rule-based FLSs to be modeled using the new third dimension of type-2 fuzzy sets. Although a complete theory of type-2 FLSs exists for general type-2 fuzzy sets, it is only for interval type-2 fuzzy sets that type-2 FLSs are practical. This paper explains why this is so.

Application of Fuzzy Linear Programming in Production Planning

Abstract: In this paper, a new fuzzy linear programming based methodology using a specific membership function, named as modified logistic membership function is proposed. The modified logistic membership function is first formulated and its flexibility in taking up vagueness in parameters is established by an analytical approach. This membership function is tested for its useful performance through an illustrative example by employing fuzzy linear programming. The developed methodology of FLP has provided a confidence in applying to real life industrial production planning problem. This approach of solving industrial production planning problem can have feed back within the decision maker, the implementer and the analyst. In such case this approach can be called as IFLP (Interactive Fuzzy Linear Programming). There is a possibility to design the self organizing of fuzzy system for the mix products selection problem in order to find the satisfactory solution. The decision maker, the analyst and the implementer can incorporate their knowledge and experience to obtain the best outcome.

Twelve considerations in choosing between Gaussian and trapezoidal membership functions in interval type-2 fuzzy logic controllers

Abstract: Interval type-2 fuzzy logic controllers (IT2 FLCs) have been attracting great research interests recently. There are many decisions to be made in designing an IT2 FLC. One of them is to determine which membership function type to use, e.g., Gaussian or trapezoidal. There have not been comprehensive studies on this problem so far. In this paper we present 12 considerations in choosing between Gaussian and trapezoidal membership functions for an IT2 FLC, including representation, construction, optimization, adaptiveness, novelty, analytical structure, continuity, monotonicity, stability, robustness, computational cost, and control performance. It can help practitioners select the appropriate membership function type in IT2 FLC design, and researchers identify new research opportunities on IT2 FLCs. Our study shows that each MF type has its own advantages: Gaussian IT2 FLCs are simpler in design because they are easier to represent and optimize, always continuous, and faster for small rulebases, whereas trapezoidal IT2 FLCs are simpler in analysis.