Showing papers on "Membership function published in 1970"

Decision-making in a fuzzy environment

Abstract: By decision-making in a fuzzy environment is meant a decision process in which the goals and/or the constraints, but not necessarily the system under control, are fuzzy in nature. This means that the goals and/or the constraints constitute classes of alternatives whose boundaries are not sharply defined. An example of a fuzzy constraint is: “The cost of A should not be substantially higher than α,” where α is a specified constant. Similarly, an example of a fuzzy goal is: “x should be in the vicinity of x0,” where x0 is a constant. The italicized words are the sources of fuzziness in these examples. Fuzzy goals and fuzzy constraints can be defined precisely as fuzzy sets in the space of alternatives. A fuzzy decision, then, may be viewed as an intersection of the given goals and constraints. A maximizing decision is defined as a point in the space of alternatives at which the membership function of a fuzzy decision attains its maximum value. The use of these concepts is illustrated by examples involving multistage decision processes in which the system under control is either deterministic or stochastic. By using dynamic programming, the determination of a maximizing decision is reduced to the solution of a system of functional equations. A reverse-flow technique is described for the solution of a functional equation arising in connection with a decision process in which the termination time is defined implicitly by the condition that the process stops when the system under control enters a specified set of states in its state space.

An Algorithm for Detecting Unimodal Fuzzy Sets and Its Application as a Clustering Technique

Abstract: An algorithm is presented which partitions a given sample from a multimodal fuzzy set into unimodal fuzzy sets. It is proven that if certain assumptions are satisfied, then the algorithm will derive the optimal partition in the sense of maximum separation.

The Safe Ship Control With Minimum Risk Of Collision

Abstract: In this paper, safe ship trajectory in collision situation is presented as multistage decision-making in a fuzzy environment*. The model of process takes under consideration the Collision Avoidance Regulations, the manoeuvrability parameters of ship and the navigator's subjective assessment in making a decision. The time of taking the observation of an object and the time of collision avoidance manoeuvre are determined on the membership function of the fuzzy set of a collision risk. The algorithm has been worked out with regard to an on-line control status. A situations of a multiship encounter have also been simulated.

Adjustment of membership functions, generation and reduction of fuzzy rule base from numerical data

Abstract: In this paper we introduce a new approach for adjustment of membership functions, generation, and reduction of fuzzy rule base from data in the same time. The proposed approach consists of five steps: First, generate fuzzy rules from data using Mendel & Wang Method introduced in [1]. Second, calculate the degree of similarity between rules. Third, measure the distance between the numerical values which induces similar rules. Four, if the distance is greater than base value then merge membership functions. Finally, regenerate rules from data with new fuzzy sets. This approach is applied to truck backer-upper control and Liver trauma diagnostic. A comparative study with a simple Mendel Wang method shows the advantages of the developed approach.