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941.
Michael P. Windham 《Fuzzy Sets and Systems》1981,5(2):177-185
The proportion exponent is introduced as a measure of the validity of the clustering obtained for a data set using a fuzzy clustering algorithm. It is assumed that the output of an algorithm includes a fuzzy nembership function for each data point. We show how to compute the proportion of possible memberships whose maximum entry exceeds the maximum entry of a given membership function, and use these proportions to define the proportion exponent. Its use as a validity functional is illustrated with four numerical examples and its effectiveness compared to other validity functionals, namely, classification entropy and partition coefficient. 相似文献
942.
In this paper we study the question whether, given a fuzzy measure (as defined in [3] and [4]). there exists a classical measure such that the fuzzy measure of a measurable fuzzy set μ equals the classical measure of the area below the membership function of μ. The results are that in the case of finite additivity there is a one-to-one correspondence between classical measures and fuzzy measures, whereas in the case of countable additivity this result only holds for generated fuzzy σ-algebras. Finally, some connections of that problem with the existence of an extension of a fuzzy measure defined on an arbitrary fuzzy σ-algebra σ to the generated fuzzy σ-algebra are discussed. 相似文献
943.
In this paper we study a geometrical representation of a special class of fuzzy preference relations by establishing a one-one correspondence between the set of all these relations and a hypercube of an n(n?1)/2 dimensional space.Furthermore, we study some geometrical figures (called H-spheres) and properties of the points which represent the preference relations in the above mentioned euclidean space. 相似文献
944.
Hideyuki Nojiri 《Fuzzy Sets and Systems》1980,3(2):137-150
This paper formulates a fuzzy team decision problem in a changing environment. The concept of a fuzzy set is introduced to formulate the team decision processes in a dynamic environment which contains fuzzy states, fuzzy information functions, fuzzy information signals, fuzzy decision functions and fuzzy actions. 相似文献
945.
Richard Willmott 《Fuzzy Sets and Systems》1980,4(1):31-36
The theory of fuzzy power sets requires the use of an implication operator acting within the set of values taken by the membership functions of the fuzzy sets. Two such operators and resulting relationships between fuzzy sets are studied here, and the results compared with previous ones obtained with other implication operators. 相似文献
946.
947.
The problem of integrating mappings over fuzzy domains has already received some attention in the literature. However, there is not a unique approach, but several definitions have been proposed, each carrying its own meaning. This paper tries to emphasize the relationships and the differences between the various points of view. 相似文献
948.
In this paper, contributions to fuzzy probability and to differential equations with fuzzy parameters are made.After an introductory section, a review of fuzzy sets and fuzzy algebra is given in Section 2. The main new results of the investigation are contained in Section 3.In Section 3, Zadeh's definition of the probability of a ‘fuzzy event’ the average value of a fuzzy function are extended into the time domain. It is then shown that not only grades of membership, but also probabilistic processes with notions of fuzziness contained, can be defined which obey ordinary, matric, or integro-differential equations. Applications are also given in Section 3. 相似文献
949.
In [4] Höhle has defined fuzzy measures on G-fuzzy sets [2] where G stands for a regular Boolean algebra. Consequently, since the unit interval is not complemented, fuzzy sets in the sense of Zadeh [8] do not fit in this framework in a straightforward manner. It is the purpose of this paper to continue the work started in [5] which deals with [0,1]-fuzzy sets and to give a natural definition of a fuzzy probability measure on a fuzzy measurable space [5]. We give necessary and sufficient conditions for such a measure to be a classical integral as in [9] in the case the space is generated. A counterexample in the general case is also presented. Finally it is shown that a fuzzy probability measure is always an integral (if the space is generated) if we replace the operations ∧ and ∨ by the t-norm To and its dual S0 (see [6]). 相似文献
950.