TAILIEUCHUNG - Note on fuzzy sets

We present some improvements for the landmark paper of fuzzy sets for distributive law, convex combination and convex fuzzy sets. Our enhancement will help researcher absorb the original paper of fuzzy sets. | Yugoslav Journal of Operations Research 24 (2014) Number 2, 299 - 303 DOI: NOTE ON FUZZY SETS Robert LIN Department of Information Management Science, Oriental Institute Technology, Taiwan, R. O. C. hjlin@ Received: February 2013 / Accepted: Аpril 2013 Abstract: We present some improvements for the landmark paper of fuzzy sets for distributive law, convex combination and convex fuzzy sets. Our enhancement will help researcher absorb the original paper of fuzzy sets. Keywords: Fuzzy sets, convex combination. MSC: 94D05. 1. INTRODUCTION Zadeh [11] is the pioneer paper for fuzzy sets that opens a new academic subject on vague objects and uncertain linguistic description. We may demonstrate the tremendous influence of this paper by the following two statistic data. There are 22 scientific journals with “fuzzy” in their title and according to Google Scholar there are more than 26,000 papers that have cited Zadeh [11] in their references. Nevertheless, in this note, we provide three comments for Zadeh [11] to help researchers realize full importance of Zadeh [11]. Fuzzy set theory has been studied a lot and applied to many diverse areas. For examples, Brown [1] considered a note on fuzzy sets to obtain some analytical findings on convex fuzzy sets, star-shaped fuzzy sets, and arcwise connected fuzzy sets. Mizumoto and Tanaka [7] found some properties of fuzzy sets for intuitive fuzzy sets. They applied the extension principle to show that convex fuzzy grades form a commutative semi-ring and normal convex fuzzy grades form a distributive lattice under join and meet. Cheng [2] developed a new approach for ranking fuzzy numbers to calculate the distance to the centroid point with the special characteristics: higher mean and lower spread to incorporate with human intuition. Kumar et al. [3] investigated some 300 R. Lin / Note On Fuzzy Sets operations on intuitive fuzzy sets and then verified some propositions and provided .

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