L-fuzzifying antimatroids: A fuzzy approach to the generalization of shelling precedence structures

Article type: Research Article

Authors: Lin, Fu-Ning^{a; b} | Yu, Guang-Ji^{a; b; *} | Xue, Guang-Ming^{a; b; *} | Han, Jiang-Feng^{a; b}

Affiliations: [a] College of Information and Statistics, Guangxi University of Finance and Economics, Nanning, China | [b] Guangxi Key Laboratory Cultivation Base of Cross-Border E-Commerce Intelligent Information Processing, Nanning, China

Correspondence: [*] Corresponding author. Guang-Ji Yu and Guang-Ming Xue, E-mails: xueguangming0417@126.com (G.-M. Xue) and guangjiyu100@126.com. (G.-J. Yu).

Abstract:  Crisp antimatroid is a combinatorial abstraction of convexity. It also can be incorporated into the greedy algorithm in order to seek the optimal solutions. Nevertheless, this kind of significant classical structure has inherent limitations in addressing fuzzy optimization problems and abstracting fuzzy convexities. This paper introduces the concept of L-fuzzifying antimatroid associated with an L-fuzzifying family of feasible sets. Several relevant fundamental properties are obtained. We also propose the concept of L-fuzzifying rank functions for L-fuzzifying antimatroids, and then investigate their axiomatic characterizations. Finally, we shed light upon the bijective correspondence between an L-fuzzifying antimatroid and its L-fuzzifying rank function.

Keywords: Antimatroid, L-fuzzifying antimatroid, L-fuzzifying family of feasible sets, L-fuzzifying rank function

DOI: 10.3233/JIFS-200274

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 3, pp. 4183-4196, 2020