Phân tích và ứng dụng các toán tử tập hợp Aczel–Alsina $$\text {r},\text {s},\text {t}$$ -spherical fuzzy trong quyết định đa tiêu chí

Granular Computing - Tập 9 - Trang 1-29 - 2024
Jawad Ali1
1Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, Pakistan

Tóm tắt

Nghiên cứu này tập trung vào việc phát triển và ứng dụng các toán tử tập hợp Aczel–Alsina (AA) trong bối cảnh tập hợp mờ hình cầu $$\textsf {r},\textsf {s},\textsf {t}$$ (SPFS) cho các vấn đề quyết định đa tiêu chí (MCDM). Chúng tôi bắt đầu bằng cách định nghĩa các luật hoạt động AA SPF $$\textsf {r},\textsf {s},\textsf {t}$$ khác nhau và thiết lập các thuộc tính chính của chúng. Tiếp theo, một loạt các toán tử AA được giới thiệu, bao gồm toán tử trung bình có trọng số $$\textsf {r},\textsf {s},\textsf {t}$$ -SPF, toán tử trung bình đánh giá có trọng số $$\textsf {r},\textsf {s},\textsf {t}$$ -SPF, toán tử trung bình hỗn hợp $$\textsf {r},\textsf {s},\textsf {t}$$ -SPF, toán tử hình học có trọng số $$\textsf {r},\textsf {s},\textsf {t}$$ -SPF, toán tử hình học có trọng số đánh giá $$\textsf {r},\textsf {s},\textsf {t}$$ -SPF, và toán tử hình học hỗn hợp $$\textsf {r},\textsf {s},\textsf {t}$$ -SPF. Mỗi toán tử được thảo luận liên quan đến các thuộc tính cụ thể của nó, chẳng hạn như tính đồng nhất, tính đơn điệu, giới hạn và tính giao hoán. Hơn nữa, chúng tôi sử dụng các toán tử này để phát triển một phương pháp MCDM được thiết kế riêng để giải quyết các vấn đề quyết định $$\textsf {r},\textsf {s},\textsf {t}$$ -SPF, đặc biệt là khi trọng số tiêu chí hoàn toàn không xác định. Để chứng minh tính thực tiễn và hiệu quả của phương pháp chúng tôi, một nghiên cứu điển hình được trình bày, tiếp theo là phân tích tham số và nghiên cứu so sánh.

Từ khóa

#Aczel–Alsina operators #spherical fuzzy sets #multi-criteria decision-making #aggregation operators #decision-making methodology.

Tài liệu tham khảo

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