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퍼지 디터미니스틱 관계

Fuzzy Deterministic Relations

  • 성열욱 (공주대학교 응용수학과) ;
  • 이현규 (공주대학교 응용수학과) ;
  • 양은목 (국민대학교 금융정보보안학과)
  • Sung, Yeoul Ouk (Department of Applied Mathematics, Kongju National University) ;
  • Lee, Hyun Kyu (Department of Applied Mathematics, Kongju National University) ;
  • Yang, Eunmok (Department of Financial Information Security, Kookmin University)
  • 투고 : 2021.07.08
  • 심사 : 2021.10.20
  • 발행 : 2021.10.28

초록

X와 Y사이의 퍼지 관계를 곱집합 X × Y의 퍼지 부분집합으로 Zadeh에 의해 처음으로 소개된 이후 퍼지집합에 대한 개념은 자연과학 및 컴퓨터과학에서 많은 연구성과가 이루어져 왔다. 그 결과 Muralli와 Nemitz는 동치관계 및 함수와 관련하여 퍼지관계를 연구하였고, Ounalli와 Jaoua는 중요한 수학적 도구로서 퍼지 다이펑션날 관계를 정의하여 소프트디자인과 데이터베이스 이론에서 중요한 역할을 하는 것으로 증명되었으며, 또한 프로그램 표식과 프로그램 정확도를 정의하는데 유용한 것으로 밝혀졌다. 본 논문에서는 한 집합 위에 퍼지 디터미니스틱 관계를 정의하여 퍼지 디터미니스틱 관계를 레벨 부분집합으로 특성화 하였고, 퍼지 디터미니스틱 관계와 관련하여 일부 성질을 증명하였다. 특히, 퍼지 디터미니스틱 관계와 퍼지 함수가 동치임을, 퍼지 함수가 퍼지 다이펑션날 관계가 동치임을 증명하였다.

A fuzzy relation between X and Y as fuzzy subset of X × Y was proposed by Zadeh. Subsequently, several researchers have applied the notion of fuzzy subsets to various branches of mathematics and computer sciences. Murali an Nemitz have studied fuzzy relations connected with fuzzy equivalence relations and fuzzy functions. Ounalli and Jaoua defined a fuzzy difunctional relation on a set. difunctional relations are versatile mathematical tool, which can be used in software design and in database theory. Their work have revealed the usefulness of difunctional relations in program specification and in defining program correctness. The main goal of this paper is to define a fuzzy deterministic relation on a set, characterize the fuzzy deterministic relation as its level subsets and investigate some properties in connection with fuzzy deterministic relation. In particular we prove that a fuzzy relation R is fuzzy deterministic iff R is a fuzzy function.

키워드

과제정보

This work was supported by the research grant of the Kongju National University in 2020

참고문헌

  1. L.A.Zadeh. (1971). Similarity Relations and Fuzzy orderings. Inf, Sci, 3,177-200 https://doi.org/10.1016/S0020-0255(71)80005-1
  2. V,Murali. (1980). Fuzzy Equivalence Relations. Fuzzy Sets and System, 30, 153-163. DOI : 10.1016/0165-0114(89)90077-8
  3. H.Ounalli and A.Jaoua. (1996). On Fuzzy Difunctional Relations, Information Sciences. 96, 219-232. DOI : 10.1016/S0020-0255(96)00142-9
  4. C.H.Seo, K.H.Han, Y.O.Sung and H.C.Eun (2000). On the relationships between Fuzzy equivalence relations and Fuzzy difunctional relations, and their properties. Fuzzy Sets and Systems. 109, 459-462. DOI : 10.1016/S0165-0114(98)00114-6
  5. Nemitz, W. C. (1986). Fuzzy relations and fuzzy functions. Fuzzy Sets and Systems, 19(2), 177-191. DOI : 10.1016/0165-0114(86)90036-9
  6. Chakraborty, M. K., & Das, M. (1983). On fuzzy equivalence I. Fuzzy sets and Systems, 11(1), 185-193. https://doi.org/10.1016/S0165-0114(83)80078-5
  7. Chakraborty, M. K., & Das, M. (1983). On fuzzy equivalence II. Fuzzy sets and Systems, 11(1), 299-307. https://doi.org/10.1016/S0165-0114(83)80088-8
  8. Ovchinnikov, S. V. (1981). Structure of fuzzy binary relations. Fuzzy Sets and Systems, 6(2), 169-195. DOI : 10.1016/0165-0114(81)90023-3
  9. Ovchinnikov, S. (1991). Similarity relations, fuzzy partitions, and fuzzy orderings. Fuzzy Sets and Systems, 40(1), 107-126. DOI : 10.1016/0165-0114(91)90048-U
  10. Ovchinnikov, S. (2002). Numerical representation of transitive fuzzy relations. Fuzzy Sets and Systems, 126(2), 225-232. DOI : 10.1016/S0165-0114(01)00027-6
  11. Sanchez, E. (1976). Resolution of composite fuzzy relation equations. Information and control, 30(1), 38-48. https://doi.org/10.1016/S0019-9958(76)90446-0
  12. Sung, Y. O., & Seo, D. W. (2015). Fuzzy idempotent relations. Far East Journal of Mathematical Sciences, 96(8), 967-980. DOI : 10.17654/FJMSOct2015_365_374
  13. Sung, Y. O. (2019). NOTES OF G-CONGRUENCES. Far East Journal of Mathematical Sciences, 114(2), 155-165 DOI : 10.17654/MS114020155
  14. Y.O.Sung and H.K.Lee (2020), Further Relations on Fuzzy Difuctional Relations. Far East J.Math, Sci, 124(1), 75-85.
  15. Valverde, L. (1985). On the structure of F-indistinguishability operators. Fuzzy Sets and Systems, 17(3), 313-328. DOI : 10.1016/0165-0114(85)90096-X
  16. L.A.Zadeh. (1965). Fuzzy Sets, Information and Control. 8, 338-353 https://doi.org/10.1016/S0019-9958(65)90241-X