JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (3): 48-54.doi: 10.6040/j.issn.1671-9352.0.2022.461

Previous Articles     Next Articles

L-valued modules based on L-valued universal algebras

ZHOU Xin1,2, LIU Miao1,2   

  1. 1. College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China;
    2. Institute of Applied Mathematics, Yili Normal University, Yining 835000, Xinjiang, China
  • Published:2023-03-02

PDF (PC)

73

Abstract: L-valued modules are lattice-valued algebraic structures, defined on universal algebras of the same type as modules, but which are not necessary modules. First, the classical equality is replaced by a fuzzy identity, and the concept of L-valued modules are given based on L-valued universal algebras. Next, the necessary and sufficient conditions for L-valued universal algebras to be L-valued modules are given by using quotient structure of fuzzy algebras. Furthermore, this gives some basic properties of L-valued modules. Finally, we shows the structure of L-valued submodules.

Key words: fuzzy set, L-valued set, L-valued universal algebra, L-valued module, fuzzy identity

CLC Number: 

  • O159
[1] ZADEH L A. Fuzzy sets[J]. Information and Control, 1965, 8(3):338-353.
[2] GOGUEN J A. L-fuzzy sets[J]. Journal of Mathematical Analysis and Applications, 1967, 18(1):145-174.
[3] ROSENFELD A. Fuzzy groups[J]. Journal of Mathematical Analysis and Applications, 1971, 35(3):512-517.
[4] DIXIT V N, KUMAR R, AJMAL N. On fuzzy rings[J]. Fuzzy Sets and Systems, 1992, 49(2):205-213.
[5] NANDA S. Fuzzy fields and fuzzy linear spaces[J]. Fuzzy Sets and Systems, 1986, 19(1):89-94.
[6] MALIK D S, MORDESON J N. Fuzzy vector spaces[J]. Information Sciences, 1991, 55(1/2/3):271-281.
[7] PAN F Z. Fuzzy finitely generated modules[J]. Fuzzy Sets and Systems, 1987, 21(1):105-113.
[8] LÓPEZ-PERMOUTH S R, MALIK D S. On categories of fuzzy modules[J]. Information Sciences, 1990, 52(2):211-220.
[9] YEHIA S E B. Fuzzy ideals and fuzzy subalgebras of Lie algebras[J]. Fuzzy Sets and Systems, 1996, 80(2):237-244.
[10] KIM C G, LEE D S. Fuzzy lie ideals and fuzzy Lie subalgebras[J]. Fuzzy Sets and Systems, 1998, 94(1):101-107.
[11] FOURMAN M P, SCOTT D S. Sheaves and logic[M] //Applications of Sheaves. Berlin: Springer, 1979: 302-401.
[12] HÖHLE U. Quotients with respect to similarity relations[J]. Fuzzy Sets and Systems, 1988, 27(1):31-44.
[13] FILEP L. Study of fuzzy algebras and relations from a general viewpoint[J]. Computer Science, 1998, 14:49-55.
[14] DEMIRCI M. Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part I: fuzzy functions and their applications[J]. International Journal of General Systems, 2003, 32(2):123-155.
[15] DEMIRCI M. L-equivalence relations on L-fuzzy sets, L-partitions of L-fuzzy sets and their one-to-one connections[J]. International Journal of Approximate Reasoning, 2019, 111:21-34.
[16] DI NOLA A, GERLA G. Lattice valued algebras [J]. Stochastica, 1987, 11(2/3):137-150.
[17] KURAOKA T, SUZUKI N Y. Lattice of fuzzy subalgebras in universal algebra[J]. Algebra Universalis, 2002, 47(3):223-237.
[18] FOKA S V, TONGA M. A note on the algebraicity of L-fuzzy subalgebras in universal algebra[J]. Soft Computing, 2020, 24(2):895-899.
[19] SESELJA B, TEPAVCEVIC A. Ω-algebras[C] //2015 IEEE Symposium Series on Computational Intelligence. Cape Town, South Africa: IEEE, 2015: 971-975.
[20] BUDIMIROVIC B, BUDIMIROVIC V, SESELJA B, et al. E-fuzzy groups[J]. Fuzzy Sets and Systems, 2016, 289:94-112.
[21] SESELJA B, TEPAVCEVIC A. L-E-fuzzy lattices[J]. International Journal of Fuzzy Systems, 2015, 17(3):366-374.
[22] KRAPEZ A,SESELJA B, TEPAVCEVIC A. Solving linear equations by fuzzy quasigroups techniques[J]. Information Sciences, 2019, 491:179-189.
[23] SESELJA B, TEPAVCEVIC A. Ω-groups in the language of Ω-groupoids[J]. Fuzzy Sets and Systems, 2020, 397:152-167.
[24] EDEGHAGBA E E. On ω-subgroup[J]. Gadau Journal of Pure and Allied Sciences, 2022, 1(1):55-67.
[25] JIMENEZ J, SERRANO M L, SESELJA B, et al. Omega-rings[J]. Fuzzy Sets and Systems, 2023, 455:183-197.
[1] LI Shou-wei, SHI Kai-quan. Inverse separated fuzzy set ((-overA)F,(-overA)(-overF)) and secure acquisition of fuzzy information [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(9): 1-14.
[2] GONG Zeng-tai, TA Guang-peng. Semantics of the soft set induced by intuitionistic fuzzy set and its three-way decision [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(8): 68-76.
[3] ZHAO Shuang-yan, WU Jia-chao. Numerical properties of Gödel semantics in fuzzy argumentation frameworks [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(8): 53-59.
[4] SHI Kai-quan, LI Shou-wei. Separated fuzzy set (A(-overF),AF) and the intelligent fusion of fuzzy information [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(7): 1-13.
[5] XUE Zhan-ao, LI Yong-xiang, YAO Shou-qian, JING Meng-meng. Data classification method based on Bayesian intuitionistic fuzzy rough sets [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(5): 1-10.
[6] LI Xing-yu, DUAN Jing-yao. Intuitionistic similarity based on triangular norms and its application [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(4): 37-47.
[7] HUANG Lin, YUAN Xiu-jiu, SUO Zhong-ying, PANG Meng-yang, BAO Zhuang-zhuang, LI Zhi-wei. Interval-valued q-rung hesitant fuzzy frank aggregation operators and their application in multi-attribute decision making [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(3): 54-66.
[8] DU Wen-sheng, XU Tao. Generalized orthopair fuzzy hybrid aggregation operator and its application to multiple attribute decision making [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(1): 35-42.
[9] ZHENG Huan-ke, ZHANG Jing, YANG Ya-qi, XIONG Mei-hui. Method of uncertain temporal event flow sequence reasoning based on multiple attribute decision making [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(7): 67-80.
[10] SHAO Ya-bin, WANG Ning. Entropy and decision rules based on trapezoidal fuzzy number Pythagorean fuzzy sets [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(4): 108-117.
[11] HAO Xiu-mei, LIU Ji-qin. Cut sets of outer P-fuzzy sets and extended rough sets models [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 1-6.
[12] SUN Qian-qian, LI Xiao-nan. Information measures of interval valued Pythagorean fuzzy sets and their applications [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(9): 43-53.
[13] LUO Qing-jun. L-fuzzy ideals in Quantale [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 63-67.
[14] HU Qian, MI Ju-sheng, LI Lei-jun. The fuzzy belief structure and attribute reduction based on multi-granulation fuzzy rough operators [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(7): 30-36.
[15] PENG Jia-yin. Soft filters of pseudo-BL algebras related to fuzzy set theory [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(08): 40-45.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd