Some Results on Godel Implication Operator over Bipolar Fuzzy Matrices
DOI:
https://doi.org/10.64060/ANMI1V1i1Keywords:
Bipolar fuzzy sets, Bipolar fuzzy matrices, Reflexive, Transitive, IdempotentAbstract
At present, bipolar fuzzy sets indeed have robust area of on many fields. Also bipolar fuzzy matrices are admired subject in various wisdoms for example, multi criteria decision making, psychology, qualitative reasoning, etc. Both negative and positive issues to deal with problems live in a society. In this paper, we introduce Godel implication operator on bipolar fuzzy set and also we extend the same to bipolar fuzzy matrices. Some basic algebraic properties like reflexive, transitive, idempotent are obtained and also we give some example. Further, we introduce a new composition using the existing operator min(⋀) along with Go ̈del implication on bipolar fuzzy matrices. Various results of this new composition are discussed.
References
[1] L.A.Zadeh, Fuzzy sets, Journal of Information and Control, Vol.8 (1965) 338-353.
[2] M.G.Thomason, Convergence of powers of a fuzzy matrix, J.Math. Anal. Appl., 57 (1977), 476-480.
[3] W-R Zhang Bipolar fuzzy sets and relations. First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference, (1994) 305-309.
[4] M.Pal and Sanjib Mondal, Bipolar fuzzy matrices, Soft Computing Oct. 2019, 9885-9897.
[5] M.M.Gupta and J.R.Kiszka, Go ̈del’s implication operators for fuzzy logic control, Proceedings of the 28th IEEE conference on decision and control 1989, 746-750.
[6] H.Hashimoto, Decomposition of Fuzzy Matrices, society for Industrial and Applied mathematics, J.ALG.Disc. Math., (1985) 32-38.
[7] P.Murugadas and K.Lalitha, Bi implication Operator on Intuitionstic fuzzy set, International Journal of Computer Applications (0975 8887) Mar. 2014, 1-5.
[8] E.G.Emam and M.A Fndh , Some results associated with the (max-min) and (min-max) compositions of bifuzzy matrices , JOEMS , 24(2016) , 515-521.
[9] Sanjib Mondal and M.Pal, Similarity relations, eigenvalues and eigenvectors of bipolar fuzzy matrix, Journal of Intelligent and fuzzy systems 30(4), 2016, 2297-2307.
[10] Li Pingke and Jin Qingwel On the resolution of bipolar max-min equations, kybernetika 52(4), 2016, 514-530.
[11] Xiao-Peng Yang, Resolution of bipolar fuzzy relation equations with max-Lukasiewicz composition, Fuzzy sets and systems 397, 2020, 41-60.
[12] Ghous Ali and Muhammad Akram , Jose carlos R Alcantud , Attributes reductions of bipolar fuzzy relation decision systems , Neural computing and applications 32(14),(2020) 10051- 10071.
[13] T.Muthuraji and R.Punitha, Commutative Monoids on Algebraic Sum and Algebraic Product over Bipolar Fuzzy Set and Bipolar Fuzzy Matrices, European Chemical Bulletin, 12(4), 2023, 18843-18852.
[14] T.Muthuraji, K.Lalitha and P.Punitha Elizabeth, Commutative Monoids on Bounded Sum and Bounded Product over Bipolar Fuzzy Matrices, European Chemical Bulletin, 12(8), 2023, 3949.
[15] Naime Demirtas and Orhan Dalkilic, Bipolar Fuzzy Soft Set Theory Applied to Medical Diagnosis, Turk. J. Math. Computing Science, 16(2), 2024, 314-324.
[16] H.Hashimoto, Subinverses of Fuzzy Matrices, Fuzzy sets and systems 12 (1984) 155-168, North Holland.
[17] E.G.Eman, An operation on intuitionstic fuzzy matrices, Filomat 34(1), (2020) 79-88.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Dr. ANITHA (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.
