Properties of Composition of Fuzzy Relations and its Verifications
C. Gowrishankar1, R. Dharshinee2, K. Geetha3
1C. Gowrishankar, Department of Mathematics, Government Arts and Science College, Gudalur-643 212, Tamil Nadu, India.
2R. Dharshinee, Department of Mathematics, Government Arts and Science College, Gudalur-643 212, Tamil Nadu, India.
3K. Geetha, Department of Mathematics, Government Arts and Science College, Gudalur-643 212, Tamil Nadu, India.
Manuscript received on January 02, 2020. | Revised Manuscript received on January 03, 2020. | Manuscript published on January 15, 2020. | PP: 01-07 | Volume-4 Issue-5, January 2020 | Retrieval Number: E0514014520/2020©BEIESP | DOI: 10.35940/ijmh.E0514.014520
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© The Authors. Published By: Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: This paper, deals with fundamental notions in pure and applied sciences, i.e., basic operations related to fuzzy relations. The composition of fuzzy relations are defined in two ways such as max-min composition and max-product composition with suitable example. This paper also introduces the properties of composition of fuzzy relations. The newly introduced properties inculcates zero, identity, equal, not-equal, subset, associative, union, intersection and distributive fuzzy relations. Finally, the paper verifies the properties of composition of fuzzy relations using some numerical values for 2×2 order of matrix. Also gives some exercise problems related to the above concepts with accurate answer keys.
Keywords: Fuzzy sets, Fuzzy relations, Cartesian product, Union, Intersection, Composition of fuzzy relations