Compositions of Picture Fuzzy Relations with Application in Decision Making


  •   Mohammad Kamrul Hasan

  •   Abeda Sultana

  •   Nirmal Kanti Mitra


Picture fuzzy relation is an important and powerful concept which is suitable for describing correspondences between objects. It represents the strength of association of the elements of picture fuzzy sets. In this paper we have defined min-max composition for picture fuzzy relations and some properties are explored based on this definition. Also we have discussed some properties of max-min composition for picture fuzzy relations. Finally, an application is discussed as illustration to show how the picture fuzzy relation are applied in decision making.

Keywords: Composition of picture fuzzy relations, linguistic terms, picture fuzzy relation, picture fuzzy set


Zadeh LA. Fuzzy sets. Information and Control. 1965; 8: 338-353.

Atanassov KT. Intuitionistic fuzzy set. Fuzzy Sets and Systems. 1986; 20: 87-97.

Cuong BC. Picture fuzzy sets. J. Comput. Sci. Cybern. 2014; 30: 409-420.

Zadeh LA. Similarity relations and fuzzy orderings. Information Sciences. 1971; 3:177-200.

Kaufmann A. Introduction to the Theory of Fuzzy Subsets-vol-1: Fundamental Theoretical Elements. New York: Academic Press; 1980.

Klir G, Yaun B. Fuzzy Set and Fuzzy logic: Theory and Application. Upper Saddle River NJ: Prentice Hall; 1977.

Zimmerman HJ. Fuzzy Set Theory and Its Application. Netherlands: Kluwer Academic Publishers; 1996.

Blin JM. Fuzzy Relations in Group Decision Theory. J. Cybern. 1974; 4: 17-22.

Cock MD, Kerre EE. On (un) suitable fuzzy relations to model approximate equality. Fuzzy Sets. Syst. 2003; 133: 137-153.

Yang MS, Shih HM. Cluster analysis based on fuzzy relations. Fuzzy Sets. Syst. 2001; 120: 197-212.

Tamura S, Higuchi S, Tanaka K. Pattern Classification Based on Fuzzy Relations. IEEE Trans. Syst. Man Cybern.1971;1: 61-66.

Qi F, Yang SW, Feng X. Research on the Comprehensive Evaluation of Sports Management System with Interval-Valued Intuitionistic Fuzzy Information. Bull. Sci. Technol. 2013; 2.

Yang HL, Li SG. Restudy of intuitionistic fuzzy relations. Syst. Eng. Theory Pract. 2009; 29: 114-120.

Jin JL, Wei YM, Ding J. Fuzzy comprehensive evaluation model based on improved analytic hierarchy process. J. Hydraul. Eng. 2004; 3: 65-70.

Bustinee H. Construction of intuitionistic fuzzy relations with predetermined properties. Fuzzy Sets. Syst. 2000; 109: 379-403.

Burillo P, Bustince H. Intuitionistic fuzzy relations (Part I). Mathw. Soft Comput. 1995; 2: 5-38.

Lei YJ, Wang BS, Miao QG. On the intuitionistic fuzzy relations with compositional operations. Syst. Eng.Theory Pract. 2005; 25: 30-34.

Cuong BC. Picture Fuzzy Sets-First Results, Part 1, Seminar “Neuro-Fuzzy Systems with Applications”. Preprint 03/2013. Institute of Mathematics: Hanoi, Vietnam. 2013.

Cuong BC, Hai PV. Some fuzzy logic operators for picture fuzzy sets. Seventh International Conference on Knowledge and Systems Engineering. 2015: 132-137.

Cuong BC, Ngan RT, Hai BD. An involutive picture fuzzy negator on picture fuzzy sets and some De Morgan triples. Seventh International Conference on Knowledge and Systems Engineering. 2015: 126-131.

Cuong BC, Kreinovich V, Ngan RT. A classification of representable t-norm operators for picture fuzzy sets. Departmental Technical Reports (CS), Paper 1047. 2016.

Dutta P, Saikia K. Some aspects of Equivalence Picture Fuzzy Relation. AMSE JOURNAL- AMSE IIETA.2018; 54: 424-434.


How to Cite
Hasan, M. K., Sultana, A. ., & Mitra, N. K. . (2023). Compositions of Picture Fuzzy Relations with Application in Decision Making. European Journal of Mathematics and Statistics, 4(2), 19–28.