Decision making algorithmic techniques based on aggregation operations and similarity measures of possibility intuitionistic fuzzy hypersoft sets

Atiqe Ur Rahman; Muhammad Saeed; Hamiden Abd El-Wahed Khalifa; Walaa Abdullah Afifi; Atiqe Ur Rahman; Muhammad Saeed; Hamiden Abd El-Wahed Khalifa; Walaa Abdullah Afifi

doi:10.3934/math.2022214

AIMS Mathematics

2022, Volume 7, Issue 3: 3866-3895. doi: 10.3934/math.2022214

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Research article

Decision making algorithmic techniques based on aggregation operations and similarity measures of possibility intuitionistic fuzzy hypersoft sets

1.
Department of Mathematics, University of Management and Technology, Lahore, Pakistan
2.
Department of Mathematics, College of Science and Arts, Al- Badaya, Qassim University, Saudi Arabia
3.
Operations Research Department, Faculty of Graduate Studies for Statistical Research, Cairo University Giza, Egypt
4.
Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
5.
Mathematics and Statistics Department, College of Science, Taibah University, Yanbu, Saudi Arabia

Received: 07 July 2021 Accepted: 06 December 2021 Published: 10 December 2021
MSC : 03E72, 68T35, 90B50

Soft set has limitation for the consideration of disjoint attribute-valued sets corresponding to distinct attributes whereas hypersoft set, an extension of soft set, fully addresses this scarcity by replacing the approximate function of soft sets with multi-argument approximate function. Some structures (i.e., possibility fuzzy soft set, possibility intuitionistic fuzzy soft set) exist in literature in which a possibility of each element in the universe is attached with the parameterization of fuzzy sets and intuitionistic fuzzy sets while defining fuzzy soft set and intuitionistic fuzzy soft set respectively. This study aims to generalize the existing structure (i.e., possibility intuitionistic fuzzy soft set) and to make it adequate for multi-argument approximate function. Therefore, firstly, the elementary notion of possibility intuitionistic fuzzy hypersoft set is developed and some of its elementary properties i.e., subset, null set, absolute set and complement, are discussed with numerical examples. Secondly, its set-theoretic operations i.e., union, intersection, AND, OR and relevant laws are investigated with the help of numerical examples, matrix and graphical representations. Moreover, algorithms based on AND/OR operations are proposed and are elaborated with illustrative examples. Lastly, similarity measure between two possibility intuitionistic fuzzy hypersoft sets is characterized with the help of example. This concept of similarity measure is successfully applied in decision making to judge the eligibility of a candidate for an appropriate job. The proposed similarity formulation is compared with the relevant existing models and validity of the generalization of the proposed structure is discussed.
- fuzzy set,
- intuitionistic fuzzy set,
- soft set,
- intuitionistic fuzzy soft set,
- hypersoft set
Citation: Atiqe Ur Rahman, Muhammad Saeed, Hamiden Abd El-Wahed Khalifa, Walaa Abdullah Afifi. Decision making algorithmic techniques based on aggregation operations and similarity measures of possibility intuitionistic fuzzy hypersoft sets[J]. AIMS Mathematics, 2022, 7(3): 3866-3895. doi: 10.3934/math.2022214

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Abstract

Soft set has limitation for the consideration of disjoint attribute-valued sets corresponding to distinct attributes whereas hypersoft set, an extension of soft set, fully addresses this scarcity by replacing the approximate function of soft sets with multi-argument approximate function. Some structures (i.e., possibility fuzzy soft set, possibility intuitionistic fuzzy soft set) exist in literature in which a possibility of each element in the universe is attached with the parameterization of fuzzy sets and intuitionistic fuzzy sets while defining fuzzy soft set and intuitionistic fuzzy soft set respectively. This study aims to generalize the existing structure (i.e., possibility intuitionistic fuzzy soft set) and to make it adequate for multi-argument approximate function. Therefore, firstly, the elementary notion of possibility intuitionistic fuzzy hypersoft set is developed and some of its elementary properties i.e., subset, null set, absolute set and complement, are discussed with numerical examples. Secondly, its set-theoretic operations i.e., union, intersection, AND, OR and relevant laws are investigated with the help of numerical examples, matrix and graphical representations. Moreover, algorithms based on AND/OR operations are proposed and are elaborated with illustrative examples. Lastly, similarity measure between two possibility intuitionistic fuzzy hypersoft sets is characterized with the help of example. This concept of similarity measure is successfully applied in decision making to judge the eligibility of a candidate for an appropriate job. The proposed similarity formulation is compared with the relevant existing models and validity of the generalization of the proposed structure is discussed.

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