Fuzzy sets and their variants
Sapan Kumar Das; Indrani Maiti; RAJEEV PRASAD; Surapati Pramanik; Tarni Mandal
Abstract
The prediction of a real-life problem like in industrial sector or health sector the outcome is impossible or sometimes it is difficult. Due to high information uncertainty and complicated influencing factors of industrial sector, the traditional data-driven prediction approaches can hardly reflect the ...
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The prediction of a real-life problem like in industrial sector or health sector the outcome is impossible or sometimes it is difficult. Due to high information uncertainty and complicated influencing factors of industrial sector, the traditional data-driven prediction approaches can hardly reflect the real changes in practical situation. Fuzzy programming is a powerful prediction reasoning and risk assessment model for uncertain environment. This article mainly explores and applies a modified form of fuzzy programming; namely Fuzzy Linear Fractional Programming Problem (FLFPP) having the coefficients of the objectives and constraints as triangular fuzzy numbers (TFNs). The FLFPP is converted into an equivalent crisp multi-objective linear fractional programming problem (MOLFPP) and solved individually to associate an aspiration level to it. Then by applying fuzzy goal programming (FGP) technique the maximum degree of each membership goal is obtained by minimizing the negative deviational variables. We carry out two industrial application simulations in a hypothetical industrial scenario. Our study shows that the proposed model is practical and applicable to the uncertain practical environment to realize the prediction and the obtained results are compared with that of the existing methods.
Z-numbers and their variants
Nik Muhammad Farhan Hakim Nik Badrul Alam; Ku Muhammad Naim Ku Khalif; Nor Izzati Jaini; Ahmad Syafadhli Abu Bakar; Lazim Abdullah
Abstract
In fuzzy decision-making, incomplete information always leads to uncertain and partially reliable judgements. The emergence of fuzzy set theory helps decision-makers in handling uncertainty and vagueness when making judgements. Intuitionistic Fuzzy Numbers (IFN) measure the degree of uncertainty better ...
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In fuzzy decision-making, incomplete information always leads to uncertain and partially reliable judgements. The emergence of fuzzy set theory helps decision-makers in handling uncertainty and vagueness when making judgements. Intuitionistic Fuzzy Numbers (IFN) measure the degree of uncertainty better than classical fuzzy numbers, while Z-numbers help to highlight the reliability of the judgements. Combining these two fuzzy numbers produces Intuitionistic Z-Numbers (IZN). Both restriction and reliability components are characterized by the membership and non-membership functions, exhibiting a degree of uncertainties that arise due to the lack of information when decision-makers are making preferences. Decision information in the form of IZN needs to be defuzzified during the decision-making process before the final preferences can be determined. This paper proposes an Intuitive Multiple Centroid (IMC) defuzzification of IZN. A novel Multi-Criteria Decision-Making (MCDM) model based on IZN is developed. The proposed MCDM model is implemented in a supplier selection problem for an automobile manufacturing company. An arithmetic averaging operator is used to aggregate the preferences of all decision-makers, and a ranking function based on centroid is used to rank the alternatives. The IZN play the role of representing the uncertainty of decision-makers, which finally determine the ranking of alternatives.
