Extension Of TOPSIS Technique To Solve MCDM Problems For Some Hybrid Structures Of Fuzzy Sets

Intuitionistic fuzzy sets(IFS)and Pythagorean fuzzy sets(PFS)are powerful mathematical tools to deal with uncertain and vague information.Pythagorean fuzzy soft set(PFSS)is a suitable extension of PFS and generalization of the intuitionistic fuzzy soft set(IFSS).This Ph.D.dissertation aims to extend the idea of the correlation coefficient,weighted correlation coefficient,aggregation operators,and TOPSIS technique to solve multi-criteria decision making(MCDM),multi-attribute decision making(MADM),and multi-criteria group decision making(MCGDM)problems under some hybrid structures of fuzzy sets.The existing IFSS is unable to handle the uncertainty when information is given in intervals.To overcome such difficulties the TOPSIS technique and aggregation operators for the interval-valued intuitionistic fuzzy soft set(IVIFSS)have been developed.Also,a decision-making approach has been established to solve decision-making complications.The existing IFSS and developed IVIFSS fails to solve those problems in which the sum of membership and non-membership degree exceed one.To deal with such types of concerns,the author developed some aggregation operators,interaction aggregation operators,and TOPSIS method for PFSS.The author established some decision-making methodologies to solve multi-criteria decision-making and multi-criteria group decision-making problems utilizing aggregation operators,interaction aggregation operators,and TOPSIS technique.The author utilized the established decision-making methodologies for the selection of suppliers in green supply chain management,and effective hand sanitizer to reduce COVID-19 effects.But these developed techniques are unable to deal with problems when any one attribute of a set of parameters has further sub-attributes and is further bi-furcated.The presented decision-making approaches are unable to deal with the sub-attributes of the considered parameters.The author proposed the concept of intuitionistic fuzzy hypersoft set(IFHSS)which is a most generalized form of IFS and extension of IFSS to handle the above-mentioned concerns.In it,the author proposed the correlation and weighted correlation coefficients based TOPSIS technique and aggregation operators for IFHSS to solve multi-attribute decision-making issues.Furthermore,the author introduced the fuzzy versions of the axiom of choice,Zorn?s lemma,and well-ordering principle,such as the fuzzy axiom of choice,fuzzy Zorn?s lemma,and fuzzy well-ordering principle,and discuss the relations between them.Also,the fuzzy version of the Hausdorff maximal principle has been proposed with its application in fuzzy filters.In the future,the proposed approaches PFSS,and IFHSS can be extended to interval-valued PFSS and interval-valued IFHSS.The concept of TOPSIS technique,aggregation operators,and interaction aggregation operators can be developed with their decision-making approaches under-considered environment.Furthermore,utilizing proposed operators the AHP,VIKOR,ELECTRE family,and PROMETHEE family methods can be introduced with their decision-making methodologies.