Abstract
T-spherical fuzzy set is a recently developed model that copes with imprecise and uncertain events of real-life with the help of four functions having no restrictions. This article’s aim is to define some improved algebraic operations for T-SFSs known as Einstein sum, Einstein product and Einstein scalar multiplication based on Einstein t-norms and t-conorms. Then some geometric and averaging aggregation operators have been established based on defined Einstein operations. The validity of the defined aggregation operators has been investigated thoroughly. The multi-attribute decision-making method is described in the environment of T-SFSs and is supported by a comprehensive numerical example using the proposed Einstein aggregation tools. As consequences of the defined aggregation operators, the same concept of Einstein aggregation operators has been proposed for q-rung orthopair fuzzy sets, spherical fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and intuitionistic fuzzy sets. To signify the importance of proposed operators, a comparative analysis of proposed and existing studies is developed, and the results are analyzed numerically. The advantages of the proposed study are demonstrated numerically over the existing literature with the help of examples.
Highlights
To deal with imprecise and uncertain events has always been a challenging task as imprecision and vagueness lie in almost every field of science
Zadeh [1] proposed the notion of a fuzzy set (FS) where he described the uncertainty of an object/event by a membership grade m that has a value from the interval [0, 1]
Some new Einstein aggregation operators (AOs) are proposed by pointing out the shortcomings of the existing operators
Summary
To deal with imprecise and uncertain events has always been a challenging task as imprecision and vagueness lie in almost every field of science. Proposed the framework of q-rung orthopair fuzzy set (q-ROPFS) with the condition that the sum of the qth power of m and n must be less than or equal to 1, for a positive integer q Cuong [5] used the grades to degree respectively Realizing this problem, Mahmood et al [6]fuzzy developed thewith important concept model such events and developed the concept of the picture set (PFS). T-SFS allows thetheir decision restriction structure of PFS left choice forfuzzy decision values of consent for three m,closed i and unit n denoting and non-membership makers to choose any functions value from intervalmembership, regardless ofabstinence, any restriction.
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