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Aggregation operators can be used to combine and synthesise a finite number of numerical values into a single numerical value. Many areas, including decision-making, expert systems, risk analysis, and image processing, rely heavily on aggregating functions. In real-world situations, the neutrosophic set can manage the uncertainties associated with information from any decision-making challenge, whereas the fuzzy set and intuitionistic set cannot. The term "bipolarity" refers to the propensity of the human mind to weigh pros and drawbacks when thinking through decisions. Triangular norms are aggregation operators in a variety of fields, including fuzzy set theory, probability and statistics, and decision sciences. Thus, the individual assessments in this paper's study of and approach to multi-criteria decision-making (MCDM) problems that use bipolar neutrosophic numbers as the individual evaluations. Frank operational laws of bipolar neutrosophic numbers, bipolar neutrosophic Frank weighted geometric aggregation (BNFWGA) and the bipolar neutrosophic frank ordered weighted geometric aggregation (BNFOWGA) operators have been developed with its desirable properties. Additionally, the suggested aggregation operators have been used in the selection of bridges. The outcomes demonstrate the applicability and validity of the suggested approach. Comparative analysis has been performed using the current approach. [ABSTRACT FROM AUTHOR]

Type-2 fuzzy sets (T2FSs) can deal with higher modeling and uncertainties which exist in the real-world application, specifically in the control systems. Particularly the climate changes are always uncertain and thus, the type-2 fuzzy controller is an effective system to handle those situations. Polyhouse is a methodology used to cultivate the plants. It breaks the seasonal hurdle of the formulation and it is also suitable for the conflictive climate conditions. Controlling and directing internal parameters of the polyhouse play an essential role in the growth of the plant. Among those, humidity is an important element when one deals with the growth of the plant in polyhouse. It affects the weather, as well as the global change of the climate and hence, the inner climate of the polyhouse will be disturbed. In this paper, operational laws for triangular interval type-2 fuzzy numbers and derived triangular interval type-2 weighted geometric (TIT2WG) operator with their desired mathematical properties using Dombi triangular norms. Also, humidity control is analyzed using interval type-2 fuzzy controller (IT2FC) with the use of derived aggregation operator which is the aim of the paper. Further stability of the system has been analyzed by applying four different defuzzification methods and the method is recommended which gives a better response. [ABSTRACT FROM AUTHOR]

There are various mathematical tools available to measure the level of accuracy such as Crisp, Fuzzy, Intuitionistic fuzzy sets and Neutosophic set. Further, Plithogenic set is a generalization of these four sets. This paper aims to test whether Plithogenic aggregation operation is more effective than other sets in its accuracy, while decision making. In order to obtain a better accuracy, the Plithogenic aggregation operation such as Fuzzy set [FS], Intuitionistic fuzzy set [IFS] and Neutrosophic set [NS] used tnorm and tconorm. An illustration is examined in this paper to prove the result of better accuracy using plithogenic aggregation operators in decision making. [ABSTRACT FROM AUTHOR]