ABSTRACT
In recent days researchers have tried to handle the maximum information and use those techniques and methods in which there is no chance of data loss or loss of information is minimum. The structure like fuzzy set and complex fussy set cannot discuss the upper and lower approximations. Moreover, we can observe that a fuzzy rough set cannot discuss the second dimension and in this case, there is a chance of data loss. To cover all these issues in previous ideas, the notion of a complex fuzzy rough set in Cartesian form is the demand of the day because this structure can discuss the second dimension as well as upper and lower approximations. For this purpose, in this manuscript, we have developed the theory of complex fuzzy relation and complex fuzzy rough set in Cartesian form. Moreover, we have initiated the fundamental laws for complex fuzzy rough numbers based on Frank t-norm and t-conorm. The fundamental tools that can convert the overall input into a single output are called aggregation operators (AOs). So based on the characteristics of AOs, we have defined the notion of complex fuzzy rough Frank average and complex fuzzy rough Frank geometric AOs. The utilization of the developed theory is necessary to show the importance and validity of the delivered approach. So based on developed notions, we have defined an algorithm for this purpose along with an illustrative example. We have utilized the introduced structure for the classification of AI tools for civil engineering. Moreover, the comparative analysis of the delivered approach shows the advancement of the introduced structure as compared to existing notions.
ABSTRACT
In many decision-making situations, we are not restricted to two kinds of aspects, such as membership degree or nonmembership degree, and sometimes we need to include the abstinence degree (AD). However, many fuzzy set theories fail to cover issues, such as an intuitionistic fuzzy soft set, Pythagorean fuzzy soft set and q-rung orthopair fuzzy soft set. All the above notions can only consider membership degree and a nonmembership degree in their structures. The spherical fuzzy soft set compensates for these drawbacks in its structure. Moreover, the Dombi t-norm and Dombi t-conorm are the fundamental apparatuses to generalize the basic operational laws of sum and product. Therefore, in this article, based on the dominant features of spherical fuzzy soft sets and valuable features of the Dombi t-norm and Dombi t-conorm, we initially developed the basic Dombi operational laws for spherical fuzzy soft numbers. Moreover, based on these newly developed operational laws, we introduced aggregation operators called spherical fuzzy soft Dombi average (weighted, ordered weighted, hybrid) aggregation operators. We discussed the basic properties of these aggregation operators. Additionally, we have developed a multiple criteria decision making (MCDM) approach using an explanatory example via our approach to show its effective utilization. Furthermore, a comparative study of our approach shows the superiority of our introduced notions.
ABSTRACT
Due to more advanced features of the picture fuzzy soft set and valuable characteristics of aggregation operators, in this article, we present the notion of picture fuzzy soft Bonferroni mean aggregation operators and weighted picture fuzzy soft Bonferroni mean aggregation operators. Moreover, some basic properties of these introduced aggregation operators have been given. As cancer is one of the most rapidly increasing diseases globally. But due to different kinds of cancer diseases, it is very difficult to say which type of cancer disease is increasing rapidly. So to reduce this difficulty in the medical field, we have applied our work to medical diagnosis problems to ensure that fuzzy ideas can also help in the medical field. Also, an algorithm along with a descriptive example is established that conforms to the authenticity of initiated work. Furthermore, a comparative analysis of the introduced work has been given to show how this work is more efficient and dominant than other existing theories.
ABSTRACT
Energy storage is a way of storing energy to reduce imbalances between demand and energy production. The ability to store electricity and use it later is one of the keys to reaching large quantities of renewable energy on the grid. There are several methods to store energy such as mechanical, electrical, chemical, electrochemical, and thermal energy. Regarding their operation, storage, and cost, the choice of these energy storage techniques appears to be interesting. This issue becomes very serious when there involves uncertainty. To consider this kind of uncertain information, a picture fuzzy soft set is found to be a more appropriate parameterization tool to deal with imprecise data. Based on the advanced structure of picture fuzzy soft set, here in this article, firstly, we have developed the notions of basic operational laws for picture fuzzy soft numbers. Then based on these developed operational laws, we have established the notions of picture fuzzy soft power average [Formula: see text], weighted picture fuzzy soft power average [Formula: see text] and ordered weighted picture fuzzy soft power average [Formula: see text] aggregation operators. Moreover, we have introduced the notions for picture fuzzy soft power geometric [Formula: see text], weighted picture fuzzy soft power geometric [Formula: see text] and ordered weighted picture fuzzy soft power geometric [Formula: see text] aggregation operators. Furthermore, we have established the application of picture fuzzy soft power aggregation operators for the selection of thermal energy storage techniques. For this, we have developed a decision-making approach along with an explanatory example to show the effective use of the developed theory. Furthermore, a comparative analysis of the introduced work shows the advancement of developed notions.
