The q-Fractional Fuzzy Sets (q-FrFSs) offers information in Membership Grade (MG) and Non-membership Grade (NMG) of an object; however, both grades have the hesitancy factor because complex information usually does not give single MG and single NMG. Therefore, in this study we initiate the concept of q-Fractional Hesitant Fuzzy Sets (q-FrHFSs) and its basic properties. In q-FrHFSs not only hesitancy factor is taken into account but it also consider all possible values of uncertainties in {0,1}× {0,1}. Thus Correlation Coefficients (CCs) on q-FrHFSs are necessary to cope uncertain information with hesitancy, MGs and NMGs. In this study we introduce two types of CCs namely CCs on q-FrHFSs and weighted CCs on q-FrHFSs. We investigate underlying properties of these CCs and give a MCDM method on q-FrHFSs environment. We consider an application of our method to agricultural land selection across a set of cities for cultivation of apples crop. At the end, we compare our method of q-FrHFSs to some existing frameworks.

Green industry development focuses on balancing economic and financial growth with environmental stewardship and ensuring that companies and industries are contributing positively to both environmental sustainability and prosperity. This manuscript aims to develop the novel technique of circular complex p, q-quasirung orthopair fuzzy 2-tuple linguistic (CCp, q-QOF2-TL) set and their operational laws based on algebraic t-norms and Hamacher t-norms, where the algebraic t-norms and Einstein t-norms are the special cases of the Hamacher t-norms for parameter ϜℲ^s=l and ϜℲ^s=2. Further, we derive the Hamacher power aggregation operators based on any finite collection of CCp, q-QOF2-TL numbers (CCp, q-QOF2-TLNs), called CCp, q-QOF2-TL Hamacher power average (CCp, q-QOF2-TLHPA) operator, CCp, q-QOF2-TL Hamacher power weighted average (CCp, q-QOF2-TLHPWA) operator, CCp, q-QOF2-TL Hamacher power geometric (CCp, q-QOF2-TLHPG) operator, CCp, q-QOF2-TL Hamacher power weighted geometric (CCp, q-QOF2-TLHPWG) operator, and described their basic properties, called idempotency, monotonicity, and boundedness. Further, we demonstrate the technique of multi-attribute decision-making (MADM) problem based on the above operators to evaluate the major factor that will be playing in the development of the green industry. Finally, we compare the proposed ranking values with the obtained ranking values of existing techniques to show the supremacy and superiority of the initiated approaches.

The model of bipolar complex fuzzy linguistic set is a very famous and dominant principle to cope with vague and uncertain information. The bipolar complex fuzzy linguistic set contained the positive membership function, negative membership function, and linguistic variable, where the technique of fuzzy sets to bipolar fuzzy sets are the special cases of the bipolar complex fuzzy linguistic set. In this manuscript, we describe the model of Aczel-Alsina operational laws for bipolar complex fuzzy linguistic values based on Aczel-Alsina t-norm and Aczel-Alsina t-conorm. Additionally, we compute the Aczel-Alsina power aggregation operators based on bipolar complex fuzzy linguistic data, called bipolar complex fuzzy linguistic Aczel-Alsina power averaging operator, bipolar complex fuzzy linguistic Aczel-Alsina power weighted averaging operator, bipolar complex fuzzy linguistic Aczel-Alsina power geometric operator, and bipolar complex fuzzy linguistic Aczel-Alsina power weighted geometric operator with some dominant and fundamental laws such as idempotency, monotonicity, and boundedness. Moreover, we initiate the model of the Weighted Aggregates Sum Product Assessment technique with the help of consequent theory. In the context of geographic information systems and spatial information systems, coupling aims to find out the relationships among different components within a geographic information system, where coupling can occur at many stages, for instance, spatial coupling, data coupling, and functional coupling. To evaluate the above dilemma, we perform the model of multi-attribute decision-making for invented operators to compute the best technique for addressing geographic information systems. In the last, we deliberate some numerical examples for comparing the ranking results of proposed and prevailing techniques.