Keeping in view the importance of new defined and well growing spherical fuzzy sets, in this study, we proposed a novel method to handle the spherical fuzzy multi-criteria group decision-making (MCGDM) problems. Firstly, we presented some novel logarithmic operations of spherical fuzzy sets (SFSs). Then, we proposed series of novel logarithmic operators, namely spherical fuzzy weighted average operators and spherical fuzzy weighted geometric operators. We proposed the spherical fuzzy entropy to find the unknown weights information of the criteria. We study some of its desirable properties such as idempotency, boundary and monotonicity in detail. Finally, the detailed steps for the spherical fuzzy decision-making problems were developed, and a practical case was given to check the created approach and to illustrate its validity and superiority. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantages of our proposed method. Results indicate that the proposed method is suitable and effective for the decision process to evaluate their best alternative.

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of $\left[0, 1\right]$ that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from $\left[0, 1\right]$ intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

The T-spherical fuzzy set (TSFS) is a modification of the fuzzy set (FS), intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PyFS), q-rung orthopair fuzzy set (q-ROFS), and picture fuzzy set (PFS), with three characteristic functions: the membership degree (MD) denoted by $S$, the nonmembership degree (NMD) denoted by $D$, and the abstinence degree (AD) denoted by $I$. It can be used to solve problems of uncertain information with no restrictions. The distance measure (DM) is a tool that sums up the difference between points, while the similarity measure (SM) is a method applied to calculate the similarity between objects within an interval of $\left[0,1\right]$. The current work aims to introduce novel DMs and SMs in the environment of TSFSs to show the limitations of the previously defined DMs and SMs. The suggested DMs and SMs provide more room for all three degrees to be selected without restriction. We investigated the effectiveness of the proposed DMs and SMs by applying a pattern-recognition technique, and we determined their applicability for multicriteria decision making (MCDM) using numerical examples. The newly proposed DMs and SMs are briefly compared to existing DMs and SMs, and appropriate conclusions are drawn.

As a generalization of several fuzzy tools, picture fuzzy sets (PFSs) hold a special ability to perfectly portray inherent uncertain and vague decision preferences. The intention of this paper is to present a Pearson’s picture fuzzy correlation-based model for multi-attribute decision-making (MADM) analysis. To this end, we develop a new correlation coefficient for picture fuzzy sets, based on which a Pearson’s picture fuzzy closeness index is introduced to simultaneously calculate the relative proximity to the positive ideal point and the relative distance from the negative ideal point. On the basis of the presented concepts, a Pearson’s correlation-based model is further presented to address picture fuzzy MADM problems. Finally, an illustrative example is provided to examine the usefulness and feasibility of the proposed methodology.

In this paper, Dombi t-norm (TN) and Dombi t-conorm (TCN) are used to generate more complex, flexible and feasible operation rules by managing a parameter in bipolar neutrosophic fuzzy (BNF) environment. We introduce the notion of bipolar neutrosophic Dombi weighted geometric aggregation (BNDWGA) and bipolar neutrosophic Dombi ordered weighted geometric aggregation (BNDOWGA) operators. We discuss their different properties along with proofs and also investigate multi-attribute decision making (MADM) methods on basis of propose aggregation operators under bipolar neutrosophic fuzzy (BNF) environment. We propose an algorithm of selection of cultivating crop to explain the proposed methods under bipolar neutrosophic fuzzy (BNF) environment. The effect of parameter on our proposed bipolar neutrosophic Dombi aggregation operators are discussed graphically. Moreover, the comparison of our proposed methods with existing methods to test their suitable preferences are discussed in detail.

As the main way of providing care for elderly people, home-based old-age care puts forward higher requirements for the environmental adaptability of the community. Five communities in Wuhu were selected for a comprehensive assessment of environmental suitability. In order to ensure a comprehensive and accurate assessment of the environmental adaptability of the community, we used the analytic hierarchy process (AHP) to calculate the weight of each indicator and the technique for order preference by similarity to ideal solution (TOPSIS) method to evaluate the adaptability of community, as well as further analyses using a two-dimensional data space map. The results show that the Weixing community is the most suitable for the elderly and outdoor activities of the community.