Optimizing crop yields through picture fuzzy soft set analysis: A comprehensive approach

Emerging trends in soft set theory and related topics.

The notion of fuzzy sets initiated to overcome the uncertainty of an object. Fuzzy topological space, in- tuitionistic fuzzy sets in topological structure space, vagueness in topological structure space, rough sets in topological space, theory of hesitancy and neutrosophic topological space, etc. are the extension of fuzzy sets. Soft set is a family of parameters which is also a set. Fuzzy soft topological space, intuitionistic fuzzy soft and neutrosophic soft topological space are obtained by incorporating soft sets with various topological structures. This motivates to write a review and study on various soft set concepts. This paper shows the detailed review of soft topological spaces in various sets like fuzzy, Intuitionistic fuzzy set and neutrosophy. Eventually, we compared some of the existing tools in the literature for easy understanding and exhibited their advantages and limitations.

In a fuzzy set (FS), there is a concept of alpha-cuts of the FS for alpha in [0,1]. Further, this concept was extended into (alpha,delta)-cuts in an intuitionistic fuzzy set (IFS) for delta in [0,1]. One of the expansions of FS and IFS is the picture fuzzy set (PFS). Hence, the concept of (alpha,delta)-cuts was developed into (alpha,delta,beta)-cuts in a PFS where beta is an element of [0,1]. Since a picture fuzzy graph (PFG) consists of picture fuzzy vertex or edge sets or both of them, we have an idea to construct the notion of the (alpha,delta,beta)-cuts in a PFG. The steps used in this paper are developing theories and algorithms. The objectives in this research are to construct the concept of (alpha,delta,beta)-cuts in picture fuzzy graphs (PFGs), to construct the (alpha,delta,beta)-cuts coloring of PFGs, and to design an algorithm for finding the cut chromatic numbers of PFGs. The first result is a definition of the (alpha,delta,beta)-cut in picture fuzzy graphs (PFGs) where (alpha,delta,beta) are elements of a level set of the PFGs. Further, some properties of the cuts are proved. The second result is a concept of PFG coloring and the chromatic number of PFG based on the cuts. The third result is an algorithm to find the cuts and the chromatic numbers of PFGs. Finally, an evaluation of the algorithm is done through Matlab programming. This research could be used to solve some problems related to theories and applications of PFGs.

Soft rough fuzzy sets and soft fuzzy rough sets

The researcher has been facing problems while handling imprecise and vague information, i.e., the problems of networking, decision-making, etc. For encountering such complicated data, the notion of fuzzy sets (FS) has been considered an influential tool. The notion was extended to its generalizations by a number of researchers in different ways which helps to understand and assess even more complex issues. This article characterizes imprecision with four kinds of values of membership. In this work, we aim to define and examine cubic picture fuzzy sets and give an application on averaging aggregation operators. We first introduce the notion of a cubic picture fuzzy set, which is a pair of interval-valued picture fuzzy set and a picture fuzzy set by giving examples. Then, we define two kinds of ordering on these sets and also discuss some set-theoretical properties. Moreover, we introduce three kinds of averaging aggregation operators based on cubic picture fuzzy sets and, at the end, we illustrate the results with a decision-making problem by using one of the provided aggregation operators.

In this paper we introduce some types of generalized fuzzy soft separated sets and study some of their properties. Next, the notion of connectedness in fuzzy soft topological spaces due to Karata et al, Mahanta et al, and Kandil et al., extended to generalized fuzzy soft topological spaces. The relationship between these types of connectedness in generalized fuzzy soft topological spaces is investigated with the help of number of counter examples.

A new concept of picture fuzzy sets (PFS) were introduced in 2013, which are directextensions of the fuzzy sets and the intuitonistic fuzzy sets. Then some operations on PFS withsome properties are considered in [ 9,10 ]. Some basic operators of fuzzy logic as negation, tnorms, t-conorms for picture fuzzy sets firstly are defined and studied in [13,14]. This paper isdevoted to some classes of representable picture fuzzy t-norms and representable picture fuzzyt-conorms on PFS and a basic algebra structure of Picture Fuzzy Logic – De Morgan triples ofpicture operators.

The objective of the work is to present some series of the aggregation operators for the picture fuzzy sets (PFSs). As PFSs have been an extended version of the intuitionistic fuzzy set theory which not only considers the degree of acceptance or rejection but also taken into the account the degree of refusal during the analysis. Thus, by considering all these degrees, some aggregation operators, namely picture fuzzy weighted average, picture fuzzy ordered weighted average, and picture fuzzy hybrid average aggregation operators, have been proposed along with their desirable properties. A decision-making approach based on these operators has also been presented. Finally, an illustrative example has been given for demonstrating the approach.

Picture fuzzy sets (PFSs) can be used to handle real-life problems with uncertainty and vagueness more effectively than intuitionistic fuzzy sets (IFSs). In the process of information aggregation, many aggregation operators under PFSs are used by different authors in different fields. In this article, a multi-attribute decision-making (MADM) problem is introduced utilizing harmonic mean aggregation operators with trapezoidal fuzzy number (TrFN) under picture fuzzy information. Three harmonic mean operators are developed namely trapezoidal picture fuzzy weighted harmonic mean (TrPFWHM) operator, trapezoidal picture fuzzy order weighted harmonic mean (TrPFOWHM) operator and trapezoidal picture fuzzy hybrid harmonic mean (TrPFHHM) operator. The related properties about these operators are also studied. At last, an MADM problem is considered to interrelate among these operators. Furthermore, a numerical instance is considered to explain the productivity of the proposed operators.

Linguistic picture fuzzy soft sets (LPFSSs) provide a powerful tool for handling uncertainties in decision-making problems, particularly when multiple parameters are involved. By integrating the advantages of linguistic picture fuzzy sets (LPFSs) and soft sets (SSs), LPFSSs prove especially effective in situations involving imprecise and ambiguous information. This study extends the conventional CRITIC (Criteria Importance Through Inter-criteria Correlation) and EDAS (Evaluation based on Distance from Average Solution) methods to the LPFSS environment. First, the definitions of LPFSSs and linguistic picture fuzzy soft numbers (LPFSNs) are introduced along with their key properties. Subsequently, a CRITIC-EDAS framework is developed under the linguistic picture fuzzy soft setting. Finally, a numerical example concerning the selection of the most suitable organic fertilizer is presented to illustrate the effectiveness of the proposed approach.

Theories of fuzzy sets and rough sets are powerful mathematical tools for modelling various types of uncertainty. Molodtsov (Comput Math Appl 37:19–31, 1999 [6]) initiated a novel concept called soft sets, a new mathematical tool for dealing with uncertainties. It has been found that fuzzy sets, rough sets, and soft sets are closely related concepts (Aktas and Cagman in Inf Sci 1(77):2726–2735, 2007 [1]). Research works on soft sets are very active and progressing rapidly in these years. In 2001, Maji et al. (J Fuzzy Math 9(3):589–602, 2001 [5]) proposed the idea of intuitionistic fuzzy soft set theory and established some results on them. Based on an equivalence relation on the universe of discourse, Dubois and Prade (Int J Gen Syst 17:191–209, 1990 [3]) introduced the lower and upper approximation of fuzzy sets in a Pawlak approximation space and obtained a new notion called rough fuzzy sets. Feng et al. (Soft Compt 14:899–911, 2009 [4]) introduced lower and upper soft rough approximation of fuzzy sets in a soft approximation space and obtained a new hybrid model called soft rough fuzzy sets which is the extension of Dubois and Prade’s rough fuzzy sets. The aim of this chapter is to consider lower and upper soft rough intuitionistic fuzzy approximation of intuitionistic fuzzy sets in intuitionistic fuzzy soft approximation space (IF soft approximation space) and obtain a new hybrid model called soft rough intuitionistic fuzzy sets which can be seen as extension of both the previous work by Dubois and Prade and Feng et al.

In order to improve the effect of precision intelligent agricultural decision support system, this paper combines big data technology to carry out precision mining of agricultural data, and combines decision tree algorithm to carry out data classification processing. Moreover, this paper obtains the most effective agricultural decision reference data through data mining, combines the agricultural decision support process to set the functional modules of the decision system, and analyzes the implementation process of each functional module. In addition, this paper studies the theoretical basis and key technologies of the agricultural production structure optimisation decision support system, and builds a precision and intelligent agricultural decision support system based on big data analysis. The system mainly performs accurate processing of agricultural data and makes effective predictions, and then makes scientific decision results. Finally, this paper verifies the structure of the model in this paper combined with experimental analysis. From the comparison of experiments, it can be seen that the precision and intelligent agricultural decision support system constructed in this paper has significant effects.

A decision-making problem using dissimilarity measure in picture fuzzy sets

This article describes how most frequently uncertainty arises due to vagueness, imprecision, partial information, etc., are encountered in medical diagnosis. To deal with this type of uncertainty, initially fuzzy set theory (FST) was explored and accordingly, medical decision making became one of the most important and interesting areas of applications of FST. Interval valued fuzzy sets (IVFSs) and intuitionistic fuzzy sets (IFS's) were developed and successfully applied in different areas including medical diagnosis. Although, IFS forms a membership degree and a non-membership degree separately in such a way that sum of the two degrees must not exceed one, but one of the important and integral part i.e., degree of neutrality is not taken into consideration in IFS, which is generally occurred in medical diagnosis. In such circumstances, picture fuzzy set (PFS) can be considered as a strong mathematical tool, which adequate in situations when human opinions involved more answers of type: yes, abstain, no. For this purpose, this article, proposes some distance measures on PFS and studies some of its properties. Also, an attempt has been made to carry out medical diagnosis via the proposed distance measures on PFSs and exhibit the technique with a suitable case study. It is found that the distance measures make it possible to introduce weights of all symptoms and consequently patient can be diagnosed directly.

The aim of this paper is to introduce the concept of \((3, 4)\)-fuzzy sets. We compare \((3, 4)\)-fuzzy sets with intuitionistic fuzzy sets, Pythagorean fuzzy sets, and Fermatean fuzzy sets. We focus on the complement of \((3, 4)\)-fuzzy sets. We construct some of the fundamental set of operations of the \((3, 4)\)-fuzzy sets. Due to their larger range of describing membership grades, \((3, 4)\)-fuzzy sets can deal with more uncertain situations than other types of fuzzy sets. For ranking \((3, 4)\)-fuzzy sets, we define a score function and an accuracy function. In addition, we introduce the concept of \((3, 4)\)-fuzzy topological space. Ultimately, we define \((3, 4)\)-fuzzy continuity of a map defined between \((3, 4)\)-fuzzy topological spaces and we characterize this concept.