The basic motivation of this research paper is the approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type which generalized the Riemann-Liouville fractional derivative. Combining with the techniques of fractional calculus, fixed point theorem for multi-value dmaps and Sobolev-type and Clarke subdifferential to the approximate controllability system we obtain new existence result of mild solutions. Next, we demonstrate linear and semilinear systems for approximate controllability. Finally, to verify our theoretical results, an illustration is also included.

Results on approximate controllability of Sobolev-type fractional neutral differential inclusions of Clarke subdifferential type

In this paper, we formulate a new set of sufficient conditions for the approximate controllability of fractional evolution stochastic integrodifferential delay inclusions of order r ∈ ( 1 , 2 ) with nonlocal conditions in Hilbert space. Martelli’s fixed point theorem, multivalued functions, cosine and sine families, fractional calculus and operator semigroups are used to establish the results under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the applicability of the obtained theoretical results.

A note on approximate controllability for nonlocal fractional evolution stochastic integrodifferential inclusions of order r∈(1,2) with delay

Decision-making methods play an important role in the real-life of human beings and consist of choosing the best options from a set of possible choices. This paper proposes the notion of complex Fermatean fuzzy N-soft set (CFFNSfS) which, by means of ranking parameters, is capable of handling two-dimensional information related to the degree of satisfaction and dissatisfaction implicit in the nature of human decisions. We define the fundamental set-theoretic operations of CFFNSfS and elaborate the CFFSfS associated with threshold. The algebraic and Yager operations on CFFNSf numbers are also defined. Several algorithms are proposed to demonstrate the applicability of CFFNSfS to multi-attribute decision making. The advanced algorithms are described and accomplished by several numerical examples. Then, a comparative study manifests the validity, feasibility, and reliability of the proposed model. This method is compared with the Fermatean fuzzy Yager weighted geometric (FFYwG) and the Fermatean fuzzy Yager weighted average (FFYwA) operators. Further, we developed a remarkable CFFNSf-TOPSIS approach by applying innovative CFFNSf weighted average operator and distance measure. The presented technique is fantastically designed for the classification of the most favorable alternative by examining the closeness of all available choices from particular ideal solutions. Afterward, we demonstrate the amenability of the initiated approach by analyzing its tremendous potential to select the best city in the USA for farming. An integrated comparative analysis with existing Fermatean fuzzy TOPSIS technique is rendered to certify the terrific capability of the established approach. Further, we decisively investigate the rationality and reliability of the presented CFFNSfS and CFFNSf-TOPSIS approach by highlighting its advantages over the existent models and TOPSIS approaches. Finally, we holistically describe the conclusion of the whole work. 

https://link.springer.com/content/pdf/10.1007/s12652-021-03629-4.pdf

Complex fermatean fuzzy N-soft sets: a new hybrid model with applications

The utilization of linguistic variables is of vital importance for qualitative information processing in mathematical modelling and decision making under uncertainty. The primary purpose of our study is to introduce a novel structure by the fusion of Fermatean fuzzy sets and linguistic term sets. This hybrid structure is termed as the linguistic Fermatean fuzzy set which can be employed for dealing with decision-making problems involving qualitative information. Several fundamental operations of linguistic Fermatean fuzzy sets are introduced. Furthermore, we present four classes of linguistic Fermatean fuzzy Hamy mean operators, namely, the linguistic Fermatean fuzzy Hamy mean operator, the linguistic Fermatean fuzzy dual Hamy mean operator, the linguistic Fermatean fuzzy weighted Hamy mean operator, and the linguistic Fermatean fuzzy weighted dual Hamy mean operator. Some basic properties of these linguistic Fermatean fuzzy Hamy mean operators are examined as well. In addition, we develop a linguistic Fermatean fuzzy extension of the COPRAS method. We also propose a novel approach to multi-attribute group decision making with linguistic Fermatean fuzzy information. With our proposed methods, we solve two practical problems regarding food company ranking and green supplier selection, respectively. Finally, the efficacy of our developed method is validated through a comparative analysis with existing methods. 

Extending COPRAS Method with Linguistic Fermatean Fuzzy Sets and Hamy Mean Operators

In this article, we introduce the 2-tuple linguistic bipolar fuzzy set (2TLBFS), a new strategy for dealing with uncertainty that incorporates a 2-tuple linguistic term into bipolar fuzzy set. The 2TLBFS is a better way to deal with uncertain and imprecise information in the decision-making environment. We elaborate the operational rules, based on which, the 2-tuple linguistic bipolar fuzzy weighted averaging (2TLBFWA) operator and the 2-tuple linguistic bipolar fuzzy weighted geometric (2TLBFWG) operator are presented to fuse the 2TLBF numbers (2TLBFNs). The Heronian mean (HM) operator, which can reflect the internal correlation between attributes and their influence on decision results, is integrated into the 2TLBF environment to analyze the effect of the correlation between decision factors on decision results. Initially, the generalized 2-tuple linguistic bipolar fuzzy Heronian mean (G2TLBFHM) operator and generalized 2-tuple linguistic bipolar fuzzy weighted Heronian mean (G2TLBFWHM) operator are proposed and properties are explained. Further, 2-tuple linguistic bipolar fuzzy geometric Heronian mean (2TLBFGHM) operator and 2-tuple linguistic bipolar weighted geometric Heronian mean (2TLBFWGHM) operator are proposed along with some of their desirable properties. Then, an approach to multi-attribute group decision-making (MAGDM) based on the proposed aggregation operators under the 2TLBF framework is developed. At last, a numerical illustration is provided for the selection of the best photovoltaic cell to demonstrate the use of the generated technique and exhibit its adequacy.

A new MAGDM method with 2-tuple linguistic bipolar fuzzy Heronian mean operators.

In this research article, we present a new framework for handling imprecisely acquired bipolar information along with parameterized graded descriptions. The formal model that implements all these desirable features is called bipolar fuzzy N-soft set (also BFNS
 $$_\text {f}$$
 S for brevity). We discuss basic operations of our proposed hybrid model, including weak complement, bipolar fuzzy complement, weak bipolar fuzzy complement, extended union, restricted union, extended intersection, restricted intersection, and BFNS
 $$_\text {f}$$
 S associated with a threshold. Furthermore, we illustrate some standard algebraic operations on BFNS
 $$_\text {f}$$
 numbers and produce related results. Moreover, we develop BFNS
 $$_\text {f}$$
 -TOPSIS methods for the solution of multi-attribute decision-making (MADM) and multi-attribute group decision-making (MAGDM) problems defined by bipolar fuzzy N-soft information. In the MAGDM version of the solution, we use the bipolar fuzzy N-soft weighted average operator to aggregate the decisions of all experts according to the performance of alternatives and traits of the attributes. We evaluate the normalized Euclidean distance of alternatives and BFNS
 $$_\text {f}$$
 positive and negative ideal solutions, respectively, and relative closeness index to find the most optimal solution. Moreover, three algorithms are proposed to handle MADM problems in the environment of BFNS
 $$_\text {f}$$
 S. To demonstrate the effectiveness of the algorithms and the BFNS
 $$_\text {f}$$
 -TOPSIS approach for MADM problems, a numerical application regarding the selection of best psychiatrist in Karachi is presented. The validity of the proposed BFNS
 $$_\text {f}$$
 -TOPSIS technique for MAGDM is illustrated through an example which examines the best construction company in West Midlands. Finally, we conduct a comparative study with the bipolar fuzzy TOPSIS method to endorse the qualities of the proposed model.

Decision-making analysis based on bipolar fuzzy N-soft information

The primary aim of this article is to extend the bipolar fuzzy 
 
 N
 
 -soft sets with the concern of pursuing the periodicity involved real-world problems and introduce a new multiskilled hybrid model, namely, complex bipolar fuzzy 
 
 N
 
 -soft sets. The novel model possesses the parametric characteristics of the versatile 
 
 N
 
 -soft set and enjoys the distinguished attributes of a complex bipolar fuzzy set to handle the double-sided periodic vague data. We illustrate that the innovative model assists as a proficient mechanism for grading-based parameterized two-dimensional bipolar fuzzy information. We present some elementary operations and results for a complex bipolar fuzzy 
 
 N
 
 -soft environment. Further, we establish the three dexterous algorithms to find the optimal solution to multiattribute decision-making problems. Moreover, the algorithms are supported with the robust assessment of a real-world application. Lastly, a comparison with existent decision-making techniques, such as choice values, weighted choice values, and 
 
 D
 
 -choice of values of bipolar fuzzy 
 
 N
 
 -soft sets, is also conducted to manifest the phenomenal accountability and authenticity of the presented decision-making approaches.

/pdf/decision-making-approach-with-complex-bipolar-fuzzy-n-soft-1gth6pr5.pdf

Umaira Amjad

Papers

Complex fermatean fuzzy N-soft sets: a new hybrid model with applications

Decision-making analysis based on bipolar fuzzy N-soft information

Decision-Making Approach with Complex Bipolar Fuzzy N-Soft Sets