Evaluation of the Economic Relationships on the Basis of Statistical Decision-Making in Complex Neutrosophic Environment

Fuzzy sets and fuzzy logics are used to model events with imprecise, incomplete, and uncertain information. Researchers have developed numerous methods and techniques to cope with fuzziness or uncertainty. This research intends to introduce the novel concepts of complex neutrosophic relations (CNRs) and its types based on the idea of complex neutrosophic sets (CNSs). In addition, these concepts are supported by suitable examples. A CNR discusses the quality of a relationship using the degree of membership, the degree of abstinence, and the degree of nonmembership. Each of these degrees is a complex number from the unit circle in a complex plane. The real part of complex-valued degrees represents the amplitude term, while the imaginary part represents the phase term. This property empowers CNRs to model multidimensional variables. Moreover, some interesting properties and useful results have also been proved. Furthermore, the practicality of the proposed concepts is verified by an application, which discusses the use of the proposed concepts in statistical decision-making. Additionally, a comparative analysis between the novel concepts of CNRs and the existing methods is carried out.

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A novel complex fuzzy N-soft sets and their decision-making algorithm

Complex & Intelligent Systems ◽

10.1007/s40747-021-00373-2 ◽

2021 ◽

Author(s):

Tahir Mahmood ◽

Ubaid ur Rehman ◽

Zeeshan Ali

Keyword(s):

Decision Making ◽

Fuzzy Sets ◽

Uncertain Information ◽

The Novel ◽

Soft Sets ◽

Numerical Examples ◽

Life Problems ◽

Special Cases ◽

Novel Concept

AbstractComplex fuzzy N-soft set (CFN-SS) is an important technique to manage awkward and unreliable information in realistic decision-making problems. CFN-SS is a blend of two separate theories, called N-soft sets (N-SSs) and complex fuzzy sets (CFSs), which are the modified versions of soft sets (SSs) and fuzzy sets (FSs) to depict vague and uncertain information in daily life problems. In this manuscript, the novel concept of CFN-SS is explored and their fundamental laws are discussed. CFN-SS contains the grade of truth in the form of a complex number whose real and imaginary parts are limited to the unit interval. Besides, we examine some algebraic properties for CFN-SS like union, intersections and justify these properties with the help of some numerical examples. To examine the superiority and effectiveness of the proposed approaches, the special cases of the investigated approaches are also discussed. A decision-making procedure is developed by using the investigated ideas based on CFN-SSs. Further, some numerical examples are also illustrated with the help of explored ideas to find the reliability and effectiveness of the proposed approaches. Finally, the comparative analysis of the investigated ideas with some existing ideas is also demonstrated to prove the quality of the proposed works. The graphical expressions of the obtained results are also discussed.

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Correction to "Statistical Decision Making in the Real-Time Control of an Arm Aid for the Disabled"

IEEE Transactions on Systems Man and Cybernetics ◽

10.1109/tsmc.1973.5408586 ◽

1973 ◽

Vol SMC-3 (1) ◽

pp. 111-111 ◽

Cited By ~ 4

Author(s):

Peter D. Lawrence ◽

Wen-Chun Lin

Keyword(s):

Decision Making ◽

Real Time ◽

Real Time Control ◽

Statistical Decision ◽

The Real ◽

Time Control ◽

The Disabled ◽

Statistical Decision Making

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Intelligent systems using Web-pages as knowledge base for statistical decision making

New Generation Computing ◽

10.1007/bf03037241 ◽

1999 ◽

Vol 17 (4) ◽

pp. 349-358 ◽

Cited By ~ 7

Author(s):

Kazunori Fujimoto ◽

Kazumitsu Matsuzawa

Keyword(s):

Decision Making ◽

Knowledge Base ◽

Intelligent Systems ◽

Web Pages ◽

Statistical Decision ◽

Statistical Decision Making

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Some Similarity and Distance Measures between Complex Interval-Valued q-Rung Orthopair Fuzzy Sets Based on Cosine Function and their Applications

Mathematical Problems in Engineering ◽

10.1155/2021/5534915 ◽

2021 ◽

Vol 2021 ◽

pp. 1-25

Author(s):

Harish Garg ◽

Zeeshan Ali ◽

Tahir Mahmood ◽

Sultan Aljahdali

Keyword(s):

Decision Making ◽

Solution Method ◽

Similarity Measures ◽

Cosine Similarity ◽

Distance Measures ◽

Uncertain Information ◽

Cosine Similarity Measures ◽

Complex Valued ◽

Interval Valued ◽

The Ideal

The purpose of this paper is to present a new method to solve the decision-making algorithm based on the cosine similarity and distance measures by utilizing the uncertain and vague information. A complex interval-valued q-rung orthopair fuzzy set (CIVQROFS) is a reliable and competent technique for handling the uncertain information with the help of the complex-valued membership grades. To address the degree of discrimination between the pairs of the sets, cosine similarity measures (CSMs) and distance measures (DMs) are an accomplished technique. Driven by these, in this manuscript, we defined some CSMs and DMs for the pairs of CIVQROFSs and investigated their several properties. Choosing that the CSMs do not justify the axiom of the similarity measure (SM), then we investigate a technique to developing other CIVQROFSs-based SMs using the explored CSMs and Euclidean DMs, and it fulfills the axiom of the SMs. In addition, we find the cosine DMs (CDMs) by considering the inter-relationship between the SM and DMs; then, we have modified the procedure for the rank of partiality by similarity to the ideal solution method for the CDMs under investigation, which can deal with the associated decision-making problems not only individually from the argument of the opinion of geometry but also the fact of the opinion of algebra. Finally, we provide a numerical example to demonstrate the practicality and effectiveness of the proposed procedure, which is also in line with existing procedures. Graphical representations of the measures developed are also used in this manuscript.

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