Roughness of soft sets and fuzzy sets in semigroups based on set-valued picture hesitant fuzzy relations

<abstract><p>In the philosophy of rough set theory, the methodologies of rough soft sets and rough fuzzy sets have been being examined to be efficient mathematical tools to deal with unpredictability. The basic of approximations in rough set theory is based on equivalence relations. In the aftermath, such theory is extended by arbitrary binary relations and fuzzy relations for more wide approximation spaces. In recent years, the notion of picture hesitant fuzzy relations by Mathew et al. can be considered as a novel extension of fuzzy relations. Then this paper proposes extended approximations into rough soft sets and rough fuzzy sets from the viewpoint of its. We give corresponding examples to illustrate the correctness of such approximations. The relationships between the set-valued picture hesitant fuzzy relations with the upper (resp., lower) rough approximations of soft sets and fuzzy sets are investigated. Especially, it is shown that every non-rough soft set and non-rough fuzzy set can be induced by set-valued picture hesitant fuzzy reflexive relations and set-valued picture hesitant fuzzy antisymmetric relations. By processing the approximations and advantages in the new existing tools, some terms and products have been applied to semigroups. Then, we provide attractive results of upper (resp., lower) rough approximations of prime idealistic soft semigroups over semigroups and fuzzy prime ideals of semigroups induced by set-valued picture hesitant fuzzy relations on semigroups.</p></abstract>

Information structures and entropy measurement for a fuzzy probabilistic information system

An information system (IS), an important model in the field of artificial intelligence, takes information structure as the basic structure. A fuzzy probabilistic information system (FPIS) is the combination of some fuzzy relations in the same universe that satisfy probability distribution. A FPIS as an IS with fuzzy relations includes three types of uncertainties (i.e., roughness, fuzziness and probability). This paper studies information structures in a FPIS from the perspective of granular computing (GrC). Firstly, two types of information structures in a FPIS are defined by set vectors. Then, equality, dependence and independence between information structures in a FPIS are proposed, and they are depicted by means of the inclusion degree. Next, information distance between information structures in a FPIS is presented. Finally, entropy measurement for a FPIS is investigated based on the proposed information structures. These results may be helpful for understanding the nature of structures and uncertainty in a FPIS.

Some results on fuzzy relations

Fuzzy relation is one of the main research contents of fuzzy set theory. This paper obtains some results on fuzzy relations by studying relationships between fuzzy relations and their uncertainty measurement. The concepts of equality, dependence, partial dependence and independence between fuzzy relations are first introduced. Then, uncertainty measurement for a fuzzy relation is investigated by using dependence between fuzzy relations. Moreover, the basic properties of uncertainty measurement are obtained. Next, effectiveness analysis is carried out. Finally, an application of the proposed measures in attribute reduction for heterogeneous data is given. These results will be helpful for understanding the essence of a fuzzy relation.

A Study on Fuzzy Query with Weights Based on Fuzzy Logic

Natural Language Processing (NLP) is the electronic tactic to analyzing text that is depends on both a set of ideas and a set of technologies. Natural Language Processing (NLP) is a subfield of artificial intelligence and etymology it thinks about the issues of computerized era and comprehension of regular human dialects. Common dialect era frameworks change over data from PC databases into ordinary sounding human dialect, and normal dialect understanding frameworks change over specimens of human dialect into more formal representations that are less demanding for PC projects to control. The Fuzzy logic-based approach provides another alternative for effective natural language analysis. It is commonly recognized that many phenomena in natural language lend themselves to descriptions by Fuzzy mathematics, including Fuzzy sets, Fuzzy relations and Fuzzy logic. By defining a Fuzzy logic system and acquiring proper rules, we hope that difficulties in analysis of speech can be alleviated. The goal of NLP is to enable communication between people and computers without resorting to memorization of complex commands and procedures.

Functional Partial Fuzzy Relations

We study fuzzy relations that satisfy the functionality property and that their membership functions can be partial functions. Such fuzzy relations are called partial fuzzy relations, and the variable-domain fuzzy set theory is a framework that provides powerful tools for handling these objects. There, the special operations based on connectives and quantifiers of a partial fuzzy logic are in use. The undefined degrees of membership are carried via those special operations. Furthermore, we show that a suitable combination of these operations leads to a meaningful definition of the functionality property, and we investigate its basic characteristics.

Investigation of Cyber-Security and Cyber-Crimes in Oil and Gas Sectors Using the Innovative Structures of Complex Intuitionistic Fuzzy Relations

Recently, there has been enormous development due to advancements in technology. Industries and enterprises are moving towards a digital system, and the oil and gas industries are no exception. There are several threats and risks in digital systems, which are controlled through cyber-security. For the first time in the theory of fuzzy sets, this research analyzes the relationships between cyber-security and cyber-crimes in the oil and gas sectors. The novel concepts of complex intuitionistic fuzzy relations (CIFRs) are introduced. Moreover, the types of CIFRs are defined and their properties are discussed. In addition, an application is presented that uses the Hasse diagram to make a decision regarding the most suitable cyber-security techniques to implement in an industry. Furthermore, the omnipotence of the proposed methods is explained by a comparative study.

Cybersecurity against the Loopholes in Industrial Control Systems Using Interval-Valued Complex Intuitionistic Fuzzy Relations

Technology is rapidly advancing and every aspect of life is being digitalized. Since technology has made life much better and easier, so organizations, such as businesses, industries, companies and educational institutes, etc., are using it. Despite the many benefits of technology, several risks and serious threats, called cyberattacks, are associated with it. The method of neutralizing these cyberattacks is known as cybersecurity. Sometimes, there are uncertainties in recognizing a cyberattack and nullifying its effects using righteous cybersecurity. For that reason, this article introduces interval-valued complex intuitionistic fuzzy relations (IVCIFRs). For the first time in the theory of fuzzy sets, we investigated the relationships among different types of cybersecurity and the sources of cyberattacks. Moreover, the Hasse diagram for the interval-valued complex intuitionistic partial order set and relation is defined. The concepts of the Hasse diagram are used to inspect different cybersecurity techniques and practices. Then, using the properties of Hasse diagrams, the most beneficial technique is identified. Furthermore, the best possible selection of types of cybersecurity is made after putting some restrictions on the selection. Lastly, the advantages of the proposed methods are illuminated through comparison tests.

Reduction in a fuzzy probabilistic information system

An information system (IS) is an important mathematical tool for artificial intelligence. A fuzzy probabilistic information system (FPIS), the combination of some fuzzy relations in the same universe which satisfies the probability distribution, can be seen as an IS with fuzzy relations. A FPIS overcomes the shortcoming that rough set theory assumes elements in the universe with equal probability and leads to lose some useful information. This paper integrates the probability distribution into the fuzzy relations in a FPIS and studies its reduction. Firstly, the concept of a FPIS is introduced and its reduction is proposed. Then, the fuzzy relations in a FPIS are divided into three categories (P-necessary, P-relatively necessary and P-unnecessary fuzzy relations) according to their importance. Next, entropy measurement for a FPIS is investigated. Moreover, some reduction algorithms are constructed. Finally, an example is given to verify the effectiveness of these proposed algorithms.

L-Fuzzy Rough Approximation Operators Based on Co-Implication and Their (Single) Axiomatic Characterizations

For L a complete co-residuated lattice and R an L-fuzzy relation, an L-fuzzy upper approximation operator based on co-implication adjoint with L is constructed and discussed. It is proved that, when L is regular, the new approximation operator is the dual operator of the Qiao–Hu L-fuzzy lower approximation operator defined in 2018. Then, the new approximation operator is characterized by using an axiom set (in particular, by single axiom). Furthermore, the L-fuzzy upper approximation operators generated by serial, symmetric, reflexive, mediate, transitive, and Euclidean L-fuzzy relations and their compositions are characterize through axiom set (single axiom), respectively.