Distance-based Knowledge measure of Hesitant Fuzzy Linguistic Term Set with its application in Multi-criteria decision-making

Motivated by the structural aspect of the probabilistic entropy, the concept of fuzzy entropy enabled the researchers to investigate the uncertainty due to vague information. Fuzzy entropy measures the ambiguity/vagueness entailed in a fuzzy set. Hesitant fuzzy entropy and hesitant fuzzy linguistic term set based entropy presents a more comprehensive evaluation of vague information. In the vague situations of multiple-criteria decision-making, entropy measure is utilized to compute the objective weights of attributes. The weights obtained due to entropy measures are not reasonable in all the situations. To model such situation, a knowledge measure is very significant, which is a structural dual to entropy. A fuzzy knowledge measure determines the level of precision in a fuzzy set. This article introduces the concept of a knowledge measure for hesitant fuzzy linguistic term sets (HFLTS) and show how it may be derived from HFLTS distance measures. Authors also investigate its application in determining the weights of criteria in multi-criteria decision-making (MCDM).

Distance-Based Knowledge Measure for Intuitionistic Fuzzy Sets with Its Application in Decision Making

Much attention has been paid to construct an applicable knowledge measure or uncertainty measure for Atanassov’s intuitionistic fuzzy set (AIFS). However, many of these measures were developed from intuitionistic fuzzy entropy, which cannot really reflect the knowledge amount associated with an AIFS well. Some knowledge measures were constructed based on the distinction between an AIFS and its complementary set, which may lead to information loss in decision making. In this paper, knowledge amount of an AIFS is quantified by calculating the distance from an AIFS to the AIFS with maximum uncertainty. Axiomatic properties for the definition of knowledge measure are extended to a more general level. Then the new knowledge measure is developed based on an intuitionistic fuzzy distance measure. The properties of the proposed distance-based knowledge measure are investigated based on mathematical analysis and numerical examples. The proposed knowledge measure is finally applied to solve the multi-attribute group decision-making (MAGDM) problem with intuitionistic fuzzy information. The new MAGDM method is used to evaluate the threat level of malicious code. Experimental results in malicious code threat evaluation demonstrate the effectiveness and validity of proposed method.

ІНТЕЛЕКТУАЛЬНІ СИСТЕМИ: ПОСТ-ДЕКАРТОВЕ ПРЕДСТАВЛЕННЯ МЕТАЗНАНЬ

The main problem in the general problem of knowledge manipulation is the problem of determining the composition and content of the subject area for which this problem is being solved. It has been established that there are two fundamentally different approaches to solving knowledge manipulation problems. The first approach consists in the application of methods of automatic data processing using computers and corresponding algorithms based on the rules of formal logic to obtain new knowledge about objects in the subject area. For the first approach, the objects of the domain are precisely the physical objects of animate and inanimate nature in their existence, which have their characteristics and between which the corresponding relations are established. The second approach is to use the ability of the human intellect to measure things and their properties based on the laws of dialectical logic. The second approach is characterized by the cognition of knowledge about the activity of objects of living nature, primarily humans. In this case, computers are used, as a rule, to represent already established knowledge in an appropriate form. One such form of knowledge representation is a logical model of a Cartesian coordinate system. The analysis of this model has shown that the logical principle of its formation is the principle of the dialectical unity of the concepts of “general” and “unit”, which is used to form the composition and content of diametrically opposite coordinate axes from numerical sets. On the other hand, there are a significant number of logical models in which the composition and content of the elements of the sets that form the coordinate axes correspond to certain knowledge about human activity. These models also implement the principle of their formation in the form of a dialectical unity of the concepts of “general” “unit”, which is used to form the composition and content of diametrically opposite coordinate axes from the sets of which certain knowledge is. It should be noted that in each of the studied approaches to knowledge manipulation, the concept of “measure” is not applied. On the other hand, this concept is decisive in the formation of knowledge about human activities and their manipulation. The research of the properties of the logical model of the meta-knowledge measure has been carried out. For this model, the content of the concepts “measure of meta-knowledge”, “unit of measure of meta-knowledge” and “unit of measure of knowledge” is established. The graphical representation of the logical model of knowledge representation about human activity in the logical model of the meta-knowledge measure is the architecture of the matrix representation. The main advantage of this view is that it implements a many-to-many (M: N) relationship, which is prohibited in relational databases. The analysis of the level of compliance of the proposed logical model of the meta-knowledge measure with certain requirements for knowledge manipulation models is carried out. A high level of compliance with these requirements has been established. Taking into account the established properties of the architecture of the logical model of meta-knowledge, it is proposed to define this model in the form of a post-Descartes representation of meta-knowledge about the activity.