A New Approach Towards Intuitionistic Fuzzy Multisets

In this paper a new definition of Intuitionistic fuzzy multisets (IFMS) has been introduced. Algebraic operations on these intuitionistic fuzzy multisets are defined and their properties under these algebraic operations are studied. The author has also introduced a new notion of complement for an IFMS in which the complement of the original set is also an IFMS. The notion of distance and similarity between two IFMS’s has been defined and their properties have also been studied here. An application of IFMS in solving a medical diagnosis problem has been provided at the end.

A Study on Cooperative Continuous Static Games without Differentiability under Fuzzy Environment

In this study, a fuzzy cooperative continuous static game (PQFCCSG) with n players having fuzzy parameters in all of the cost functions and the right- hand-side of constraints is characterized. Their fuzzy parameters are represented by piecewise quadratic fuzzy numbers. The α-pareto optimal solution concept is specified. In addition, the stability sets of the first and second kind without differentiability are conceptualized and established. An illustrated numerical example is discussed for proper understanding and interpretation of the proposed concept.

A Theoretical Linguistic Fuzzy Rule-Based Compartmental Modeling for the COVID-19 Pandemic

Recently COVID-19 pandemic has affected the whole world quite seriously. The number of new infectious cases and death cases are rapidly increasing over time. In this study, a theoretical linguistic fuzzy rule-based Susceptible-Exposed-Infectious-Isolated-Recovered (SEIIsR) compartmental model has been proposed to predict the dynamics of the transmission of COVID-19 over time considering population immunity and infectiousness heterogeneity based on viral load in the model. The model’s equilibrium points have been calculated and stability analysis of the model’s equilibrium points has been conducted. Consequently, the fuzzy basic reproduction number, R0f of the fuzzy model has been formulated. Finally, the temporal dynamics of different compartmental populations with immunity and infectiousness heterogeneity using the fuzzy Mamdani model are delineated and some disease control policies have been suggested to get over the infection in no time.

A novel intuitionistic fuzzy correlation algorithm and its applications in pattern recognition and students’ admission process

Many computing methods have been studied in intuitionistic fuzzy environment to enhance the resourcefulness of intuitionistic fuzzy sets in modelling real-life problems, among which, correlation coefficient is prominent. This paper proposes a new intuitionistic fuzzy correlation algorithm via intuitionistic fuzzy deviation, variance and covariance by taking into account the complete parameters of intuitionistic fuzzy sets. This new computing technique does not only evaluates the strength of relationship between the intuitionistic fuzzy sets but also indicates whether the intuitionistic fuzzy sets have either positive or negative linear relationship. The proposed technique is substantiated with some theoretical results, and numerically validated to be superior in terms of performance index in contrast to some hitherto methods. Multi-criteria decision-making processes involving pattern recognition and students’ admission process are determined with the aid of the proposed intuitionistic fuzzy correlation algorithm coded with JAVA programming language.

GENERALIZED FUZZY DIVERGENCE MEASURE, PATTERN RECOGNITION AND INEQUALITIES

Many fuzzy information and divergence measures developed by various researchers and authors. Here, authors proposed new fuzzy divergence measure using the properties of convex function and fuzzy concept. The applications of novel fuzzy divergence measures in pattern recognition with case study, are discussed. Obtained various novel fuzzy information inequalities on fuzzy divergence measures. The new relations among new and existing fuzzy divergence measure by new f-divergence, Jensen inequalities, properties of convex functions and inequalities have studied. Finally, verified these results and proposed fuzzy divergence measures by numerical example.

Unification of imprecise data - translation of fuzzy to multi-valued knowledge over Y-axis

Inference systems are a well-defined technology derived from knowledge-based systems. Their main purpose is to model and manage knowledge as well as expert reasoning to insure a relevant decision making while getting close to human induction. Although handled knowledge are usually imperfect, they may be treated using a non classical logic as fuzzy logic or symbolic multi-valued logic. Nonetheless, it is required sometimes to consider both fuzzy and symbolic multi-valued knowledge within the same knowledge-based system. For that, we propose in this paper an approach that is able to standardize fuzzy and symbolic multi-valued knowledge. We intend to convert fuzzy knowledge into symbolic type by projecting them over the Y-axis of their membership functions. Consequently, it becomes feasible working under a symbolic multi-valued context. Our approach provides to the expert more flexibility in modeling their knowledge regardless of their type. A numerical study is provided to illustrate the potential application of the proposed methodology.

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).

The Intuitionistic Fuzzy FlowSort Method for Multicriteria Group Decision Making

The real life problems are multidimensional in nature and may involve some ambiguity when it comes to decision making. It is, therefore, difficult to design the evaluation criteria precisely and determine the exact value of the attributes in the multicriteria analysis. The intuitionistic fuzzy set (IFS) achieved great success in treating this kind of ambiguity in a great deal of research. The study of sorting problems is an active research issue in the multiple criteria decision aid (MCDA) area. This paper investigated one of the sorting methods, FLOWSORT, and extended it to the multicriteria group decision making based on the output aggregation of the individual sorting results. The rating of each alternative was described through linguistic terms that can be expressed in triangular intuitionistic fuzzy numbers. An illustrative example as well as an empirical comparison with other multi-criteria decision making methods were carried out to validate our extension.

A GENERIC FUZZY-BASED RECOMMENDATION APPROACH (GFBRA)

Recommender Systems aim to automatically provide users with personalized information in an overloaded search space. To dual with vagueness and imprecision problems in RS, several researches have been proposed fuzzy based approaches. Even though, these works have incorporated experimental evaluation; they were used in different recommendation scenarios which makes it difficult to have a fair comparison between them. Also, some of them performed an items and/or users clustering before generating recommendations. For this reason they need additional information such as item attributes or trust between users which are not always available. In this paper, we propose to use fuzzy set techniques to predict the rating of a target user for each unrated item. It uses the target user's history in addition with rating of similar users which allows to the target user to contribute in the recommendation process. Experimental results on several datasets seem to be promising in term of MAE (Mean Average Error), RMSE (Root Mean Square Error), accuracy, precision, recall and F-measure.

The Compromise Ratio Method With Intuitionistic Fuzzy Distance for FMAGDM

The compromise ratio method (CRM) is an effective method to solve multiple attribute group decision making (MAGDM). Distance measure of intuitionistic fuzzy (IF) numbers (IFNs) is important for CRM. In this paper, according to the IF distance of IFNs, an extended compromise ratio method (CRM) is developed for (MAGDM) problems which attribute weights and evaluation values of alternatives on attributes are expressed in linguistic variables parameterized using TIFNs. Finally, the effectiveness and practicability of the extended CRM with IF distance are demonstrated by solving a software selection problem.