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Atanassov's intuitionistic fuzzy sets (IFSs) are a very convenient tool for describing alternatives/options while making decisions because they make it possible to naturally represent the pros, cons, and hesitation. The IFSs have attracted a significant interest and have been applied in various fields. Of course, their use poses some challenges. One of the main challenges is the ranking of alternatives/options described by the intuitionistic fuzzy sets, to be called for brevity the intuitionistic fuzzy alternatives. This is a crucial issue, notably for the applications, for instance, in decision making. We first present in detail and analyze the benefits of a method we introduced previously (cf. Szmidt and Kacprzyk [1]). For this method, we augment the original assumptions with an additional assumption, which is justified and inherently reasonable. As a result, we obtain formulas which are better justified than those previously used as they explicitly consider the arguments in favor (pro), against (con), and hesitance. Since the intuitionistic fuzzy alternatives can not be linearly ranked, then the additional assumptions during the ranking process are necessary. We address these issues and analyze examples to clarify our new approach. We examine some other methods discussed in the literature and analyze their results, and show that the new assumptions reconcile some misconceptions raised by those other papers. [ABSTRACT FROM AUTHOR]

Group decision-making involves selecting among limited options. Experts share their perspectives in a comparative debate but then evaluate alternatives using preference relations, which can result in inconsistencies between their expressions and assessments. To address this, a method is proposed that automates the generation of these relationships from the debate comments, classifying them into positive and negative using sentiment analysis, namely with the Large Language Model. A new operator is introduced that weights these comments to calculate preference relations. Furthermore, modification of the relationships is allowed if the experts so wish. Moreover, another operator is incorporated that adjusts the weight of each expert according to his or her active participation in the discussion, assigning more weight to those who contribute more comments. Finally, this innovative method promotes coherence and equal participation in group decision-making by employing an innovative sentiment analysis detection system. [ABSTRACT FROM AUTHOR]

Fuzzy graphs (FGs) are efficient mathematical models for analyzing many problems of daily life. Various problems in the fields of physics, telecommunication science, psychology and genetics can be modeled and solved with the help of fuzzy graph theory. One of the most widely used types of FG is vague graph (VG). VGs play an important role in various fields such as computer science, psychology, medicine, and political sciences and are used to find effective people in an organization or social institution. Today, connectivity indices are used in computer networks and economics to find the most suitable place for construction. These indices also have many applications in medical sciences, including ultrasound and radiology. Hence, in this research, we introduce connectivity index (CI), average connectivity index (ACI), and randic index (RI) in VGs with some examples. Likewise, some new vertices such as enhancing vertex (EV), reducing vertex (RV), and neutral vertex (NV) are described. Finally, an application of CI in the selecting town for building a school is given. [ABSTRACT FROM AUTHOR]

A new approach to the solution of an important problem of a better use of personnel, sales representatives, for cable television service system providers in Taiwan is discussed. A new multi-criteria decision-making (MCDM) model is proposed for personnel selection meant as a process of selecting candidates who are qualified to perform specific jobs in the best possible way. The new approach involves first the selection of criteria for the sales representatives. Fuzzy importanceperformance analysis (FIPA) is used to design a questionnaire, and interviews with executives are performed. A new method for the determination of importance and degree of satisfaction of the criteria proposes is developed. Decision making trial and evaluation laboratory (DEMATEL) method is used to establish interactions between the dimensions and criteria. Analytic network process (ANP) is then used to find the weights of each dimension and selection criterion based on their interaction via pairwise comparison. The integrated weights obtained for each selection criterion are then employed in technique for order preference by similarity to ideal solution (TOPSIS) to select the best sales representative. A realistic example is provided. [ABSTRACT FROM AUTHOR]

Today, fuzzy graphs (FGs) have made significant progress in other sciences and help researchers to always make the best choice in complex problems. A type of FG that is widely used in medical and psychological sciences is vague graph (VG). VGs play an important role in various fields such as computer science, psychology, medicine, and political sciences and are used to find effective people in an organization or social institution. Regularity is very important in the VG theory because it can help a lot in identifying people with high ability in an institute or social group. In addition to regularity, the degree of nodes and edges also play an effective role in this relationship and can evaluate the ability and knowledge of people. Therefore, in this paper, first perfectly regular vague graph (PRVG) is introduced and investigated the regularity of vertices. The totally accurate communication between all connected vertices is described by defining completely open neighborhood degree (COND) and completely closed neighborhood degree (CCND) of vertices and edges in a VG. In the following, ((s1, s2),m, (t1, t2))- regular vague graph and totally ((s1, s2),m, (t1, t2))-regular vague graph are introduced and a necessary and sufficient condition under which they are equivalent is presented. Psychologists play a significant role in creating a healthy society in terms of physical and mental health. They help people in the society to better understand their emotions and behaviors and manage them to live a better life. So in the final part, an application of COND and CCND in psychological sciences has been introduced. [ABSTRACT FROM AUTHOR]

Problems of modeling uncertainty and imprecision for the analysis of insufficient expert data (IED) are considered in the environment of interactive multi-group decision-making (MGDM). Based on the Choquet finite integral, a moments' method for the IED is developed for the evaluation of the associated probabilities class (APC) of Choquet's second-order capacity based on the informational entropy maximum principle. Based on the IED new approach of the lower and upper Choquet's second-order capacities, identification is developed. The second pole of insufficient expert data, the data imprecision indicator, is presented in the form of a fuzzy subset and image on the alternatives set. In the environment of the Dempster–Shafer belief structure, connections between an associated possibilities class (APosC), with the APC, and an associated focal probabilities class (AFPC) are constructed. In the approach of A. Kaufman's theory of expertons, based on the APosC and the AFPC unique fuzzy subset, the IED image on the alternatives set is constructed. Based on Sugeno's finite integral most typical value (MTV), as a prediction on possible alternatives set, the IED is constructed. In the example, a sensitive and comparative analysis is provided for the evaluation of the new approach's stability and reliability. [ABSTRACT FROM AUTHOR]

By reviewing the current state of the art, this paper opens a Special Section titled "The Internet of Things and AI-driven optimization in the Industry 4.0 paradigm". The topics of this section are part of the broader issues of integration of IoT devices, cloud computing, big data analytics, and artificial intelligence to optimize industrial processes and increase efficiency. It also focuses on how to use modern methods (i.e. computerization, robotization, automation, machine learning, new business models, etc.) to integrate the entire manufacturing industry around current and future economic and social goals. The article presents the state of knowledge on the use of the Internet of Things and optimization based on artificial intelligence within the Industry 4.0 paradigm. The authors review the previous and current state of knowledge in this field and describe known opportunities, limitations, directions for further research, and industrial applications of the most promising ideas and technologies, considering technological, economic, and social opportunities. [ABSTRACT FROM AUTHOR]

Socio-cognitive computing is a paradigm developed for the last several years in our research group. It consists of introducing mechanisms inspired by inter-individual learning and cognition into metaheuristics. Different versions of the paradigm have been successfully applied in hybridizing Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), Genetic Algorithms, Differential Evolution, and Evolutionary Multi-agent System (EMAS) metaheuristics. In this paper, we have followed our previous experiences in order to propose a novel mutation based on socio-cognitive mechanism and test it based on Evolution Strategy (ES). The newly constructed versions were applied to popular benchmarks and compared with their reference versions. [ABSTRACT FROM AUTHOR]

The document is an editorial from the Bulletin of the Polish Academy of Sciences: Technical Sciences. It introduces a special section on IIoT (Industrial Internet of Things) and AI-based optimization. The aim of the section is to present the latest developments and applications in these areas, including methods and systems in IIoT, IoT infrastructure, and applications of AI in IoT. The topics covered align with current research trends in computer science, telecommunications, and mechanical engineering. The document also highlights the importance of integrating intelligent machines and systems in industry and the role of AI in solving complex problems. [Extracted from the article]

Vague graphs (VGs) play an important role in various fields such as computer science, psychology, medicine, political science, etc. and are used to effectively and efficiently find proper people in an organization or social institution. Therefore, in this paper, for the first time, we define the concept of a vague picture fuzzy graph (VPFG) and examine its properties. Likewise, the concepts of a complete-VPFG and a strong- VPFGs are introduced. First, we present several kinds of operations to the VPFGs and then give various products of the VPFGs. New terms such as the order and size, path, busy value, neighborhood degree, isomorphism, and complement of the VPFG are defined. Finally, an application of the VPFG to find the most effective person in a hospital is shown. [ABSTRACT FROM AUTHOR]

For decreasing service centers' selection risks in emergency facility location selection, it is crucial to have selected candidate service centers within deeply detailed facility location selection model. To achieve this, a new approach developed in this article involves two stages. In the first stage, the fuzzy multi-attribute group decision making (MAGDM) model for evaluation of the selection of candidate service centers is created. For the aggregation of experts' assessments of candidate service centers (with respect to attributes) aggregation operators' approach is used. Experts' assessments are presented in fuzzy terms with semantic form of triangular fuzzy numbers. For the deeply detailed facility location selection modeling and for the intellectual activity of experts in their evaluations, pairwise interactions between attributes of MAGDM model are considered in the construction of the second-order additive triangular fuzzy valued fuzzy measure (TFVFM). The associated triangular fuzzy probability averaging (As-TFPA) aggregation operators' family is constructed with respect to TFVFM. Analytical properties of the As-TFPA operators are studied. The new operators are certain extensions of the well-known Choquet integral operator. The extensions, in contrast to the Choquet aggregation, consider all possible pair-wise interactions of the attributes by introducing associated fuzzy probabilities of a TFVFM. At the end of the first stage, a candidate service center's selection index is defined as As-TFPA operator's aggregation value on experts' assessments with respect to attributes. At the second stage, fuzzy multi-objective facility location set covering problem (MOFLSCP) is created for facility location selection optimal planning with new criteria: (1) maximization of candidate service centers selection index and classical two criteria, (2) minimization of the total cost needed to open service centers and (3) minimization of number of agents needed to operate the opened service centers. For the constructed two-stage methodology a simulation example of emergency service facility location planning for a city is considered. The example gives the Pareto fronts obtained by As-TFPA operators, the Choquet integral-TFCA operator and well-known TOPSIS approach, for optimal selecting candidate sites for the servicing of demand points. The comparative analysis identifies that the differences in the Pareto solutions, obtained by using As-TFPA operators and TFCA operator or TOPSIS aggregation, are also caused by the fact that TFCA operator or TOPSIS approach considers the pair interaction indexes for only one consonant structure of attributes. While new As-TFPA aggregations provide all pairwise interactions for all consonant structures. [ABSTRACT FROM AUTHOR]

We discuss some aspects of similarity measures in the context of Atanassov's intuitionistic fuzzy sets (IFSs, for short). IFSs, proposed in 1983, are a relatively new tool for the modeling and simulation and, because of their construction, present us with new challenges as far the similarity measures are concerned. Specifically, we claim that the distances alone are not a proper measure of similarity for the IFSs. We stress the role of a lack of knowledge concerning elements (options, decisions, etc.) and point out the role of the opposing (complementing) elements. We also pay attention to the fact that it is not justified to talk about similarity when one has not enough knowledge about the compared objects/elements. Some novel measures of similarity are presented. [ABSTRACT FROM AUTHOR]

We propose a new approach to the bipolar database queries, which involve a necessary (required) and optional (desired) conditions, connected with a non-conventional aggregation operator "and possibly", combined with a context, exemplified by "find houses which are cheap and – with respect to other houses in town – possibly close to a railroad station". We use our winnow operator based interpretation of the bipolar queries. We assume that the query, posed by the human user, involves terms, which do not directly relate to attributes, and which are then to be decoded using a concept of a query hierarchy, leading to the queries, which involve terms directly related to attribute values. The original query is considered to be of level 0, at the bottom of the precisiation hierarchy, then its required and optional parts are assumed to be bipolar queries themselves, both accounting for context. The precisiation proceeds further, to level 1 queries, level 2, etc. A real estate related example is provided as illustration. [ABSTRACT FROM AUTHOR]

The use of discrete probabilistic distributions is relevant to many practical tasks, especially in present-day situations where the data on distribution are insufficient and expert knowledge and evaluations are the only instruments for the restoration of probability distributions. However, in such cases, uncertainty arises, and it becomes necessary to build suitable approaches to overcome it. In this direction, this paper discusses a new approach of fuzzy binomial distributions (BDs) and their extensions. Four cases are considered: (1) When the elementary events are fuzzy. Based on this information, the probabilistic distribution of the corresponding fuzzy-random binomial variable is calculated. The conditions of restrictions on this distribution are obtained, and it is shown that these conditions depend on the ratio of success and failure of membership levels. The formulas for the generating function (GF) of the constructed distribution and the first and second order moments are also obtained. The Poisson distribution is calculated as the limit case of a fuzzy-random binomial experiment. (2) When the number of successes is of a fuzzy nature and is represented as a fuzzy subset of the set of possible success numbers. The formula for calculating the probability of convolution of binomial dependent fuzzy events is obtained, and the corresponding GF is built. As a result, the scheme for calculating the mathematical expectation of the number of fuzzy successes is defined. (3) When the spectrum of the extended distribution is fuzzy. The discussion is based on the concepts of a fuzzy-random event and its probability, as well as the notion of fuzzy random events independence. The fuzzy binomial upper distribution is specifically considered. In this case the fuzziness is represented by the membership levels of the binomial and non-binomial events of the complete failure complex. The GF of the constructed distribution and the first-order moment of the distribution are also calculated. Sufficient conditions for the existence of a limit distribution and a Poisson distribution are also obtained. (4) As is known, based on the analysis of lexical material, the linguistic spectrum of the statistical process of word-formation becomes two-component when switching to vocabulary. For this, two variants of the hybrid fuzzy-probabilistic process are constructed, which can be used in the analysis of the linguistic spectrum of the statistical process of word-formation. A fuzzy extension of standard Fuchs distribution is also presented, where the fuzziness is reflected in the growing numbers of failures. For better representation of the results, the examples of fuzzy BD are illustrated in each section. [ABSTRACT FROM AUTHOR]

We advocate the use of the concept of a vague graph which provides powerful tools and techniques for the modeling of many processes and systems, notably namely dynamic process in physical, biological and social systems. By making it possible to use the upper and lower degree of membership of an element, the vague graph can provide an additional expressive power for the representation and modeling under uncertain and imprecise information. The existence of an upper and lower degree of membership may in many cases be more natural and convenient for the human being than the degree of membership and non-membership as in the intuitionistic graphs which can be considered equivalent, up to the isomorphism, to the vague graphs. An application of the new concept of domination in the vague graphs to an analysis of some nonmedical aspects related to the Covid-19 vaccination is shown. [ABSTRACT FROM AUTHOR]

Symbiotic autonomous systems (SAS) are advanced intelligent and cognitive systems that exhibit autonomous collective intelligence enabled by coherent symbiosis of human–machine interactions in hybrid societies. Basic research in the emerging field of SAS has triggered advanced general-AI technologies that either function without human intervention or synergize humans and intelligent machines in coherent cognitive systems. This work presents a theoretical framework of SAS underpinned by the latest advances in intelligence, cognition, computer, and system sciences. SAS are characterized by the composition of autonomous and symbiotic systems that adopt bio-brain-social-inspired and heterogeneously synergized structures and autonomous behaviours. This paper explores the cognitive and mathematical foundations of SAS. The challenges to seamless human–machine interactions in a hybrid environment are addressed. SAS-based collective intelligence is explored in order to augment human capability by autonomous machine intelligence towards the next generation of general AI, cognitive computers, and trustworthy mission-critical intelligent systems. Emerging paradigms and engineering applications of SAS are elaborated via autonomous knowledge learning systems that symbiotically work between humans and cognitive robots. This article is part of the theme issue 'Towards symbiotic autonomous systems'. [ABSTRACT FROM AUTHOR]

The negative results arising from the application of modern social choice theory to the aggregation of individual opinions may be minimized by modifying the assumptions and problem formulations. This may be achieved by using the theories of probability or randomness, fuzziness, and rough sets to characterize imprecision in voting and collective choice problems. An example is the use of fuzzy preference relations and fuzzy majorities in probabilistic voting schemes.

Fuzzy graphs, notably fuzzy incidence graphs, have been known to be an effective and efficient tool to represent and solve many complex real world problems in which imprecise data and information are crucial. We extend the concept of a fuzzy incidence graph to an intuitionistic fuzzy incidence graph, and show some of its important properties. In particular, we discuss the well known problems of: edge domination, irredundant sets and their cardinalities related to the domination, etc. Some examples of applications of the new intuitionistic fuzzy incidence graphs we outlined. [ABSTRACT FROM AUTHOR]

The volatility is a dispersion technique widely used in statistics and economics. This paper presents a new way to calculate volatility by using different extensions of the ordered weighted average (OWA) operator. This approach is called the induced heavy ordered weighted moving average (IHOWMA) volatility. The main advantage of this operator is that the classical volatility formula only takes into account the standard deviation and the average, while with this formulation it is possible to aggregate information according to the decision maker knowledge, expectations and attitude about the future. Some particular cases are also presented when the aggregation information process is applied only on the standard deviation or on the average. An example in three different exchange rates for 2016 are presented, these are for: USD/MXN, EUR/MXN and EUR/USD. [ABSTRACT FROM AUTHOR]

This work presents a new perspective on how Zadeh's ideas related to fuzzy logic and computing with words have influenced the crucial issue of information aggregation and have led to what may be called a human-centric aggregation. We indicate a need to develop tools and techniques to reflect some fine shades of meaning regarding what can be considered the very purpose of human-centric aggregation, notably stated by various modalities in natural language specifications, in particular the usuality. We advocate the use of the ordered weighted average (OWA) operator, which is a formidable tool that can easily be tailored to a user?s intention as to the purpose and method of aggregation, generalizing many simple and natural aggregation types, such as the arithmetic mean, maximum and minimum, and probability. We show some of the most representative extensions and generalizations, including the induced OWA, the generalized OWA, the probabilistic OWA, and the OWA distance. We show their use in the basic case of the aggregation of numerical values and in social choice (voting) results. Then, we claim that linguistic data summaries in Yager?s sense can be considered an "ultimately human consistent" form of human-centric aggregation and show how the OWA operators can be used therein. [ABSTRACT FROM AUTHOR]

The paper deals with the problem of clustering of intuitionistic fuzzy data. A modification of a heuristic algorithm of possibilistic clustering for intuitionistic fuzzy data that account for the information coming from the labeled objects is proposed. The paper describes the basic ideas of the method and gives the plan of the partially supervised version of a direct possibilistic clustering algorithm. Illustrative examples of application of the method to two intuitionistic fuzzy data sets are provided. Preliminary conclusions are formulated and some perspectives outlined, notably for the analysis of agricultural value chain. [ABSTRACT FROM AUTHOR]

Abstract: Human beings represent and process imperfect information in a natural way, whereas effective approaches are still being looked for in the area of soft computing. Atanassov's intuitionistic fuzzy sets and especially Atanassov's intuitionistic fuzzy relations are are tools that make it possible to model in an effective way imperfect information. In this paper, we discuss the transitivity problem of Atanassov's intuitionistic fuzzy relations. The transitivity property reflects the consistency of a preference relation. Therefore, transitivity is important from the point of view of real problems appearing, e.g., in group decision making, choice, and utility theories widely making use of the preference procedures. We study here in detail transitivity property of Atanassov's intuitionistic fuzzy relations and propose a new algorithm for generating weakly transitivity among the alternatives (options) considered. Next, making use of the new algorithm we propose a procedure of ranking of the alternatives in a group decision‐making problem. [ABSTRACT FROM AUTHOR]

The Hamming distance is a well-known measure that is designed to provide insights into the similarity between two strings of information. In this study, we use the Hamming distance, the optimal deviation model, and the generalized ordered weighted logarithmic averaging (GOWLA) operator to develop the ordered weighted logarithmic averaging distance (OWLAD) operator and the generalized ordered weighted logarithmic averaging distance (GOWLAD) operator. The main advantage of these operators is the possibility of modeling a wider range of complex representations of problems under the assumption of an ideal possibility. We study the main properties, alternative formulations, and families of the proposed operators. We analyze multiple classical measures to characterize the weighting vector and propose alternatives to deal with the logarithmic properties of the operators. Furthermore, we present generalizations of the operators, which are obtained by studying their weighting vectors and the lambda parameter. Finally, an illustrative example regarding innovation project management measurement is proposed, in which a multi-expert analysis and several of the newly introduced operators are utilized. [ABSTRACT FROM AUTHOR]