This work introduces Fuzzy Implication Modeling Theory, a connective-centered framework that supplies an intermediate structural layer between the class and family levels in the subset of fuzzy implications generated by compositions of the three basic fuzzy connectives. The theory distinguishes Fuzzy Implication Models from Fuzzy Implication Model Instances and formalizes their relationship through three propositions addressing generation, traceability and non-uniqueness. Two model-level quantitative descriptors—a Behavior Index and an Intra-Model Variability Index—are proposed to enable comparative analysis across models, and a new Fuzzy Implication Model is introduced and proven to satisfy the defining conditions of a fuzzy implication. A MATLAB-based companion tool with a dedicated model-design module operationalizes the theory. Taken together, the framework provides a structured lens for organizing, analyzing and selecting fuzzy implication operators, and opens paths for both further theoretical development and applied studies.

The aim of this paper is the construction and comparison of fuzzy implications derived from four different fuzzy negations, namely Zadeh, Yager, Sugeno, and Power. A comparative framework is developed by examining all pairwise combinations of these negations to determine how the corresponding fuzzy implications are ranked. The proposed methodology incorporates the fuzzification of real meteorological data, using four membership functions. The resulting membership degrees are used as inputs for the fuzzy implication operators. The results after extensive tests indicate that the fuzzy implication constructed using Sugeno negation, with parameter λ = −0.9, provides the highest percentages of values greater than or equal to 0.9 and equal to 1. For the winter dataset, the scalene triangle achieves optimal performance for m = 470 and strong performance for m = 40. For the summer dataset, the isosceles trapezium yields optimal performance for m = 83 and strong performance for m = 7. In conclusion, when the parameter λ = −0.9, the Sugeno fuzzy implication is ranked among the first or the second ranking category depending on the fuzzified values of parameter x demonstrating its effectiveness for real-data applications.

The objective of this paper is to compare a fuzzy implication produced by t-conorm probor with three other fuzzy implications constructed by t-conorms max, Einstein, and Lukasiewicz. Firstly, in methodology, six pairs of combinations of five t-conorm comparisons are performed in order to find the ranking order of five fuzzy implications. Moreover, the evaluation and calculation of the four fuzzy implications (probor, max, Einstein, and Lukasiewicz) are made using meteorological data, fuzzifying the crisp values of temperature and humidity, constructing four membership degree functions, and inserting as inputs the membership degrees of meteorological variables into the two variables of the fuzzy implications. Finally, extensive tests are made so as to find which membership degree function and which fuzzy implication receives the best and the worst results. The key findings are that the application of isosceles trapezium to the fuzzy implications of Probor and Einstein gives the best values, while fuzzy implication Lukasiewicz, although it was found to be first in the ranking order, is rejected due to unreliable results. As a result, the crucial role of these implications lies in the fact that they are non-symmetrical, i.e., there is a clear difference between the cause and the causal.

In this paper a family of fuzzy implications is derived using the operation of disjunction repeatedly and a new methodology of generating fuzzy implications is proposed. The set of the related fuzzy implication axioms was considered in order to check, which of them are satisfied. A relation is found and proven seeking the optimum number of repetitions according to the desired truth value of the implications. Finally, a large number of fuzzy implications was applied and compared using the data from temperature and humidity in a certain period of time. The proposed general formulae are verified by the computed results.

In this paper, we present two new classes of fuzzy negations. They are an extension of a well-known class of fuzzy negations, the Sugeno Class. We use it as a base for our work for the first two construction methods. The first method generates rational fuzzy negations, where we use a second-degree polynomial with two parameters. We investigate which of these two conditions must be satisfied to be a fuzzy negation. In the second method, we use an increasing function instead of the parameter δ of the Sugeno class. In this method, using an arbitrary increasing function with specific conditions, fuzzy negations are produced, not just rational ones. Moreover, we compare the equilibrium points of the produced fuzzy negation of the first method and the Sugeno class. We use the equilibrium point to present a novel method which produces strong fuzzy negations by using two decreasing functions which satisfy specific conditions. We also investigate the convexity of the new fuzzy negation. We give some conditions that coefficients of fuzzy negation of the first method must satisfy in order to be convex. We present some examples of the new fuzzy negations, and we use them to generate new non-symmetric fuzzy implications by using well-known production methods of non-symmetric fuzzy implications. We use convex fuzzy negations as decreasing functions to construct an Archimedean copula. Finally, we investigate the quadratic form of the copula and the conditions that the coefficients of the first method and the increasing function of the second method must satisfy in order to generate new copulas of this form.

Fuzzy implication models play a crucial role in the field of fuzzy logic. The reason behind this reality is the fact that fuzzy implications are influenced by the properties of the model used for their creation. The importance of the mentioned models increases due to the fact that there is a need for new fuzzy implications for use in artificial intelligence and other applications. So, this paper aims to resolve this problem by creating a new model. This model, named (S,T,N) by the authors, is an evolution from previous models as it utilizes all of the basic logical fuzzy connectives in a new composition that emphasizes the use of as many connectives as practically possible. Moreover, a computer program has been developed to display various interpretations of the proposed model and allow the readers to form a deeper understanding of the paper’s research. The results provided by the research conducted are mainly due to the development of the new fuzzy implication model and, secondarily, the new tool for displaying the capabilities of the implication model. Finally, the conclusions drawn from the paper proved that the search for new fuzzy implications should not only be targeted at new research directions but also at more established ones. Furthermore, the program displayed the strong capabilities of computer-assisted computations since it allowed for rapid checking of multiple implications, thus easing the researcher’s task of practically verifying the new model’s validity.

In this paper, we develop a new computational model of Fuzzy Credibility Numbers (FCNs) with the usage of Archimedean Copulas. This process is achieved through the extension of the existing operations of FCNs. Following this extension procedure, the introduction of Archimedean Copula Weighted Arithmetic Averaging Aggregation Operator (ACWAAAO) for FCNs is achieved. Finally, a case study and comparison of the Multiple Attribute Decision Making (MADM) results is conducted.

The scientific field of fuzzy logic has provided multiple practical applications that have proven it's usefulness. However, there are still many consepts that have not been completely studied. So, in order to further expand the applications of fuzzy logic, the purpose of this paper is the creation of new parametric fuzzy implications via the two main fuzzy connectives, N-negations and T-norms. The N-negations used are the Nλ, Nω and Nα and the conjunctions are the TM, TP and TLK. The main benefit of the approach mentioned is that the produced parametric fuzzy implications as well as the strategy used to create them offer more flexibility and speed in comparison to other methods of generating fuzzy implications and their products.

In this research paper, a generator of fuzzy methods based on theorems and axioms of fuzzy logic is derived, analyzed and applied. The family presented generates fuzzy implications according to the value of a selected parameter. The obtained fuzzy implications should satisfy a number of axioms, and the conditions of satisfying the maximum number of axioms are denoted. New theorems are stated and proven based on the rule that the fuzzy function of fuzzy implication, which is strong, leads to fuzzy negation. In this work, the data taken were fuzzified for the application of the new formulae. The fuzzification of the data was undertaken using four kinds of membership degree functions. The new fuzzy functions were compared based on the results obtained after a number of repetitions. The new proposed methodology presents a new family of fuzzy implications, and also an algorithm is shown that produces fuzzy implications so as to be able to select the optimal method of the generator according to the value of a free parameter.

Fuzzy logic is becoming one of the most-influential fields of modern mathematics with applications that impact not only other sciences, but society in general. This newly found interest in fuzzy logic is in part due to the crucial role it plays in the development of artificial intelligence. As a result, new tools and practices for the development of the above-mentioned field are in high demand. This is one of the issues this paper was composed to address. To be more specific, a sizable part of fuzzy logic is the study of fuzzy connectives. However, the current method used to generalize them is restricted to the use of basic automorphisms, which hinders the creation of new fuzzy connectives. For this reason, in this paper, a new method of generalization is conceived of that aims to generalize the fuzzy connectives using polynomial automorphism functions instead. The creation of these automorphisms is achieved through numerical analysis, an endeavor that is supported with programming applications that, using mathematical modeling, validate and visualize the research. Furthermore, the automorphisms satisfy all the necessary criteria that have been established for use in the generalization process and, consequently, are used to successfully generalize fuzzy connectives. The result of the new generalization method is the creation of new usable and flexible fuzzy connectives, which is very promising for the future development of the field.

In the present research paper we propose a new generator of families of numerical methods with increasing number of internal layers in an attempt to achieve higher order accuracy. The intermediate stages consist of predictor-corrector methods. The final layer is a symmetric two step method with constant coefficients and also free parameters. Those parameters define each family of methods. At first the method is constructed with unknown parameters and subsequently their value is estimated in order to fulfill the requirement of maximum phase-lag order. The stability of the new numerical algorithm is analyzed and the local truncation error is computed. The generator of the new families is applied to well known problems and is found to be more efficient compared to other methods and numerical methods generators with similar characteristics, which attempt to numerically solve such problems.

In this paper, we propose a fuzzy logic–based mathematical model of a sequence of earthquakes using fuzzy reasoning tools. We formed a set of fuzzy implications in order to study them, and we computed their deviation, so that we could compare them and conclude about the most accurate one. The compositional rule of inference was considered, which is based on the generalized modus ponens scheme. The new fuzzy methodology was used for each implication. The data required for the implications were obtained from the aftershocks of an earthquake with significant effects in a specific area. The magnitude of the aftershocks and their time difference from the main incident provided the values for the new fuzzy algorithm application. Two samples were selected relative with the seismic activity, which occurred the following days. The one sample consisted of 30 values, and the other sample from all the values found in the data archives of the National Observatory of Athens. Results were shown for both samples. So a mathematical technique, which reproduces the incidents using basic information and based on only two parameters, is developed for the simulation of a seismic sequence, which follows a strong earthquake.

In this paper we deal with the subject of a seismic sequence. Assuming that the major earthquake in a specified region has a certain intensity level, we study all the earthquakes, which follow, according to their magnitude and to the time difference from the main one. Therefore, using a sample and collecting our data about the main incident and the seismic activity for the next days, we compute the empirical implication and a number of another fuzzy implications in order to compare them and choose the most appropriate.

Nearly 1.3 million people die in road crashes annually in a global scale, on average 3,287 deaths per day [1]. Moreover, 20-50 million are injured or disabled [1]. Road traffic crashes rank as the 9th leading cause of deaths (2.2% of deaths globally) [1]. This research paper presents the contribution of soft computing (fuzzy logic) towards modeling of this huge problem. More specifically, the municipalities of Greece are classified according to their respective road accidents occurrence, by means of a special measure of similarity and consideration of the generating fuzzy transitive closure (FTC).