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In this work, our interest is restricted to study the links among $L$-fuzzy pre-proximity spaces and $L$-fuzzy ideals. We also show that there is a Galois correspondence between the categories of stratified $L$-fuzzy ideals and $L$-fuzzy pre-proximity spaces. Finally, we establish the relationship between $L$-fuzzy prime ideal spaces and $L$-fuzzy co-topological spaces.

The development index (DI) of a region is defined by various elements such as geography, population density, gross domestic product (GDP), GDP per capita, natural resources, markets, economic development, and other relevant factors. The traditional approach to classification usually depends on the country’s total land area measured in square kilometers. Nevertheless, the transition points between different levels of development size (small, medium, and giant) are highly subjective, resulting in frequent inconsistencies and conflicts. Fuzzy logic, a superset of conventional (Boolean) logic, extends the framework to include partial truth values, ranging from “fully true” to “totally false”. This development is especially essential since human reasoning, particularly commonsense reasoning, is approximate rather than precise. This study offers a model that uses fuzzy logic and the Mamdani fuzzy inference system (MFIS) to evaluate nine main cities in Pakistan based on their populations (POPs), gross domestic products (GDPs), and literacy rates (LR). The model includes variables for the antecedents (inputs) and the consequences (outputs). The input variables are the population (POP), GDP, and LR, while the output variable is the DI. The MFIS is used with Python programming tools, including the scikit-fuzzy library for inference and aggregation and matplotlib for graphics.

Fuzzy logic is extended toward dynamic adaptation of the degree of fuzziness. The motivation is to explain the process of learning as a joint model improvement and fuzziness reduction. A learning system with fuzzy models is introduced. Initially, the system is in a highly fuzzy state of uncertain knowledge, and it dynamically evolves into a low-fuzzy state of certain knowledge. We present an image recognition example of patterns below clutter. The paper discusses relationships to formal logic, fuzzy logic, complexity and draws tentative connections to Aristotelian theory of forms and working of the mind.

Image enhancement is used to correct contrast deficiencies and to improve the quality of an image. It is essential and critical to extracting features and segmenting images. This paper presents a novel contrast enhancement algorithm based on newly defined texture histogram and fuzzy entropy with the ability to preserve edges and details, while avoiding noise amplification and over-enhancement. To demonstrate the performance, the proposed algorithm is tested on a variety of images and compared with other enhancement algorithms. Experimental results proved that the proposed method has better performance in enhancing images without over-enhancement and under-enhancement.

The information coded in natural language is called natural language information. It can be employed to analyze risks by computing with words. The disjunction and Cartesian product of fuzzy sets are the basic arithmetics to compute a probability distribution representing the random uncertainty of the risk source. An approach to infer a risk with words is to represent the risk system by using probabilistic and possibilistic constraints. In this paper, with fuzzy logic, we give a sample to verify that the suggested approach is more flexible and effective.

This paper deals with the validity in fuzzy logic of some classical schemes of reasoning, namely, with those of disjunctive reasoning, resolution, reductio ad absurdum, and the so-called constructive dilemma.

In this paper, we propose a wet lab algorithm for classification of SODAR data by DNA computing. The concept of DNA computing is essentially exploited to generate the classifier algorithm in the wet lab. The classifier is based on a new concept of similarity-based fuzzy reasoning suitable for wet lab implementation. This new concept of similarity-based fuzzy reasoning is different from conventional approach to fuzzy reasoning based on similarity measure and also replaces the logical aspect of classical fuzzy reasoning by DNA chemistry. Thus, we add a new dimension to the existing forms of fuzzy reasoning by bringing it down to nanoscale. We exploit the concept of massive parallelism of DNA computing by designing this new classifier in the wet lab. This newly designed classifier is very much generalized in nature and apart from SODAR data, this methodology can be applied to other types of data also. To achieve our goal we first fuzzify the given SODAR data in a form of synthetic DNA sequence which is called fuzzy DNA and which handles the vague concept of human reasoning. In the present approach, we can avoid the tedious choice of a suitable implication operator (for a particular operation) necessary for the classical approach to fuzzy reasoning based on fuzzy logic. We adopt the basic notion of DNA computing based on standard DNA operations. We consider double stranded DNA sequences, whereas, most of the existing models of DNA computation are based on single stranded DNA sequences. In the present model, we consider double stranded DNA sequences with a specific aim of measuring similarity between two DNA sequences. Such similarity measure is essential for designing the classifier in the wet lab. Note that, we have developed a completely new measure of similarity based on base pair difference which is absolutely different from the existing measure of similarity and which is very much suitable for expert system approach to classifier design, using DNA computing. In the present model of DNA computing, the end result of the wet lab algorithm produces multi valued status which can be linguistically interpreted to match the perception of an expert.

Computing with words, CWW, is considered in the context of natural language functioning, unifying language with thinking. Previous attempts at modeling natural languages as well as thinking processes in artificial intelligence have met with computational complexity. To overcome computational complexity we use dynamic logic (DL), an extension of fuzzy logic describing fuzzy to crisp transitions. We suggest a possible architecture motivated by mathematical and neural considerations. We discuss the reasons why CWW has to be modeled jointly with thinking and propose an architecture consistent with brain neural structure and with a wealth of psychological knowledge. The proposed architecture implies the existence of relationships between languages and cultures. We discuss these implications for further evolution of English and Chinese cultures, and for cultural effects of interactions between natural languages and CWW.

Carotid intima-medial thickness (CIMT) allows for early detection of carotid atherosclerotic vascular disease. Using fuzzy logic techniques, we propose a model for calculating the risk for predicting CIMT using expert opinion and various factors associated with CIMT in recently menopausal women. Study participants were enrolled in the Kronos Early Estrogen Prevention Study (KEEPS), a four year study where participants were assigned to either oral or transdermal hormone therapy or to the placebo group. The fuzzy mathematical model uses five fuzzy logic methods to calculate this risk factor for CIMT, including the analytic hierarchy process (AHP) method, Guiasu method, Yen method, Dempster–Shafer (DS) method, and the set valued statistical method (SVSM). The four methods, AHP, Guiasu, Yen, DS, and SVSM, were correlated to each other according to the Pearson ranking method. In addition, results showed that the estrogen treatment groups showed a statically significant decrease in calculated CIMT risk compared to placebo when all the methods were combined together (p = 0.0017). Our fuzzy mathematical model provides the first fuzzy mathematical model to predict the risk of CIMT in recently menopausal women and menopausal hormone therapy may be beneficial in reducing this risk.

Previously, the biological factors were weighed by the expert opinions. In this paper, we evaluate the risk factors proposed by the expert opinions. We use fuzzy logic techniques for predicting risk for development of carotid intima–medial thickness (CIMT) using expert opinion and various factors associated with CIMT in recently menopausal women. Study participants were enrolled in the Kronos Early Estrogen Prevention Study (KEEPS), a four-year study where participants were assigned to either oral or transdermal hormone treatments or to placebo. We use preference modeling techniques to determine the consensus winner of the causal factors. We use a measure to determine the degree to which one factor is preferred to another. We also determine the extent to which a factor is preferred to another by "most" experts. We determine the degree to which the experts agree. We consider a model concerning social networks and the effects of these networks on persons' opinions.

We place the concept of dialectic synthesis in a fuzzy logic setting. Our purpose is to use the triplet thesis–antithesis–synthesis in applications to human trafficking and modern slavery. We are particularly interested in a country’s government’s response to its vulnerability to these situations.

In this paper, we propose a wet lab algorithm for prediction of visibility under radiation fog by DNA computing. The model is based on a concept of similarity based fuzzy reasoning suitable for wet lab implementation. The concept of similarity based fuzzy reasoning using DNA sequences is different from conventional approach to fuzzy reasoning. It replaces the logical aspect of classical fuzzy reasoning by DNA chemistry. By the proposed algorithm the tedious job to choose suitable implication operator, which is absolutely necessary for classical fuzzy reasoning, can be avoided. If the fuzzified forms of five observed parameters, i.e. dew point, dew point spread, the rate of change of dew point spread per day, wind speed and sky condition are given, the newly proposed algorithm efficiently predicts the possibility of visibility under radiation fog. The final result of the wet lab algorithm, which is in form of fuzzy DNA, produces multi valued status which can be linguistically interpreted to match the perception of an expert.

Inference systems are intelligent software performed generally to help people take appropriate decisions and solve problems in specific domains. Fuzzy inference systems are a kind of these systems that are based on fuzzy knowledge. To handle the fuzziness in the inference, the compositional rule of inference is used, which has two parameters: a t-norm and an implication operator. However, most of the combinations of t-norm/implication do not give an adequate inference result that coincides with human intuitions. This was the motivation for several works to study these combinations and to identify those that are compatible, in order to guarantee a performance close to that of humans. We are interested in this paper to a more general form of rules, which is complex rules, whose premise is a conjunction of propositions. To obtain the consequence in a fuzzy inference system using the compositional rule of inference with a complex rule, we study, in this work, Lukasiewicz t-norm which was not investigated before in this context. We combine it with known implications, and we verify the satisfaction of some criteria that model human intuitions.

Seas, marine, and coastal regions are integral and essential parts of our ecosystem. Many scientific approaches have been taken to ensure the sustainable use of marine resources. Artificial intelligence (AI) plays a vital role in harvesting resources so that the system regenerates itself for the long term. This paper develops a two-input and two-output fuzzy logic-based model to predict the fisheries’ remaining biomass after harvesting and maintaining a high revenue level in the Bangladesh Sundarbans region. Fishing & tourism are taken as input parameters, and revenue & biomass are taken as output parameters. A total of 20 rules (IF-THEN type) have been generated in the fuzzy rule editor of Fuzzy Inference System (FIS), considering all possible combinations between input–output parameters. The data which we obtained from the real ecosystem exactly corresponds to the results that we got from our proposed model. Our fuzzy logic model yields valid predictions of the remaining biomass level without compromising profit, only by controlling the harvesting and tourist entry.