T-norm Operators Research Articles

Bayesian Inference with Complex Knowledge Graph Evidence

Knowledge Graphs (KGs) provide a widely used format for representing entities and their relationships and have found use in diverse applications including question answering and recommendation. A majority of current research on KG inference has focused on reasoning with atomic facts (triples) and has disregarded the possibility of making complex evidential observations involving logical operators (negation, conjunction, disjunction) and quantifiers (existential, universal). Further, while the application of complex evidence has been explored in KG-based query answering (KGQA) research, in many practical online settings, observations are made sequentially. For example, in KGQA, additional context may be incrementally suggested to narrow down the answer. Or in interactive recommendation, user critiques may be expressed sequentially in order to narrow down a set of preferred items. Both settings are indicative of information filtering or tracking tasks that are reminiscent of belief tracking in Bayesian inference. In fact, in this paper, we precisely cast the problem of belief tracking over unknown KG entities given incremental complex KG evidence as a Bayesian filtering problem. Specifically, we leverage Knowledge-based Model Construction (KBMC) over the logical KG evidence to instantiate a Markov Random Field (MRF) likelihood representation to perform closed-form Bayesian inference with complex KG evidence (BIKG). We experimentally evaluate BIKG in incremental KGQA and interactive recommendation tasks demonstrating that it outperforms non-incremental methodologies and leads to better incorporation of conjunctive evidence vs. existing complex KGQA methods like CQD that leverage fuzzy T-norm operators. Overall, this work demonstrates a novel, efficient, and unified perspective of logic, KGs, and online inference through the lens of closed-form BIKG.

On t-normed integrals with respect to possibility capacities on compacta

Riesz Theorem establishes a correspondence between the set of σ-additive regular Borel measures and the set of linear positively defined functionals. We consider an idempotent analogue of this correspondence between possibility capacities and functionals preserving the maximum operation and t-norm operation using t-normed integrals. Additionally, we establish that this correspondence possesses a categorical sense, representing a morphism of monads. Furthermore, we delve into the investigation of the associated idempotent convexity.

A fuzzy logic based explicit declustering technique

During the spatial estimation of geoscience resource variables, the quantity or quality of minerals and hydrocarbons can be represented by a broad range of properties, including geochemical, geotechnical, or other physical measures. Preferential sampling within the region of interest causes biased global parameters due to clustered sampling patterns. Unbiased sample distribution is essential for conducting conditional simulations to model uncertainty of spatially distributed attributes, e.g. geochemical content of metal or porosity. Therefore, declustering procedures are applied during resource estimation to estimate an unbiased statistical distribution of the measured variables. Traditional techniques such as cell declustering do not consider grade clustering, i.e., the similarity of measured variables within a spatially clustered neighbourhood. This paper presents a declustering technique that explicitly accounts for spatial clustering and the similarity of measured samples' attributes within these spatially clustered samples. In the proposed method, samples were first classified explicitly into spatial and geochemical (grade) clusters using the Fuzzy c-means algorithm. Declustering weights were derived using the Mamdani based Fuzzy Inference System using various T-norm operations. The technique was applied to the publicly available GSLib and Walker Lake datasets. It was shown that the proposed scheme produced more accurate results than those obtained with the traditional declustering technique.

Mixed data-driven sequential three-way decision via subjective–objective dynamic fusion

In the context of granular computing, sequential three-way decision is a useful tool to triadic thinking, triadic computing and triadic processing from coarser to finer under multilevel and multiview granularity space. In this paper, we mainly explore a novel framework of sequential three-way decision for the fusion of mixed data from the subjective and objective dynamic perspectives. The former focuses on the decision maker’s dynamic behavior without considering the time-evolving data, and the latter emphasizes on dealing with dynamic mixed data over time by multi-stage decision-making. We firstly utilize four T-norm operators and kernel-based similarity relations to integrate different types of dynamic data. Then the subjective and objective models of sequential three-way decision are investigated based on decision thresholds, attribute importance and cost reduction. Finally, the comparative experiments are reported to verify that our proposed models can achieve the lower decision cost and the acceptable accuracy.

A social commerce purchasing decision model with trust network and item review information

Shopping without much experience on target items is not unusual in social commerce (s-commerce). Inexperienced users are often influenced by user reviews when making purchasing decisions, which can be easily distorted due to low review quality. To address this issue, this study integrates two important review dimensions into purchasing decision model, i.e. the trust relationships to experienced users and the reliability of experienced users’ reviews. A purchasing decision model for s-commerce is proposed based on trust computation and item reviews. The trust degree of inexperienced users to experienced ones is computed based on item reviews and propagated using the parameterized Hamacher t-norm operator. Based on the item review information, inexperienced users can make the final purchasing decisions on target items with trust information to experienced users and their reliability on item reviews. A numerical example with a data subset of Epinions.com is provided and the comparative analysis is conducted to verify the effectiveness of the proposed method. This study proposes an inexperienced purchasing decision method considering the risk attitude of users with flexible trust propagation parameters, which can provide a new perspective for the s-commerce recommendations.

Application of interval-valued triangular fuzzy numbers and their functional to the healthcare problems

Aim. In healthcare field there exist different types of uncertainty due to medical error generated by human and technologies. In general the crisp value generate loss of precision and inaccuracy about result and therefore the available data is not sufficient to assessed clinical process up to desired degree of accuracy. Therefore fuzzy set theory play as an important and advance role in accuracy of results in healthcare related problems. Methods. Here for more accuracy of result, we use functional fuzzy numbers in this paper. This study uses a new fuzzy fault tree analysis for patient safety risk modelling in healthcare. In this paper we will use level (λ, ρ) interval-valued triangular fuzzy number, their functional, t-norm operation and centre of gravity defuzzification method to evaluate fuzzy failure probability and estimate reliability of system. The effectiveness of these methods is illustrated by an example related to healthcare problems and then we analyse the result obtained with the other existing techniques. Tanaka et al.’s approach has been used to give the rank of basic events of the considered problems. Also, we use functional of fuzzy numbers to analyse the change in fuzzy failure probability. Results. The paper examines the application of the failure tree, t-norm and functional fuzzy numbers in the context of interval-valued triangular fuzzy numbers. The research examined two types of healthcare-specific problems and the corresponding defuzzification techniques for the purpose of reliability analysis using the existing methods. The authors concluded that t-norm is not associated with significant accumulation and identified how a functional fuzzy number affects reliability. Similarly, using the V index method, the least critical events were found for each system.

Incremental fuzzy probability decision-theoretic approaches to dynamic three-way approximations

As a special model of three-way decision, three-way approximations in the fuzzy probability space can be interpreted, represented, and implemented as dividing the universe into three pair-wise disjoint regions, i.e., the positive, negative and boundary regions, which are transformed from the fuzzy membership grades with respect to the fuzzy concept. To consider the temporality and uncertainty of data simultaneously, this paper focuses on the integration of dynamics and fuzziness in the context of three-way approximations. We analyze and investigate three types of fuzzy conditional probability functions based on the fuzzy T-norm operators. Besides, we introduce the matrix-based fuzzy probability decision-theoretic models to dynamic three-way approximations based on the principle of least cost. Subsequently, to solve the time-consuming computational problem, we design the incremental algorithms by the updating strategies of matrices when the attributes evolve over time. Finally, a series of comparative experiments is reported to demonstrate and verify the performance of proposed models.

Rice yield prediction using adaptive Neuro-fuzzy inference system (ANFIS)

In agriculture yield prediction is toughest task around the globe. The agriculture yield depends on various factors such as water, weather, soil characteristics, crop rotation, pest, disease etc., This paper presents a model designed using Adaptive Neuro-Fuzzy Inference System (ANFIS) to predict the yield of rice. ANFIS helps to determine the incompleteness in decision making made by human expert using the learning mechanism. Fuzzy inference system and neural network are combined in ANFIS, the input parameters are passed through input layer and output could be viewed through output layers. Training is involved with iterative adjustment of parameters of the ANFIS using hybrid learning process to diagnosis the yield of rice. ANFIS uses five layers, each layer has its own nodes. Layer1 has the input variables with membership function. T-norm operator that perform the AND operator can be used in layer2. The sum of all rules firing strengths are assigned in layer3. The nodes in layer4 are adaptive and perform the consequent of the rules. Single node that computes the overall output in layer5. With the input parameters Leaf Folder pest incidence(LFI), Sheath Blight disease (SB), Number of Tillers Hill(NH), No. of grains per panicle(GP) and 1000 grain weight(GW) the algorithm is developed to predict the yield of rice. The proposed Fuzzy Prediction Model is effectively “hand crafted” to achieve the desired performance and also used for rice yield prediction.

Generalized Geometric Aggregation Operators Based on T-Norm Operations for Complex Intuitionistic Fuzzy Sets and Their Application to Decision-making

Complex intuitionistic fuzzy set (CIFS) is a special intuitionistic fuzzy set where the membership and non-membership degrees are expressed by a complex-valued membership degree and can more easily describe the vagueness and uncertainty in the real world. Archimedean t-conorm and t-norm (ATT), as an important class of the t-norm (TN) and t-conorm (TC), have greater flexibility in the information fusion process. In this paper, we extend the ATT to CIFSs and present some generalized geometric aggregation operators, which can be used to handle the multiple criteria decision-making (MCDM) problems. For it, we firstly define some new operational laws of the CIFSs based on ATT, then some weighted geometric aggregation operators based on proposed operations are proposed. Further, some desirable properties and special cases of them are studied. Finally, a decision-making approach is developed for the MCDM problem with complex intuitionistic fuzzy information. A practical example is given to show the availability and advantages of the proposed method by comparison with some existing methods. The proposed aggregation operators are more generalized than the existing ones to utilize the uncertain and imprecise information. Several existing operators are considered as special cases of the proposed one. Finally, the proposed method will offer various choices to the decision-maker to access the finest alternatives.

A weakest t-norm based fuzzy fault tree approach for leakage risk assessment of submarine pipeline

The leakage of oil and gas due to submarine pipeline damage will result in serious consequences while the reasons are diverse and complicated. The fault tree analysis (FTA) method provides an effective tool to systematically identify various root events and perform probabilistic risk assessments. However, crisp probability values of the basic events are requested for quantitative analysis due to the characteristics of the method itself. In this paper, a weakest t-norm (Tω) based fuzzy fault tree approach is proposed to obtain a relative reliable probability value using domain experts’ evaluations. The main contributes of this method include: a set of fuzzy numbers are defined based on the DNV-RP-F107, meanwhile, a converting method is also proposed to defuzzify the integrated fuzzy numbers; the weakest t-norm operators for trapezoidal fuzzy number are employed for less uncertainty accumulation during the aggregation process. Furthermore, a case study is presented for a detailed description of the proposed approach. A probabilistic risk assessment for leakage failure of submarine pipeline is conducted using both the proposed approach and traditional method. The results show good validity and applicability of the proposed method. The critical events are recognized after quantitative analysis and some improvement measures are put forward for engineering references.

Generalized extension principle for non-normal fuzzy sets

The conventional extension principle is established on the Euclidean space and defined by considering the minimum or t-norm operator in which the fuzzy sets are usually assumed to be normal. The previous work on generalized extension principle was also based on the normal fuzzy sets. Since the non-normal fuzzy sets occur frequently in practical applications, in this paper, the generalized extension principle based on the non-normal fuzzy sets is established in which the general aggregation operator and Hausforff space are taken into account.

Maclaurin symmetric mean aggregation operators based on t-norm operations for the dual hesitant fuzzy soft set

The objective of this paper is to present a Maclaurin symmetric mean (MSM) operator to aggregate dual hesitant fuzzy (DHF) soft numbers. The salient feature of MSM operators is that it can reflect the interrelationship between the multi-input arguments. Under DHF soft set environment, we develop some aggregation operators named as DHF soft MSM averaging (DHFSMSMA) operator, the weighted DHF soft MSM averaging (WDHFSMSMA) operator, DHF soft MSM geometric (DHFSMSMG) operator, and the weighted DHF soft MSM geometric (WDHFSMSMG) operator. Further, some properties and the special cases of these operators are discussed. Then, by utilizing these operators, we develop an approach for solving the multicriteria decision-making problem and illustrate it with a numerical example. Finally, a comparison analysis has been done to analyze the advantages of the proposed operators.

Generalized Cubic Intuitionistic Fuzzy Aggregation Operators Using t-Norm Operations and Their Applications to Group Decision-Making Process

Cubic intuitionistic fuzzy (CIF) set (CIFS) is one of the newly developed extension of the intuitionistic fuzzy set (IFS) in which data are represented in terms of their interval numbers membership and non-membership degrees and further the degree of agreeness, as well as disagreeness corresponding to these intervals, are given in the form of an IFS. Its fundamental characteristic lies in the fact that it is a combined version of both interval-valued IFS and IFS rather than being confined to any single fuzzy environment. Under this environment, the present work focused on exploring the structural characteristics of the CIFS by defining operational laws between them. Further, based on these operational laws, we propose some new generalized CIF averaging aggregation operators and group decision-making methods. Finally, an illustrative example is provided to discuss the reliability of the proposed operators.

Some Generalized Complex Intuitionistic Fuzzy Aggregation Operators and Their Application to Multicriteria Decision-Making Process

The objective of this manuscript is to present some generalized weighted averaging aggregation operators for aggregating the different complex intuitionistic fuzzy sets using t-norm operations. In the existing studies of fuzzy and its extension, the uncertainties present in the data are handled with the help of degrees of membership which are the subset of real numbers, which may loose some useful information and hence consequently affect on the decision results. As a modification to these, complex intuitionistic fuzzy set handles the uncertainties with the degrees whose ranges are extended from real subset to the complex subset with the unit disk and hence handle the two-dimensional information in a single set. Thus, motivated by this, we developed some new averaging aggregation operators, namely complex intuitionistic fuzzy (CIF) weighted averaging, CIF ordered weighted averaging and CIF hybrid averaging in conjunction with their desirable properties. Then, we utilized these operators to propose a multicriteria decision-making approach and illustrated a numerical example to demonstrate the working of the proposed approach. Finally, the proposed results are compared with existing approaches results.

Risk analysis of lung cancer and effects of stress level on cancer risk through neuro-fuzzy model

A significant number of people pass away due to limited medical resources for the battle with cancer. Fatal cases can be reduced by using the computational techniques in the medical and health system. If the cancer is diagnosed early, the chance of successful treatment increases. In this study, the risk of getting lung cancer will be obtained and patients will be provided with directions to exterminate the risk. After calculating the risk value for lung cancer, status of the patient's susceptibility and resistance to stress is used in determining the effects of stress to disease. In order to resolve the problem, the neuro-fuzzy logic model has been presented. When encouraging results are obtained from the study; the system will form a pre-diagnosis for the people who possibly can have risk of getting cancer due to working conditions or living standards. Therefore, this study will enable these people to take precautions to prevent the risk of cancer. In this study a new t-norm operator has been utilized in the problem. Finally, the performance of the proposed method has been compared to other methods. Beside this, the contribution of neuro-fuzzy logic model in the field of health and topics of artificial intelligence will also be examined in this study.

Closure properties for fuzzy recursively enumerable languages and fuzzy recursive languages

There are several variations of fuzzy Turing machines in the literature, many of them require a t-norm in order to establish their accepted language. This paper generalize the concept of non-deterministic fuzzy Turing machine - NTFM, replacing the t-norm operator for several aggregation functions. We establish the languages accepted by these machines, called fuzzy recursively enumerable languages or simply LFRE and show, among other results, which classes of LFRE are closed under unions and intersections.

An Efficient Approach for Incremental Mining Fuzzy Frequent Itemsets with FP-Tree

Keeping the generated fuzzy frequent itemsets up-to-date and discovering the new fuzzy frequent itemsets are challenging problems in dynamic databases. In this paper, the classical H-struct structure is extended to mining fuzzy frequent itemsets. The extended H-mine algorithm can use any t-norm operator to calculate the support of fuzzy itemset. The FP-tree-based structure called the Initial-FP-tree and the New-FP-tree are built to maintain the fuzzy frequent itemsets in the original database and the new inserted transactions respectively. The strategy of incremental mining of fuzzy frequent itemsets is achieved by breath-first-traversing the Initial-FP-tree and the New-FP-tree. All of the fuzzy frequent itemsets in the updated database can be obtained by traversing the Initial-FP-tree. The experiments on real datasets show that the proposed approach runs faster than the batch extended H-mine algorithm. Comparing with the existing algorithm for incremental mining fuzzy frequent itemsets, the proposed approach is superior in terms of the execution time. The memory cost of the proposed approach is lower than that of the existing algorithm when the minimum support threshold is low.

Improved Fusion Machine Based on T-norm Operators for Robot Perception

Map reconstruction for autonomous mobile robots navigation needs to deal with uncertainties, imprecisions and even imperfections due to the limited sensors quality and knowledge acquisition. An improved fusion machine is proposed by replacing the classical conjunctive operator with T-norm operator in Dezert-Smarandache Theory (DSmT) framework for building grid map using noisy sonar measurements. An experiment using a Pioneer II mobile robot with 16 sonar detectors onboard is done in a small indoor environment, and a 2D Map is built online with our selfdeveloping software platform. A quantitative comparison of the results of our new method for map reconstruction with respect to the classical fusion machine is proposed. We show how the new approach developed in this work outperforms the classical one.

Intuitionistic Fuzzy Soft Matrix Theory and Multi Criteria in Decision Making Based on T-Norm Operators

The aim of this paper is to find multi criteria decision making problems to a selected project using intuitionistic fuzzy soft matrix based on generalized operators of t-norm and t-conorm. We use the concept of level operators of intuitionistic fuzzy sets ( K.T.Atanassov, On intuitionistic fuzzy sets theory , Springer - Verlag 2012 ) to define intuitionistic fuzzy soft level matrix. Finally, we give an application of decision making problem by using the operators of t-norm and t-conorm . intuitionistic fuzzy parameterized soft sets. They have also applied to the problems that contain uncertainties based on intuitionistic fuzzy parameterized soft sets. Chetia and Das (5) defined five types of products of intuitionistic fuzzy soft matrices . Babitha and John(11) described generalized intuitionistic fuzzy soft sets and solved multi criteria decision making problem in generalized intuitionistic fuzzy soft sets . Rajarajeswari and Dhanalakshmi(10) described intuitionistic fuzzy soft matrix with some traditional operations. In this paper , we will propose definition of intuitionistic fuzzy soft level matrix . We will also discuss their properties . Finally we will give an application of multi criteria decision making based on t- norm and t-conorm operators.

Automatic extraction of the fuzzy control system by a hierarchical genetic algorithm

The paper proposes a new method to automatically extract all fuzzy parameters of a Fuzzy Logic Controller (FLC) in order to control nonlinear industrial processes. The main objective of this paper is the extraction of a FLC from data extracted from a given process while it is being manually controlled. The learning of the FLC is performed by a hierarchical genetic algorithm (HGA), from a set of process-controlled input/output data. The algorithm is composed by a five level structure, being the first level responsible for the selection of an adequate set of input variables. The second level considers the encoding of the membership functions. The individual rules are defined on the third level. The set of rules are obtained on the fourth level, and finally, the fifth level selects the elements of the previous levels, as well as, the t-norm operator, inference engine and defuzzifier methods which constitute the FLC. To optimize the proposed method, the HGA's initial populations are obtained by an initialization algorithm. This algorithm has the main goal of providing a good initial solution for membership functions and rule based populations, enhancing the GA's tuning. Moreover, the HGA is applied to control the dissolved oxygen in an activated sludge reactor within a wastewater treatment plant. The results are presented, showing that the proposed method extracted all the parameters of the fuzzy controller, successfully controlling a nonlinear plant.