Intuitionistic Fuzzy Concept Research Articles

An optimization-based three-way decision for multi-criteria ranking strategy considering intuitionistic fuzzy concept

As information continues to expand and uncertainty intensifies, traditional three-way decision methods in multi-criteria environments often appear inadequate when dealing with ranking problems. Most traditional three-way decision methods usually rely on subjective concepts or require decision-makers to specify probability parameters when constructing scheme descriptions, which leads to high subjectivity of the methods. Based on this background, this paper proposes an optimization-based three-way decision model for multi-criteria ranking strategy considering intuitionistic fuzzy concept, with the aim of mitigating the excessive subjectivity observed in most of the three-way decision methods. Firstly, a scheme-oriented intuitionistic fuzzy concept is defined to represent the decision-maker's fuzzy perception and selection of the scheme. Then, using the scheme-oriented intuitionistic fuzzy concept and the classic description of candidate schemes obtained through intuitionistic fuzzy c-means clustering algorithm, this paper provides a new method for estimating the conditional probability of the schemes that is not limited by parameter settings. Secondly, combining the scheme-oriented intuitionistic fuzzy concept and intuitionistic fuzzy information table, a new risk loss function is proposed, which is suitable for decision problems under intuitionistic fuzzy environment. Then, based on three-way decision model formulated using an optimization-based approach, an objective new ranking strategy is constructed. In addition, numerical analysis, comparative analysis, and parameter analysis are used to validate the rationality and feasibility of the presented ranking strategy. Finally, through quantitative analysis of multiple datasets and qualitative analysis of several ranking models, the operability of the new ranking strategy is verified.

A corrosion assessment methodology based on triangular intuitionistic fuzzy comprehensive evaluation (TIFCE) with analytic network process (TIFANP): An application to external corrosion of the storage tank floor

The increasing demand for oil, natural gas, and green energy has led to massive construction of storage and transportation infrastructure, and the resulting corrosion problems have attracted increasing attention. The complexity of the factors influencing corrosion and the uniqueness of infrastructure pose great challenges to the inspection, assessment, and prediction of corrosion. This challenge is reflected in the large number of influencing factors and the intricate interrelationships between them, which often require the involvement of experts in the assessment. However, due to reasons such as incomplete data and the complexity of corrosion mechanisms, there is uncertainty in the expert's judgment. To address this problem, this work proposes a multilevel, multi-index framework for corrosion evaluation. This framework integrates both analytic network process and comprehensive evaluation method under an intuitionistic fuzzy environment. It uses the triangular intuitionistic fuzzy numbers-based analytic network process (TIFANP) to establish and analyze the weights of the interactive and employed triangular intuitionistic fuzzy comprehensive evaluation (TIFCE) to address the subjective judgment and uncertainty issues in corrosion evaluation. The introduction of the intuitionistic fuzzy concept effectively handles the uncertainty in corrosion assessment. To verify the feasibility and practicability of the framework, it was applied to external corrosion assessment of the floor of a crude oil storage tank. Soil corrosion, cathodic protection, coating protection, and stray current interference were considered the main factors influencing the external corrosion of the storage tank floor. The assessment results were consistent with the open-tank inspection. This work can provide valuable information for storage tank operation, corrosion protection, and maintenance to reduce economic losses and safety accidents caused by the corrosion of crude oil tank floors.

Intuitionistic fuzzy credibility Dombi aggregation operators and their application of railway train selection in Pakistan

<abstract><p>The degree of credibility of the fuzzy assessment value demonstrates its significance and necessity in the fuzzy decision making problem. The fuzzy assessment values should be closely related to their credibility measures in order to increase the credibility levels and degrees of fuzzy assessment values. This will increase the abundance and the credibility of the assessment information. As a new extension of the intuitionistic fuzzy concept, this study suggests the idea of an intuitionistic fuzzy credibility number (IFCN). So, based on Dombi norms, we proposed some new operational laws for intuitionistic fuzzy credibility numbers. Different intuitionistic fuzzy credibility aggregation operators are defined using Dombi t-norm and t-conorm operations. i.e., intuitionistic fuzzy credibility Dombi weighted averaging (IFCDWA), intuitionistic fuzzy credibility Dombi ordered weighted averaging (IFCDOWA), intuitionistic fuzzy credibility Dombi hybrid weighted averaging (IFCDHWA) operators. Next, we defined multiple criteria group decisions (MCGDM) approach. To ensure that their results are reliable and applicable, we also gave an example of railway train selection and discussed comparative result analysis.</p></abstract>

The intuitionistic fuzzy concept-oriented three-way decision model

Recently, some researchers have explored three-way decision models in the fuzzy multi-criteria environments from the perspective of criterion fuzzy concept. The main characteristics of these models include the subjective preference of decision-maker for criteria and the evaluation value information system provided by decision-maker. However, the criterion fuzzy concept only considers the decision-maker’s membership preference to each criterion, and ignores the decision-maker’s non-membership preference to each criterion. In view of this, this paper further proposes a new criterion fuzzy concept, namely the intuitionistic fuzzy concept, to express decision-maker’s preference for each criterion. At the same time, we build an intuitionistic fuzzy concept-oriented three-way decision model to solve the ranking and classification problem in the intuitionistic fuzzy multi-criteria environments with decision-maker’s preference. Firstly, based on the defined intuitionistic fuzzy concept, we construct a new intuitionistic fuzzy loss function model. Meanwhile, using intuitionistic fuzzy similarity, we propose a new conditional probability calculation method to express the correlation degree between the intuitionistic fuzzy concept and alternative’s evaluation values. Secondly, we introduce three decision-making perspectives from the membership degree and non-membership degree of expected loss to obtain the final three-way classification scheme. Moreover, by combining the thresholds of the positive and negative perspectives, we obtain the comprehensive thresholds of the comprehensive perspective, which can be used to rank all alternatives. Finally, a supplier selection problem is used to verify the feasibility and superiority of the model, and six data sets are used to verify the applicability of the model.

Relative Knowledge Distance Measure of Intuitionistic Fuzzy Concept

Knowledge distance is used to measure the difference between granular spaces, which is an uncertainty measure with strong distinguishing ability in a rough set. However, the current knowledge distance failed to take the relative difference between granular spaces into account under the given perspective of uncertain concepts. To solve this problem, this paper studies the relative knowledge distance of intuitionistic fuzzy concept (IFC). Firstly, a micro-knowledge distance (md) based on information entropy is proposed to measure the difference between intuitionistic fuzzy information granules. Then, based on md, a macro-knowledge distance (MD) with strong distinguishing ability is further constructed, and it is revealed the rule that MD is monotonic with the granularity being finer in multi-granularity spaces. Furthermore, the relative MD is further proposed to analyze the relative differences between different granular spaces from multiple perspectives. Finally, the effectiveness of relative MD is verified by relevant experiments. According to these experiments, the relative MD has successfully measured the differences in granular space from multiple perspectives. Compared with other attribute reduction algorithms, the number of subsets after reduction by our algorithm is in the middle, and the mean-square error value is appropriate.

Attribute reduction in intuitionistic fuzzy formal concepts

Knowledge acquisition in intuitionistic fuzzy information systems is of importance because those fuzzy information systems are often encountered in many real-life problems. Formal concept analysis is a simple and effective tool for knowledge acquisition. However, there is still little work on introducing knowledge acquisition methods based on formal concept analysis into intuitionistic fuzzy information systems. This paper mainly extends the formal concept theory into intuitionistic fuzzy information systems. Firstly, two pairs of adjoint mappings are defined in intuitionistic fuzzy formal contexts. It is verified that both pairs of adjoint mappings form Galois connections. Secondly, two types of intuitionistic fuzzy concept lattices are constructed. After that, we also present the main theorems and propositions of the intuitionistic fuzzy concept lattices. Thirdly, we deeply discuss the attribute characteristics for type-1 generalized one-sided intuitionistic fuzzy concept lattice. Furthermore, a discernibility matrix-based algorithm is proposed for attribute reduction and the effectiveness of this algorithm is demonstrated by a practical example. The construction of intuitionistic fuzzy conceptS is meaningful for the complex and fuzzy information in real life.

A New Extension to the Intuitionistic Fuzzy Metric-like Spaces

In this manuscript, we introduce the concept of intuitionistic fuzzy controlled metric-like spaces via continuous t-norms and continuous t-conorms. This new metric space is an extension to intuitionistic fuzzy controlled metric-like spaces, controlled metric-like spaces and controlled fuzzy metric spaces, and intuitionistic fuzzy metric spaces. We prove some fixed-point theorems and we present non-trivial examples to illustrate our results. We used different techniques based on the properties of the considered spaces notably the symmetry of the metric. Moreover, we present an application to non-linear fractional differential equations.

Fruit Production Planning in Semiarid Zones: A Novel Triangular Intuitionistic Fuzzy Linear Programming Approach

A triangular intuitionistic fuzzy linear programming (TIFLP) model is formulated for the planning of sustainable fruit production system for hyperarid regions while assuming the availability of resources and existing knowledge. A remarkable advancement is achieved through the composition of intuitionistic fuzzy concept with the linear programming by considering all parameters and variables in the form of triangular intuitionistic fuzzy numbers, which provides a planning or strategic tool for handling uncertain situations with more control and in a realistic way. This fuzzy optimization model is redesigning the feasible region obtained by linear programming which is presented in graphical form. Moreover, the practical application and implementation of this fruit production system for planning in real-life scenarios are accomplished considering the case study of fruit orchards of Baluchistan, Pakistan.

Multi-objective linguistic-neutrosophic matrix game and its applications to tourism management

Game theory plays an important role in numerous decision-oriented real-life problems. Nowadays, many such problems are basically characterized by various uncertainties. Uncertainties come to happen due to decision makers' collection of data, intuition, assumption, judgement, behaviour, evaluation and lastly, due to the problem itself. Fuzzy concept with membership degree made an initialization towards the treatment of uncertainty, but it was not enough. Intuitionistic fuzzy concept was evolved concerning with both membership and non-membership degrees but failed to express reality more accurately. Then, neutrosophy logic was developed with a new degree in uncertainty, say, indeterminacy degree besides membership and non-membership degrees. Multi-objective optimization is an area of multiple-criteria decision making related with mathematical optimization problems involving more than one objective function to be optimized at the same time. Game theory (matrix game) problems with imprecise, vague information, like neutrosophic, can be formed with multiple objective functions. We develop and analyse a matrix game with multiple objectives, and solve the problem under a single-valued neutrosophic environment in linguistic approach. The main achievement of our study is that we here introduce a problem-oriented example to justify our designed methodologies with a successful real-life implications using linguistic neutrosophic data rather than crisp data as used in previous researches.

On some properties of intuitionistic fuzzy soft boundary

The concept of intuitionistic fuzzy soft sets in a decision making problem and the problem is solved with the help of 'similarity measurement' technique. The purpose of this paper is to initiate the concept of Intuitionistic Fuzzy(IF) soft boundary. We discuss and explore the characterizations and properties of IF soft boundary in general as well as in terms of IF soft interior and IF soft closure. Examples and counter examples are also presented to validate the discussed results.

基于直觉模糊概念格的新型病毒分类方法

基于直觉模糊概念格的新型病毒分类方法

Reliability appraisal for consecutive-<i>k</i>-out-of-<i>n</i>:F system of non-identical components with intuitionistic fuzzy set

In this paper, the reliability of a linear (circular) consecutive k-out-of-n: F system of non-identical elements have been obtained with the help of intuitionistic fuzzy concept and Weibull lifetime distribution. The calculation of parameters of the Weibull distribution is presented by intuitionistic triangular fuzzy numbers. The Markov chain technique is employed to compute the reliability of the transition state of the system. A numerical example is also illustrated for demonstrating the reliability of the system.

Linguistic-Valued Intuitionistic Fuzzy Concept Lattice and Its Application

Linguistic-Valued Intuitionistic Fuzzy Concept Lattice and Its Application

On Intuitionistic Fuzzy Semihyperrings

In this paper, the concepts of an intuitionistic fuzzy semihyperrings and an intuitionistic fuzzy subsemihypermodule of R, where R is a semihyperring, are introduced and some of their characteristics are proved. In particular, fully idempotent semihyperrings are investigated in the context of intuitionistic fuzzy concept.

Aspiration level approach to solve matrix games with I-fuzzy goals and I-fuzzy pay-offs

The objective of this paper is to develop a new solution methodology for matrix games, in which goals are viewed as intuitionistic fuzzy sets (IFSs) and the elements of the pay-off matrix are represented by triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, a suitable ranking function is defined to establish an order relation between two TIFNs, and the concept of intuitionistic fuzzy (I-fuzzy) inequalities is interpreted. Utilizing these inequality relations and ranking functions, a pair of linear programming models is derived from a pair of auxiliary intuitionistic fuzzy programming models. Based on the aspiration levels, this pair of linear programming models is solved to determine the optimal strategies for both players of the game. The proposed method in this paper is illustrated with a voting share problem to demonstrate the validity and applicability of the method.

Some Aspects of Intuitionistic Fuzzy 2-Inner Product Space

In this paper, the concept of Intuitionistic fuzzy 2- inner product space is introduced. By virtue of this definition, parallelogram law and Polarization Identity are proved.

Attribute Reduction of Intuitionistic Fuzzy Concept Lattices

In this paper, we turn intuitionistic fuzzy information systems into 0-1 formal contexts by using dominance relation. A pair of operators is defined to get the formal concept lattices in the intuitionistic fuzzy information systems. Furthermore, some properties and attribute reduction based on discernibility matrices is investigated.

Attribute Reduction in Intuitionistic Fuzzy Concept Lattices

As an effective tool for knowledge discovery, concept lattice has been successfully applied to various fields. And one of the key problems of knowledge discovery is attribute reduction. In order to understand the problems better, the attribute reduction is necessary to perfect the theory as well as expand application of concept lattice. This paper introduces the intuitionistic fuzzy theory into the concept lattice theory and proposes a kind of intuitionistic fuzzy concept lattice. Then, an approach to attribute reduction based on the discernibility matrix is proposed and investigated, which makes the discovery of implicit knowledge easier and the representation simpler in data; furthermore, the theory of concept lattice is perfected. The theory of intuitionistic fuzzy concept lattice is useful and meaningful in view of the complexity and fuzziness of information in real world, and the potential value of dealing with information is expected in the future.

Strongly irrsolute precontinuous functions in intuitionistic fuzzy special Topological spaces

: The aim of this paper Is to generalize the concept of intuitionistic fuzzy strongly irresolute precontinuous functions due to B.Krsteska &S. Abbas , [2] to intuitionistic fuzzy special topological spaces. Also we study some of their properties and relations with intuitionistic fuzzy special strongly precontinuous functions .we investigate several characterizing theorem.

Statistical convergence of double sequences in intuitionistic fuzzy normed spaces

Recently, the concept of intuitionistic fuzzy normed spaces was introduced by Saadati and Park [Saadati R, Park JH. Chaos, Solitons & Fractals 2006;27:331–44]. Karakus et al. [Karakus S, Demirci K, Duman O. Chaos, Solitons & Fractals 2008;35:763–69] have quite recently studied the notion of statistical convergence for single sequences in intuitionistic fuzzy normed spaces. In this paper, we study the concept of statistically convergent and statistically Cauchy double sequences in intuitionistic fuzzy normed spaces. Furthermore, we construct an example of a double sequence to show that in IFNS statistical convergence does not imply convergence and our method of convergence even for double sequences is stronger than the usual convergence in intuitionistic fuzzy normed space.