Fuzzy Context Research Articles

Optimizing green solid transportation with carbon cap and trade: a multi-objective two-stage approach in a type-2 Pythagorean fuzzy context

Optimizing green solid transportation with carbon cap and trade: a multi-objective two-stage approach in a type-2 Pythagorean fuzzy context

Optimized model involving forward and inverse problem formulation for the assessment of environmentally sustainable transportation alternatives based on intuitionistic linguistic weighted average

Intuitionistic fuzzy set theory provides a versatile framework for conveying information acquired during the decision-making process, particularly adept at handling indeterminate data. This study aims to devise a robust α-cut approach for intuitionistic linguistic weighted average (ILWA) applied specifically to intuitionistic fuzzy numbers (IFN). The utilization of an extended Jaccard Similarity Measure (EJSM) within the intuitionistic fuzzy context will yield valuable insights into the accuracy of representing linguistic data through the ILWA method. These advancements hold significant implications for selecting environmentally sustainable transportation alternatives and furnish analytical techniques for addressing uncertainty and imprecision across diverse decision-making domains.

Three-way concept lattice from adjunctive positive and negative concepts

Three-way concept lattices (TCLs) have been widely explored due to their clear hierarchical structures, concise visual description and good interpretability. In contrast to classic formal contexts, lattice-valued fuzzy contexts exhibit great capability in describing and representing concepts with uncertainty. Different from conventional approaches to research of TCLs, this paper focuses on investigating the algebraic structure and properties of three-way concept lattice (TCL) stemmed from the positive concept lattice and negative concept lattice in a lattice-valued formal context. Several associated concept lattices such as the Cartesian product of positive concept lattice and negative lattice (i.e., pos-neg lattice), lattices induced from the partition of the pos-neg lattice, and their relationship are explored. Specifically, the isomorphism, embedding and order-preserving mappings between them are built. The quotient set of pos-neg lattice when being defined a specific equivalence relation on it is a complete lattice and each equivalence class is a lower semi-lattice. It is further declared that the structure of TCL is intrinsically and determined wholly by the pos-neg lattice. A practical application of the built theory of TCL is provided to sort alternatives in multi-criteria decision making.

$$\delta $$-granular reduction in formal fuzzy contexts: Boolean reasoning, graph represent and their algorithms

$$\delta $$-granular reduction in formal fuzzy contexts: Boolean reasoning, graph represent and their algorithms

Enhancing healthcare supply chain management through artificial intelligence-driven group decision-making with Sugeno–Weber triangular norms in a dual hesitant q-rung orthopair fuzzy context

The healthcare industry faces numerous challenges in managing its supply chain efficiently, where critical decisions must be made promptly to ensure the availability of essential medical resources. This research introduces a novel artificial intelligence (AI) approach, utilizing the “Sugeno–Weber (SW) t-conorms and t-norms” (SWt-CNs&t-Ns) for decision-making in a Dual Hesitant q-Rung Orthopair Fuzzy (DHq-ROF) context. The SWt-CNs&t-Ns are chosen for their adaptability in data unification, serving as prominent operations for union and intersection processes. Developing a set of fundamental operations is imperative to effectively utilize SWt-CNs&t-Ns and hybrid aggregation operators in DHq-ROF settings. Following the introduction of these processes, several aggregating operators have been provided. These operators include DHq-ROF SW weighted averaging, ordered weighted averaging, hybrid averaging, and their geometric counterparts utilizing DHq-ROF data. The SW triangular norm-based approach aggregates group preferences, facilitating a systematic decision-making process. Triangular norms ensure a realistic representation of interrelationships among decision criteria, leading to optimal healthcare supply chain management solutions. Furthermore, the SW triangular norm-based approach aggregates group preferences, enabling a systematic and comprehensive decision-making process. Choosing the best healthcare supply chain management solutions is easier when you use triangular norms because they give a more accurate picture of how the decision criteria affect each other. The effectiveness of the proposed AI framework is demonstrated through a series of experiments and case studies, showcasing its ability to enhance decision accuracy, reduce uncertainty, and improve overall supply chain performance. The research findings underscore the potential of AI-driven solutions to revolutionize healthcare supply chain management, ultimately leading to better resource allocation, cost efficiency, and improved patient care.

Sustainable and smart electric bus charging station deployment via hybrid spherical fuzzy BWM and MULTIMOORA framework

This study aims to assist public bus operators in locating electric bus charging station (EBCS) facilities from a smart and sustainable view. The selection of the most suitable EBCSs from various possible candidates involves a sophisticated decision-making procedure in terms of several contradictory criteria with imprecise information. The novelty of the study resides in exploring the EBCS site selection problem with spherical fuzzy sets (SFSs), which have shown remarkable effectiveness in limiting information loss by seizing ambiguous, and uncertain data. In this regard, a novel best–worst method (BWM) incorporating Multi-objective optimization via full multiplicative form ratio analysis (MULTIMOORA) methodology in the spherical fuzzy context is proposed to choose the optimal locations for EBCSs. The integrated framework combines the adaptability of the spherical fuzzy BWM (SF-BWM) for determining the criteria weights with the convenience of spherical fuzzy MULTIMOORA (SF-MULTIMOORA) approach for ranking the alternatives. A case study for Istanbul is provided to substantiate the propounded technique and to confirm its viability and efficiency. In the course of making a decision, a four-level hierarchical structure consisting of five main and 22 sub-criteria is built and the comparison matrices are reviewed by a panel of seven experts. A sensitivity analysis is executed, and the results demonstrate that the propositioned approach produces outcomes that are quite robust and consistent. Hence, the findings of this research can benefit public bus operators in choosing the ideal sites for electric charging stations. Finally, the formulated generic methodology is also easily applicable to diverse and complex multiple-criteria problems in the spherical fuzzy domain.

A matrix norm-based Pythagorean fuzzy metric and its application in MEREC-SWARA-VIKOR framework for solar panel selection

Due to the escalating electricity demand from industrialization and modernization, it is imperative to explore clean and sustainable energy sources. Solar energy has become a feasible solution for this surging demand. Solar panels, vital components of solar power systems, are crucial in converting sunlight into electricity. However, selecting the most suitable solar panel is a complex task involving subjective and measurable parameters involving uncertainties. To address the uncertainties and ambiguities in real-life problems, the theory of Pythagorean fuzzy sets with distance measures has emerged as a flexible and superior tool. Nevertheless, many existing distance functions often fail to meet necessary metric conditions, leading to inaccurate and unreasonable outcomes. These limitations are pointed out by many literature. In addition, we observe a serious drawback of parameter dependency of some existing measures. This paper proposes a novel metric for Pythagorean fuzzy sets using the matrix norm to overcome these drawbacks. Additionally, we discuss various mathematical properties and provide geometrical representations for the proposed distance measure. To demonstrate the superiority of the proposed measure, we conduct a comparative study against existing distance measures. Furthermore, we develop a Pythagorean fuzzy-method based on the removal effects of criteria-stepwise weight assessment ratio analysis-vlse kriterijumska optimizacija kompromisno resenje (PF-MEREC-SWARA-VIKOR) method for selecting solar panel systems. Our approach incorporates the MEREC method for objective criteria, utilizes the SWARA method to calculate subjective weights, and employs the VIKOR method in the Pythagorean fuzzy context to determine the preference order of alternatives. We conduct sensitivity analysis and comparative studies with existing developed methods to validate our method. Highlight the effectiveness and advantages of our novel approach in selecting solar panels. Finally, exploring the future research directions and challenges associated with the proposed methodology.

Common Fixed Point Theorems in Fuzzy Normed Space

. Fixed point theory is an intriguing topic with numerous applications in several branches of mathematics. In addition, fixed point theory offers useful methods for problem-solving that may be used across many subfields of mathematical analysis. Fixed point theorems are concerned with mappings f of a set X into itself that, under particular conditions, permit a fixed point, that is, a point such that . In this paper, we use the triangle property on fuzzy normed space(Fn-space) to show a common fixed point (CF-point) without continuity. First, we review some of the fundamental terms used in the fuzzy context. After that the notion of triangle fuzzy norm is given then we show that the self mappings Γ and Λ have a CF-point in the setting of Fn-space. Additionally, certain applications of our main results to the Fredholm integral equation are investigated.

Two dimensional fuzzy context-free languages and tiling patterns

Fuzzy context-free languages are powerful compared to fuzzy regular languages as they are generated by fuzzy context-free grammars and fuzzy pushdown automata, which follow an enhanced computational mechanism. A two dimensional language (picture language) is a collection of two dimensional words, which are a rectangular array of symbols made up of finite alphabets. Two dimensional automata can recognize two dimensional languages that could not be recognized by one dimensional automata. In this paper, we introduce two dimensional fuzzy context-free languages generated by the two dimensional fuzzy context-free grammars and accepted by the two dimensional fuzzy pushdown automata in order to deal with the vagueness that arises in two dimensional context-free languages. We can construct a two dimensional fuzzy context free grammar from the given two dimensional fuzzy pushdown automata and vice versa. In addition, we prove that two dimensional fuzzy context-free languages are closed under union, column concatenation, column star, homomorphism, inverse homomorphism, reflection about right-most vertical, reflection about base, conjugation and half-turn and also show that two dimensional fuzzy context-free languages are not closed under matrix homomorphism, quarter-turn and transpose. Further, we have given the applications and the uses of closure properties in the formation of tiling patterns.

Factorizing formal contexts from closures of necessity operators

Factorizing datasets is an interesting process in a multitude of approaches, but many times it is not possible or efficient the computation of a factorization of the dataset. A method to obtain independent subcontexts of a formal context with Boolean data was proposed in Dubois and Prade based on the operators used in possibility theory. In this paper, we will analyze this method and study different properties related to the pairs of sets from which a factorization of a formal context arises. We also inspect how the properties given in the classical case can be extended to the fuzzy framework, which is essential to obtain a mechanism that allows the computation of independent subcontexts of a fuzzy context.

Evaluation of micromobility risk management alternatives using interval-valued q-rung orthopair fuzzy interaction operators-based WISP method

Micro-mobility has become a mode of transportation since the 2010 s. Because this mode is relatively new, there are many unknowns, and the associated risks must be evaluated so they can be managed safely and effectively. This paper aims to introduce a decision support system (DSS) for ranking risk management alternatives in the micro-mobility sector under an interval-valued q-rung orthopair fuzzy (IVq-ROF) context. In this context, firstly IVq-ROF-interaction aggregation operators (AOs) are introduced for aggregating the information from IVq-ROF perspective. These AOs can provide a flexible mode to tackle realistic decision support problems within the IVq-ROF set (IVq-ROFS) context. Second, a definition of entropy and new entropies for IVq-ROFS is introduced. Third, a hybrid weight-determining formula is presented using an entropy-based weighting approach for the objective weight of criteria and a stepwise weight assessment ratio analysis (SWARA) method for the subjective weight of criteria. Fourth, the weighted integrated sum-product (WISP) approach is expanded from the IVq-ROF perspective. Further, the developed model is utilized in a case study of risk management alternative evaluation in the micro-mobility sector, which shows its applicability and feasibility under the IVq-ROF environment. Sensitivity and comparative investigations are studied to confirm the strength and stability of the obtained result. The best alternative has emerged as the state-private sector cooperation in successfully allocating the risk in the micro-mobility sector. The final results conclude that the developed methodology can provide more accurate decisions while considering multiple inducing indicators and input uncertainties.

Intelligent decision support system for pulmonary tuberculosis detection using bipolar fuzzy utility matrix and bipolar Mamdani fuzzy inference system

Tuberculosis (TB) stands as the second leading global infectious cause of death, following closely behind the impact of COVID-19. The standard approach to diagnose TB involves skin tests, but these tests can yield inaccurate results due to limited access to healthcare and insufficient diagnostic resources. To enhance diagnostic accuracy, this study introduces a novel approach employing a Bipolar Fuzzy Utility Matrix Inference System (BFUMIS) and a Bipolar Mamdani Fuzzy Inference System (BMFIS) to assess TB disease levels. By considering factors associated with the causation of TB, the study devises suitable membership functions for bipolar fuzzy sets (BFS) using both triangular and trapezoidal fuzzy numbers. Using a point factor scale, the study clusters the rules systematically and assesses the level of uncertainty within these grouped rules by utilizing bipolar triangular fuzzy numbers (BTFN). To handle the BTFN, this study proposes converting bipolar triangular fuzzy into bipolar crisp score (CBTFBCS) algorithm as a defuzzification method. The optimal bipolar fuzzy utility sets (BFUS) are determined from the bipolar fuzzy utility matrix to identify patients’ TB disease levels. These sets play a pivotal role in characterizing the severity of TB disease levels in patients. Additionally, rigorous validation of the utility framework is accomplished through measures of bipolar fuzzy satisfactory factors and sensitivity analyses. Furthermore, the study introduces the BMFIS, which presents a novel perspective on the conventional fuzzy inference system. This innovative system integrates the Mamdani fuzzy inference system (MFIS) into a bipolar fuzzy context, enriching the diagnostic process with enhanced insights. To demonstrate the efficacy of the proposed methods, extensive validation is carried out using actual clinical data. The performance metrics used in this validation effectively demonstrate the superiority of the proposed approach.

Characterization of a Cournot–Nash Equilibrium for a Fishery Model with Fuzzy Utilities

The article deals with the extensions of discrete-time games with infinite time horizon and their application in a fuzzy context to fishery models. The criteria for these games are the total discounted utility and the average utility in a fishing problem. However, in the fuzzy case, game theory is not the best way to represent a real fishing problem because players do not always have enough information to accurately estimate their utility in the context of fishing. For this reason, in this paper, trapezoidal-type fuzzy utility values are considered for a fishing model, and the terms of the Nash equilibrium are given in the fuzzy context, i.e., this equilibrium is represented using the partial order of the α-cuts of the fuzzy numbers; to the best of the authors’ knowledge, there is no work with this type of treatment. To obtain each equilibrium, a suitable fully determined fuzzy game is used in combination with the dynamic programming technique applied to this game in the context of fishing. The main results are (i) the Nash equilibria of the fuzzy games coincide with the Nash equilibria of the nonfuzzy games and are explicitly determined in a fishery model and (ii) the values of the fuzzy games are of trapezoidal type and are also explicitly given in the fishery model.

Admissible OWA operators for fuzzy numbers

Ordered Weighted Averaging (OWA) operators are some of the most widely used aggregation functions in classic literature, but their application to fuzzy numbers has been limited due to the complexity of defining a total order in fuzzy contexts. However, the recent notion of admissible order for fuzzy numbers provides an effective method to totally order them by refining a given partial order. Therefore, this paper is devoted to defining OWA operators for fuzzy numbers with respect to admissible orders and investigating their properties. Firstly, we define the OWA operators associated with such admissible orders and then we show their main properties. Afterward, an example is presented to illustrate the applicability of these AOWA operators in linguistic decision-making. In this regard, we also develop an admissible order for trapezoidal fuzzy numbers that can be efficiently applied in practice.

Uncertainty analysis of the tumour population logistic model in a fuzzy context

Uncertainty analysis of the tumour population logistic model in a fuzzy context

A synthetic measure for ranking overall satisfaction based on multidimensional ordinal data. The case of airlines on the TripAdvisor website

A multi-criteria method has been proposed to measure global consumer satisfaction by handling graphical information represented in circles or star ratings available on the website for several criteria. The Synthetic Measure for Ordinal Data (SMOD) is based on Hellwig’s framework measuring distances between the object and the ideal object. In the construction of the synthetic measure, the distance between the ideal and anti-ideal object is also used. GDM2 distance measure was used for the calculation of distances between objects evaluated by ordinal scale. The proposed framework can be an alternative for the fuzzy or intuitionistic fuzzy transformations of linguistic data into fuzzy context. The SMOD method was applied for evaluation and ranking airlines based on passengers’ reviews accessed on the TripAdvisor website. We found that the proposed multi-criteria method enables us to discriminate and rank airlines based on incomplete information presented on this website. According to SMOD, the best is Singapore Airlines, while the last is Air China when considering Star Alliance members.

Applications of conjunctive complex fuzzy subgroups to Sylow theory

<abstract><p>Sylow's theorems are fundamental theorems in classical group theory that are of paramount importance. The extension of these theorems into diverse fuzzy contexts emerges as a compelling area of exploration. This study introduces the novel concept of the conjunctive complex fuzzy conjugate element within the conjunctive complex fuzzy subgroup of a group, elucidating numerous crucial properties of this concept. Additionally, it propounds the notion of the conjunctive complex fuzzy <italic>p</italic>-subgroup within the conjunctive complex fuzzy subgroup (CCFSG) and delineates various indispensable characteristics associated with this construct. Additionally, the paper formulates the conjunctive complex fuzzy version of the Cauchy theorem for finite groups. Lastly, it defines the concept of the conjunctive complex fuzzy Sylow <italic>p</italic>-subgroup for a finite group and conducts a generalization of Sylow's theorems within a conjunctive complex fuzzy environment.</p></abstract>

Formula omitted]-spherical fuzzy Hamacher Heronian mean geometric operators for multiple criteria group decision making using SMART based TODIM method

T-spherical fuzzy set studied in this paper adequately defines the uncertain information of any decision making situations. This paper aims to provide a solution approach to a multiple criteria group decision making situation under T-spherical fuzzy context. Every group decision making process utilizes aggregation operators to combine the different expert’s opinions. This paper aims to construct several aggregation operators such as T-spherical fuzzy Hamacher Heronian mean-geometric, weighted geometric, ordered geometric, and hybrid geometric operators. The fundamental properties of the proposed operators are thoroughly investigated. The introduced operators are more potent in considering the criteria interrelationships. Criteria weights play an essential role while aggregating different criteria during multiple criteria decision making processes. This work adopts the simple multi-attribute rating technique (SMART) to compute the criteria weights. Utilizing the proposed operators and SMART technique, a multiple criteria group decision making approach called the TODIM (an acronym in Portuguese for Iterative Multi-Criteria Decision Making) is defined based on the Euclidean distance between the T-spherical fuzzy numbers. A decision making situation of selecting the most deserving one from a set of lecturers based on their research capacity is solved using the proposed TODIM approach to show its applicability. Sensitivity analysis is carried out to reveal the effect of parameters on the decision results. A comparative study is made to exhibit the feasibility of the proposed approach.

Group decision-making method based on advanced aggregation operators with entropy and divergence measures under 2-tuple linguistic Pythagorean fuzzy environment

2-tuple linguistic Pythagorean fuzzy values (2TLPFVs) are flexible and more efficient tools to represent fuzzy linguistic information in complex real-world situations than 2-tuple linguistic values (2TLVs) and 2-tuple linguistic intuitionistic fuzzy values (2TLIFVs). This paper introduces a new score value function for 2TLPFVs and discusses its major properties. Two new aggregation operators (AOs) are presented, namely, the advanced 2-tuple linguistic Pythagorean fuzzy weighted average (Adv-2TLPFWA) operator and the advanced 2-tuple linguistic Pythagorean fuzzy weighted geometric (Adv-2TLPFWG) operator, which aggregate 2-tuple linguistic Pythagorean fuzzy information based on novel operational laws of 2TLPFVs. The work also exhibits several properties of these AOs in detail. Furthermore, the article discusses entropy and divergence measures under the 2-tuple linguistic Pythagorean fuzzy information environment. Finally, a new multiple attribute group decision-making (MAGDM) method is constructed to solve group decision-making problems in the 2-tuple linguistic Pythagorean fuzzy context. A real-life group decision-making problem of selecting the best green supplier for fruits and vegetables is investigated to verify the applicability and validity of the proposed approach. The sensitivity investigation and comparative analysis are conducted to illustrate the advantages of the proposed method.

Decision-theoretic rough set model and spatial analysis-based waste-to-energy incineration plant site selection: a case study in first-tier cities of China.

Selecting a sustainable waste-to-energy (WTE) incineration plant site is important for handling huge challenges created by on-going municipal solid waste. However, many studies with WTE incineration plant site problems fail to determine alternative evaluation criteria and cities beforehand, which may increase decision costs and evaluation risks. This paper proposes a novel methodology based on decision-theoretic rough set model and suitable analysis for selecting the optimal WTE incineration plant site. Firstly, from the features of cities, alternative evaluation criteria are determined by three-phase method. Considering different geographical features, a geographical index system is established. Secondly, subjective and objective criteria weights are determined by an improved DEMATEL (Decision Making Trial and Evaluation Laboratory) method and TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method-based linear programming model under the hesitant fuzzy linguistic context, respectively. Subjective and objective criteria weights are combined to form the final criteria weights by building an optimization model. Thirdly, the decision-theoretic rough set model is utilized to select alternative WTE incineration plant sites. We utilize spatial analysis adopting Geographic Information System technology to rank all alternative cities to build facilities. Finally, a numerical case is performed to illustrate the feasibility of the proposed methodology. The sensitivity analysis with the parameter [Formula: see text] ranking from 0 to 1 is performed, the result confirms that the proposed methodology has better robustness. Compared with the multi-criteria decision-making methods, the effectiveness and superiority of the proposed methodology are demonstrated.