Complex Decision Modeling Framework with Fairly Operators and Quaternion Numbers under Intuitionistic Fuzzy Rough Context

The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper investigates the potential applications of intuitionistic fuzzy sets(IFS)with rough sets in the context of sparse data.When it comes to capture uncertain information emanating fromboth upper and lower approximations,these intuitionistic fuzzy rough numbers(IFRNs)are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets,respectively.We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties.We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles.These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator(IFRWFA)and intuitionistic fuzzy rough ordered weighted fairly aggregation operator(IFRFOWA).These operators successfully adjust to membership and non-membership categories with fairness and subtlety.We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multiattribute decision-making field.We use the intuitionistic fuzzy rough environment’s architecture to create a novel strategy in situation involving several decision-makers and non-weighted data.Additionally,we developed a novel technique by combining the IFSs with quaternion numbers.We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers(IFQNs).With the help of this framework,we can simulate uncertainty in real-world situations and address a number of decision-making problems.Using the examples we have released,we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity ofmedical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology.

Dynamic Analysis of Customer Demand Based on Intuitionistic Fuzzy Number in Product Planning

To address the fuzziness and variability in determining customer demand importance,a dynamic analysis method based on intuitionistic fuzzy numbers is proposed.First,selected customers use intuitionistic fuzzy numbers to represent the importance of each demand.Then,the preference information is aggregated using customer weights and time period weights through the intuitionistic fuzzy ordered weighted average operator,yielding a dynamic vector of the subjective importance of the demand index.Finally,the feasibility of the proposed method is demonstrated through an application example of a vibrating sorting screen.

Cardinal Numbers of Fuzzy Sets

Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.

Reasoning complexity for extended fuzzy description logic with qualifying number restriction

To solve the extended fuzzy description logic with qualifying number restriction （EFALCQ） reasoning problems, EFALCQ is discretely simulated by description logic with qualifying number restriction （ALCQ）, and ALCQ reasoning results are reused to prove the complexity of EFALCQ reasoning problems. The ALCQ simulation method for the consistency of EFALCQ is proposed. This method reduces EFALCQ satisfiability into EFALCQ consistency, and uses EFALCQ satisfiability to discretely simulate EFALCQ satdomain. It is proved that the reasoning complexity for EFALCQ satisfiability, consistency and sat-domain is PSPACE-complete.

A New Method of Ranking Fuzzy Number Based on α-Cut

This paper presents a new method of comparing or ranking of interval and fuzzy numbers. Based on another way of understanding fuzzy concept, the paper proposes the concept of number meaning of interval and the comparison method of interval. The paper defines the new ranking method by the α cut intervals of fuzzy number, and proves that the new inequality relation of fuzzy numbers is transitive. Our approach is a simple way of considering all the existence levels and can be calculated at different exact level according to different applications.

Design of fuzzy number recognition based on embedded system platform

A system of number recognition with a graphic user interface （GUI） is implemented on the embedded development platform by using the fuzzy pattern recognition method. An application interface （API） of uC/ OS-Ⅱ is used to implement the features of multi-task concurrency and the communications among tasks. Handwriting function is implemented by the improvement of the interface provided by the platform. Fuzzy pattern recognition technology based on fuzzy theory is used to analyze the input of handwriting. A primary system for testing is implemented. It can receive and analyze user inputs from both keyboard and touch-screen. The experimental results show that the embedded fuzzy recognition system which uses the technology which integrates two ways of fuzzy recognition can retain a high recognition rate and reduce hardware requirements.

Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems

Intuitionistic trapezoidal fuzzy numbers and their operational laws are defined. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy weighted arithmetic averaging operator and weighted geometric averaging operator are proposed. Expected values, score function, and accuracy function of intuitionitsic trapezoidal fuzzy numbers are defined. Based on these, a kind of intuitionistic trapezoidal fuzzy multi-criteria decision making method is proposed. By using these aggregation operators, criteria values are aggregated and integrated intuitionistic trapezoidal fuzzy numbers of alternatives are attained. By comparing score function and accuracy function values of integrated fuzzy numbers, a ranking of the whole alternative set can be attained. An example is given to show the feasibility and availability of the method.

A novel similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers with applications to pattern recognition and medical diagnosis

Similarity measure is an essential tool to compare and determine the degree of similarity between intuitionistic fuzzy sets (IFSs). In this paper, a new similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers is proposed. The proposed similarity measure provides reasonable results not only for the sets available in the literature but also gives very reasonable results, especially for fuzzy sets as well as for most intuitionistic fuzzy sets. To provide supportive evidence, the proposed similarity measure is tested on certain sets available in literature and is also applied to pattern recognition and medical diagnosis problems. It is observed that the proposed similarity measure provides a very intuitive quantification.

Fuzzy Semi-continuity of fuzzy number-valued function

In this paper we discuss the conecept and property of fuzzy semi continuous function.

A METHOD OF SOLVING THE FUZZY FINITE ELEMENT EQUATIONS IN MONOSOURCE FUZZY NUMBERS

For same cases the rules of monosource fuzzy numbers con be used into the solution of fuzzy stochastic finite element equations in engineering. This method can reduce the computing quantity of the solution. It can be proved that the amount of the solution is nearly as much as that with the general stochastic finite element method (SFEM). In addition, a new method to appreciate the structural fuzzy failure probability is presented for the needs of the modem engineering design.

Evaluating the conceptual design schemes of complex products based on FAHP using fuzzy number

In the conceptual design stage of complex products, CBR（Case-Based Reasoning） tool is useful to offer a feasible set of schemes. Then the most adaptive scheme can be generated through a procedure of comparison and evaluation. The procedure is essentially a multiple criteria decision-making problem. The traditional multiple criteria programming is not flexible enough in executing the system evaluation algorithm due to both the limited experimental data and the lack of human experiences. To make the CBR tool to be more efficient, a new method for the best choice among the feasible schemes based on the Fuzzy AHP using Fuzzy numbers （FFAHP） is proposed. Since the final results become a problem of ranking the mean of fuzzy numbers by the optimism of decision-maker using the FFAHP, its execution is much more intuitive and effective than with the traditional method.

Ranking Method for Complementary Judgment Matrixes with Fuzzy Numbers Based on Hausdorff Metric Distance

A method for ranking complementary judgment matrixes with traspezoidal fuzzy numbers based on Hausdorff metric distance and fuzzy compromise decision approach is proposed. With regard to fuzzy number complementary judgment matrixes given by a decider group whose members have various weights, the expert＇s information was aggregated first by means of simple weight average（SWA） method and Bonissone calculational method. Hence a matrix including all the experts＇ preference information was got. Then the matrix＇ column members were added up and the fuzzy evaluation values of the alternatives were got. Lastly, the Hausdorff metric distance and fuzzy compromise decision approach were used to rank the fuzzy evaluation values and then the ranking values of all the alternatives were got. Because exact numbers and triangular fuzzy numbers could all be transformed into trapezoidal fuzzy numbers, the method developed can rank complementary judgment matrixes with trapezoidal fuzzy numbers, triangular fuzzy numbers and exact numbers as well. An illustrative example is also given to verify the developed method and to demonstrate its feasibility and practicality.

Success Factors of Biotechnology Industry Based on Triangular Fuzzy Number

Based on the theory of competitive advantage and value chain, this paper establishes the indicator system, and develop the strategic framework using the fuzzy Delphi method. Then the triangular fuzzy number model is established using Fuzzy Analytic Hierarchy Process, and the key factors influencing biotechnology industry are extracted. The results show that in terms of weight, the key factors influencing the success of biotechnology industry are sequenced as follows: "open innovation capacity", "quality and cost control ability", "advanced customer-oriented product manufacturing capacity", "technology R & D personnel's capacity", "brand image building capacity", "logistics and sales capacity", "grasping the market demand trends". The manufacturers and government decision-making body can use this as the basis, to promote the development of the biotechnology industry.

The Pointwise Characterizations of Fuzzy Mappings and Fuzzy Cardinal Numbers

In this paper,the pointwise characterizations of fuzzy mappings are given. Based of this definition,we give a few of new properties of fuzzy cardinal numbers.

Ideal Statistically Pre-Cauchy Triple Sequences of Fuzzy Number and Orlicz Functions

In this paper, we extend the notions of ideal statistically convergence for sequence of fuzzy number. We introduce the notions ideal statistically pre-Cauchy triple sequences of fuzzy number about Orlicz function, and give some correlation theorem. It is shown that x = {xijk} is ideal statistically pre-Cauchy if and only if D (xijk, xpqr) ≥ ε, i ≤ m, j ≤ n, t ≤ k}| ≥ δ} ∈I. At the same time, we have proved x = {xijk} is ideal statistically convergent to x0 if and only if . Also, some properties of these new sequence spaces are investigated.

Analysis of Syetem Reliability in Manufacturing Cell Based on Triangular Fuzzy Number

Due to lacking of test-data and field-data in reliability research during the design stage of manufacturing cell sys- tem.The degree of manufacturing cell system reliability research is increased.In order to deal with the deficient data and the un- certainty occurred from analysis and judgment,the paper discussed a method for studying reliability of manufacturing cell system through the analysis of fuzzy fault tree,which was based on triangular fuzzy number.At last,calculation case indicated that it would have great significance for ascertaining reliability index,maintenance and establishing keeping strategy towards manufac- turing cell system.

A NEW TECHNIQUE FOR COMPAIRING FUZZY NUMBERS USING AN INDEX OF OPTIMISM

Fuzzy numbers are convenient for representing imprecise numerical quantities in a vague environment, and their comparison or ranking is very important for application purposes. Despite many methods suggested in the literature, there is no single measure that is universally applicable to a wide variety of situations. This paper suggested a new method for comparing fuzzy numbers based on the combination of maximizing possibility and minimizing possibility using an index of optimism in [0,1] reflecting the decision makers’ risk taking attitude. The method is simple, but has many comparative advantages.

Fuzzy Modeling on L - R Fuzzy Number and Its Application

A new fuzzy modeling method, which based on L - R fuzzy number, is discussed in this paper. First, the fuzzy state equation model is constructed based on fuzzy state variable,fuzzy Input variable and fuzzy output variable whkh are represented by L - R fuzzy number. And then, identification of time - varying parameter in this model is discussed further. At the end, a simulated application is given to Indicate the effectiveness of this fuzzy modeling method.

SOME CLASSES OF DIFFERENCE SEQUENCES OF FUZZY NUMBERS DEFINED BY A SEQUENCE OF MODULI

In this article, we introduce and examine some properties of new difference sequence spaces of fuzzy numbers defined using a sequence of modulus functions.

Analysis of Helical Gear System Dynamic Response Based on Fuzzy Numbers

A non-linear dynamic model with the single degree of freedom of a helical gear pair introducing frzzy numbers is developed. In this proposed model, time-variant mesh stiffness, which is a non-linear parameter, mesh damping and composite error of a pair of meshing tooth of the gear pair are all included. Mesh stiffness is calculated by expressing Bo (r) as a Fourier series. Ⅱshape function is introduced as the membership function to characterize the fuzziness of the error. Fuzzy displacement dynamic response of the geared system at A- level, which is a closed interval, is ohtained by removing the fuzziness of the fuzzy differential equations and using Runge-Kutta numerical method. In fact, the fuzzy dynamic response and dynamic loading factor are aH the interval functions related λ. The result obtained here can be used to the fuzzy dynamic optimization design course of the helical gear system. The main advantage of this method is to introduce the concept of fuzzy number for the first time to the analysis of the gear system dynamics.