Fuzzy Inequalities Research Articles

What are the main factors of fuzzy inequality in Chad?

The purpose of this study is to identify the effects of multidimensional (fuzzy) inequalities and marginal changes on the Gini coefficients of various factors. This allows a range of social policies to be specifically targeted to reduce broader inequalities, but these policies are focused primarily on health, education, housing, sanitation, energy and drinking water. It is necessary to target policy areas that are unequally distributed, such as those with access to unevenly distributed drinking water policies. The data are from the Household and Consumption Survey of 6695 households in 2003 and 9259 households in 2011. This paper uses Lerman and Yitzhaki’s method. The results revealed that the main contributors to inequalities over the two periods were health and education. These sources have a potentially significant effect on total inequality. Health increases overall inequalities, but sources such as housing, sanitation and energy reduce them. This article provides resources to disadvantaged and vulnerable target groups. Multiple inequalities are analyzed for different subgroups of households, such as place of residence and the gender of the head of household. Analyzing fuzzy poverty inequalities makes it possible to develop targeted measures to combat poverty and inequality. This study is the first to investigate the sources of Gini’s fuzzy inequality in Chad via data analysis techniques, and in general, it is one of the few studies in Saharan Africa to be interested in this subject. Some development policies in sub-Saharan Africa should therefore focus on different sources (negative effect), sources (positive effect) and the equalization effect.

Optimality and duality for nonconvex fuzzy optimization using granular differentiability method

This paper is concerned with the optimality and duality for a class of nonconvex fuzzy optimization problems under granular differentiability. We first derive optimality conditions for fuzzy optimization problems with fuzzy inequality constraints based on granular differentiability and granular F-convexity. Then, Wolfe type and Mond-Weir type dual models corresponding to the primal problems are described, where their weak, strong, and strict converse dual theorems are explored to illustrate the connection between the optimal solutions of the primal and the dual models. Meanwhile, several examples are provided to support the corresponding theoretical results.

Arithmetic Mean-Geometric Mean Inequality for Convex Fuzzy Sets

Convex analysis is a discipline of mathematics dedicated to the explication of the properties of convex sets and convex functions. Convex functions are extremely useful in proving many famous inequalities in mathematics. It is widely known that inequalities defined by convex functions originated with the works done by Holder and Jensen among others and applied to modeling a variety of problems both in hard and soft sciences. It is said that the arsenal of an analyst is heavily stocked with inequalities. Studies related to convexity have kept occupying a central position in almost all areas of mathematics, especially in functional analysis and operations research. Following the emergence of fuzzy set theory, fuzzy convexity alongside a number of related concepts has been explicated. However, not much has been done regarding fuzzy inequalities defined by fuzzy convexity. In this paper, a novel attempt to study arithmetic mean-geometric mean is proposed. In this short note, we provide two proofs of the arithmetic mean-geometric mean inequality for convex fuzzy sets. Mathematics Subject Classification 2020: 03E72, and 94D05.

Fuzzy Differential Inequalities for Convolution Product of Ruscheweyh Derivative and Multiplier Transformation

In this paper, the author combines the geometric theory of analytic function regarding differential superordination and subordination with fuzzy theory for the convolution product of Ruscheweyh derivative and multiplier transformation. Interesting fuzzy inequalities are obtained by the author.

Q-Rung orthopair fuzzy inequality derived from equality and operation

q-Rung orthopair fuzzy inequality derived from equality and operation

Some Results for Intuitionistic Fuzzy Inequality

Intuitionistic fuzzy sets, characterized by membership degree mu , non-membership degree upsilon and hesitation degree pi , are a meaningful extension of fuzzy set. Inequalities on intuitionistic fuzzy sets/values are very important in solving real problems. In this paper, some inequalities on intuitionistic fuzzy sets are derived from operations. Moreover, three unweighted intuitionistic fuzzy aggregation operators, including unweighted intuitionistic fuzzy Square, unweighted intuitionistic fuzzy Arithmetic and unweighted intuitionistic fuzzy Geometric, are developed. Later, some corresponding inequality relations on them are deeply explored. Finally, some inequalities on intuitionistic fuzzy value are constructed by equality mu +upsilon +pi =1 in critical definition and proved by some existing famous inequalities, which provide a novel basis for the intuitionistic fuzzy inequalities in operations and aggregation operators.

Some Fuzzy Inequalities for Harmonically s-Convex Fuzzy Number Valued Functions in the Second Sense Integral

Many fields of mathematics rely on convexity and nonconvexity, especially when studying optimization issues, where it stands out for a variety of practical aspects. Owing to the behavior of its definition, the idea of convexity also contributes significantly to the discussion of inequalities. The concepts of symmetry and convexity are related and we can apply this because of the close link that has grown between the two in recent years. In this study, harmonic convexity, also known as harmonic s-convexity for fuzzy number valued functions (F-NV-Fs), is defined in a more thorough manner. In this paper, we extend harmonically convex F-NV-Fs and demonstrate Hermite–Hadamard (H.H) and Hermite–Hadamard Fejér (H.H. Fejér) inequalities. The findings presented here are summaries of a variety of previously published studies.

Pythagorean fuzzy inequality derived by operation, equality and aggregation operator

Pythagorean fuzzy inequality derived by operation, equality and aggregation operator

Solving a single period inventory model with fuzzy inequality

The purpose of this paper is to present a fuzzy chance-constrained single period inventory model (FCCSPIM) in which the fuzziness appears in the space constraint and objective function is crisp. Here the partial order relation exists in between a random variable and a real number. That means the probability of the event is discussed under vague data. Our approach for the solution process uses mostly fuzzy Zimmermann technique to convert the FCCSPIM into a proper deterministic equivalent. Then the resulting nonlinear deterministic model is solved by using LINGO software. The result indicate that the fuzzy programming approach is effective for the inventory problem. The applications of an optimisation model under uncertainty are used to solve day to day problems. Many methods were developed by using tools of mathematics, probability theory and stochastic process. Here, one new approach of fuzzy programming technique is introduced to obtain a deterministic form.

Preinvexity of $ n $-dimensional fuzzy number-valued functions: characterization, variational inequality and optimization problems

<abstract><p>In this paper, the preinvexity of <italic>n</italic>-dimensional fuzzy number-valued functions are defined and discussed by means of the partial order relation in <italic>n</italic>-dimensional fuzzy number space which including preinvexity, weak preinvexity, strict preinvexity, weakly strict preinvexity, prequasiinvexity, weak prequasiinvexity, strict prequasiinvexity, weakly strict prequasiinvexity, and so on. In addition, their interrelations of the preinvexity of <italic>n</italic>-dimensional fuzzy number-valued functions are discussed, and some counterexamples are given. Furthermore, the two-parameter optimization problem, $ n $-dimensional fuzzy variational-like inequality and optimality conditions related to $ n $-dimensional preinvex fuzzy number-valued functions are discussed.</p></abstract>

Fuzzy Mixed Variational-like and Integral Inequalities for Strongly Preinvex Fuzzy Mappings

It is a familiar fact that convex and non-convex fuzzy mappings play a critical role in the study of fuzzy optimization. Due to the behavior of its definition, the idea of convexity plays a significant role in the subject of inequalities. The concepts of convexity and symmetry have a tight connection. We may use whatever we learn from one to the other, thanks to the significant correlation that has developed between both in recent years. Our aim is to consider a new class of fuzzy mappings (FMs) known as strongly preinvex fuzzy mappings (strongly preinvex-FMs) on the invex set. These FMs are more general than convex fuzzy mappings (convex-FMs) and preinvex fuzzy mappings (preinvex-FMs), and when generalized differentiable (briefly, G-differentiable), strongly preinvex-FMs are strongly invex fuzzy mappings (strongly invex-FMs). Some new relationships among various concepts of strongly preinvex-FMs are established and verified with the support of some useful examples. We have also shown that optimality conditions of G-differentiable strongly preinvex-FMs and the fuzzy functional, which is the sum of G-differentiable preinvex-FMs and non G-differentiable strongly preinvex-FMs, can be distinguished by strongly fuzzy variational-like inequalities and strongly fuzzy mixed variational-like inequalities, respectively. In the end, we have established and verified a strong relationship between the Hermite–Hadamard inequality and strongly preinvex-FM. Several exceptional cases are also discussed. These inequalities are a very interesting outcome of our main results and appear to be new ones. The results in this research can be seen as refinements and improvements to previously published findings.

Robust regression using support vector regressions

Abstract Noisy data and outliers has always been one of the main challenges in regression applications. The presence of these data among training data will produce several negative effects on the generalization ability of the built model in regression. Filtering noisy data and outliers as a preprocessing step in pattern recognition has many challenges in practice because it is really hard to distinguish noisy samples from the remaining ones. Hence, robustness of an algorithm is defined as its capability to train the model in such way that it suffers less from noisy data as well as outliers. In this study, we improve the performance of support vector regression (SVR) to be more robust. SVR is sensitive to noisy data because its trained model is built by support vectors which contain a small portion of training data. The constraints inequalities in the constraints of e-insensitive SVR are changed to fuzzy inequalities without any changes in its loss function. This gives more flexibility to the SVR constraints for satisfaction. Then, we solve the quadratic programming (QP) problem and compare the new method with standard support vector regression model. Experimental results with different data sets show the superiority of the proposed method especially in presence of noisy data and outliers.

Solving fuzzy stochastic multi-objective programming problems based on a fuzzy inequality

Probabilistic or stochastic programming is a framework for modeling optimization problems that involve uncertainty.In this paper, we focus on multi-objective linear programmingproblems in which the coefficients of constraints and the righthand side vector are fuzzy random variables. There are several methodsin the literature that convert this problem to a stochastic orfuzzy problem. By using a special type of fuzzy inequality, wetransform the problem into a convenient stochastic problem. Thensome known methods are applied to obtain the optimal solution.Finally, the equivalent multi-objective problem is solved by aninteractive approach. A numerical example is provided to illustrate the procedure.

Solving a Single Period Inventory Model with Fuzzy Inequality

Solving a Single Period Inventory Model with Fuzzy Inequality

An application of FISM and TOPSIS to a multi-objective multi-item solid transportation problem

This paper deals a multi-objective multi-item solid transportation problem (MMSTP) with fuzzy inequality constraints in profit maximization and time minimization forms. Following fuzzy chance programming, more specificity possibility-necessity theory, an approach to conversion of the imprecise MMSTP to the equivalent deterministic form is formulated. Fuzzy interactive satisfied method is adopted to derive optimal compromise solutions of the MMSTP through generalized reduced gradient technique. In order to obtain best non-dominating solution, the technique for order preference by similarity to ideal solution is applied. Finally, a numerical example and a statistical test namely, analysis of variance illustrate and signify the feasibility and validity of the proposed model and techniques.

A fuzzy evaluation approach with the quasi-ordered set: evaluating the efficiency of decision making units

This work proposes an inequality approach with the quasi-ordered set to evaluate the performances of decision making units (DMUs). In real world applications, input and output data are often imprecise and fluctuated. In this case, a fuzzy inequality approach is proposed to evaluate DMUs with fuzzy data. Fuzzy inequalities consist of fuzzy expressions of the production possibility set and the line segment joining the origin to the evaluated DMU. Moreover, under constant returns to scale, the production possibility set is spanned by all the DMUs without the evaluated DMU. Fuzzy efficiency is dependent upon whether the solution set of fuzzy inequalities is empty or not. The quasi-ordered set is used to distinguish the fuzzy efficiency. Finally, numerical examples are used to illustrate the approach.

Structures of Opposition and Comparisons: Boolean and Gradual Cases

This paper first investigates logical characterizations of different structures of opposition that extend the square of opposition in a way or in another. Blanché’s hexagon of opposition is based on three disjoint sets. There are at least two meaningful cubes of opposition, proposed respectively by two of the authors and by Moretti, and pioneered by philosophers such as J. N. Keynes, W. E. Johnson, for the former, and H. Reichenbach for the latter. These cubes exhibit four and six squares of opposition respectively. We clarify the differences between these two cubes, and discuss their gradual extensions, as well as the one of the hexagon when vertices are no longer two-valued. The second part of the paper is dedicated to the use of these structures of opposition (hexagon, cubes) for discussing the comparison of two items. Comparing two items (objects, images) usually involves a set of relevant attributes whose values are compared, and may be expressed in terms of different modalities such as identity, similarity, difference, opposition, analogy. Recently, J.-Y. Béziau has proposed an “analogical hexagon” that organizes the relations linking these modalities. Elementary comparisons may be a matter of degree, attributes may not have the same importance. The paper studies in which ways the structure of the hexagon may be preserved in such gradual extensions. As another illustration of the graded hexagon, we start with the hexagon of equality and inequality due to R. Blanché and extend it with fuzzy equality and fuzzy inequality. Besides, the cube induced by a tetra-partition can account for the comparison of two items in terms of preference, reversed preference, indifference and non-comparability even if these notions are a matter of degree. The other cube, which organizes the relations between the different weighted qualitative aggregation modes, is more relevant for the attribute-based comparison of items in terms of similarity.

A fuzzy inequality evaluation approach for measuring the relative efficiency

A fuzzy inequality evaluation approach for measuring the relative efficiency

A Revised Version of a Lexicographical-based Method for Solving Fully Fuzzy Linear Programming Problems with Inequality Constraints

Ezzati et al. (A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem. Appl Math Model. 2015;39(12):3183–3193) introduced a lexicographic criterion for ranking triangular fuzzy numbers (TFNs), and proposed a method to solve fully fuzzy linear programming (FFLP) problems based on the lexicographic method of multi-objective optimisation; the authors assumed that fuzzy inequality constraints can be transformed into fuzzy equality constraints by introducing non-negative fuzzy slack and surplus variables. They illustrated the proposed method by means of a fully fuzzy investment problem. Bhardwaj and Kumar (A note on “A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem”. Appl Math Model. 2015;39(19):5982–5985) demonstrated that introducing fuzzy slack and surplus variables is mathematically incorrect, and showed that the solution of the fuzzy investment problem is unfeasible. Towards the end of their paper, they claimed that there is no feasible solution to the fuzzy investment problem when considering Ezzati et al.’s ranking criterion. In this paper, we propose a revised version of Ezzati et al.’s method whereby the optimal solution of FFLP problems with equality and inequality constraints can be obtained. Furthermore, by using the revised method, we show that feasible solutions of the fuzzy investment problem actually exist, and therefore Bhardwaj and Kumar’s claim is false. To show the applicability of the revised method, we also consider a fully fuzzy project scheduling problem with budget constraint.

Fuzzy Iyengar-type inequalities

Here, we present fuzzy Iyengar-type inequalities for continuous fuzzy number valued functions. These functions fulfill some type of Lipschitz conditions.