Convexity and level sets for interval-valued fuzzy sets

Convexity is a deeply studied concept since it is very useful in many fields of mathematics, like optimization. When we deal with imprecision, the convexity is required as well and some important applications can be found fuzzy optimization, in particular convexity of fuzzy sets. In this paper we have extended the notion of convexity for interval-valued fuzzy sets in order to be able to cover some wider area of imprecision. We show some of its interesting properties, and study the preservation under the intersection and the cutworthy property. Finally, we applied convexity to decision-making problems.

Research on Quantitative Evaluation Methods and Influencing Factors of Natural Gas Reservoir Development

Current methods of evaluating the effects of gas reservoir exploitation primarily focus on evaluating production statistics of a well or field, and they often have a certain subjectivity. In order to further analyze key indexes that affect a gas reservoir during production, this paper considered the characteristic parameters of different types of gas reservoirs and established an index system of evaluating a gas reservoir “exploitation effect” from the three aspects of gas reservoir characteristics, rock characteristics, and economic benefits. There are numerous factors affecting the exploitation effect of a gas reservoir. The relationships between different factors are complicated, and the evaluation result of each factor can also be vague. A fuzzy optimization theoretical model for gas reservoir evaluation and optimization was established on the basis of a quantitative study on the evaluation parameters in fuzzy mathematics. In order to clearly understand the influence of each factor on the gas reservoir exploitation effect, numerical simulation was used to perform a multifactor numerical simulation study of the quantitative sensitivity to determine the sequence of different influencing factors in terms of influencing the gas reservoir exploitation effect. This study provides a quantitative scientific basis for the evaluation of gas reservoir exploitation effect.

Integral Inequalities for Generalized Harmonically Convex Functions in Fuzzy-Interval-Valued Settings

It is a well-known 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 also 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 both the concepts, owing to the significant correlation that has developed between both in recent years. In this paper, we introduce a new class of harmonically convex fuzzy-interval-valued functions which is known as harmonically h-convex fuzzy-interval-valued functions (abbreviated as harmonically h-convex F-I-V-Fs) by means of fuzzy order relation. This fuzzy order relation is defined level-wise through Kulisch–Miranker order relation defined on interval space. Some properties of this class are investigated. BY using fuzzy order relation and h-convex F-I-V-Fs, Hermite–Hadamard type inequalities for harmonically are developed via fuzzy Riemann integral. We have also obtained some new inequalities for the product of harmonically h-convex F-I-V-Fs. Moreover, we establish Hermite–Hadamard–Fej’er inequality for harmonically h-convex F-I-V-Fs via fuzzy Riemann integral. These outcomes are a generalization of a number of previously known results, as well as many new outcomes can be deduced as a result of appropriate parameter “θ” and real valued function “∇” selections. For the validation of the main results, we have added some nontrivial examples. We hope that the concepts and techniques of this study may open new directions for research.

Fuzzy optimization based Water Distribution Network design using Self-Adaptive Cuckoo Search Algorithm

Water Distribution Network(s) (WDN) design is gaining prominence in the urban planning context. Several factors that play a significant role in design are uncertainty in data, non-linear relation of head loss & discharge, combinatorial nature of the problem, and high computational requirements. In addition, many conflicting objectives are possible and required for effective WDN design, such as cost, resilience, and leakage. Most of the research work published has used multiobjective evolutionary optimization in solving such complex WDN. However, the challenge of such population based evolutionary approaches is that they provide multiple trade-off Pareto optimal solutions to the decision-maker who will have to choose another set of techniques to arrive at a single optimal solution. The present study employs a fuzzy optimization approach that would provide a single optimal WDN design for Hanoi and Pamapur, India. Maximization of network resilience (NR) and minimization of network cost (NC) are employed in a multiobjective context. Later, minimization of network leakages (NL) is also incorporated, leading to three objective problems. Hyperbolic Membership Function (HMF), Exponential Membership Function (EMF), and Non-linear Membership Function (NMF) are employed in Self-Adaptive Cuckoo Search Algorithm based fuzzy optimization. HMF is found suitable to determine the best possible WDN design for chosen case studies based on the highest degree of satisfaction. HIGHLIGHT Most of the research conducted till now have used evolutionary multiobjective optimization in solving WDNs. But, the challenge of such evolutionary approaches is that they provide multiple trade-off pareto optimal solutions to the decision maker who will have to further choose another methodology to converge to a single optimal solution. The proposed methodology would simplify the decision-making process for an engineer.

LR-Preinvex Interval-Valued Functions and Riemann–Liouville Fractional Integral Inequalities

Convexity is crucial in obtaining many forms of inequalities. As a result, there is a significant link between convexity and integral inequality. Due to the significance of these concepts, the purpose of this study is to introduce a new class of generalized convex interval-valued functions called LR-preinvex interval-valued functions (LR-preinvex I-V-Fs) and to establish Hermite–Hadamard type inequalities for LR-preinvex I-V-Fs using partial order relation (≤p). Furthermore, we demonstrate that our results include a large class of new and known inequalities for LR-preinvex interval-valued functions and their variant forms as special instances. Further, we give useful examples that demonstrate usefulness of the theory produced in this study. These findings and diverse approaches may pave the way for future research in fuzzy optimization, modeling, and interval-valued functions.

Preface to the Special Issue on “Applications of Fuzzy Optimization and Fuzzy Decision Making”

During the last decades, fuzzy optimization and fuzzy decision making have gained significant attention, aiming to provide robust solutions for problems in making decisions and achieving complex optimization characterized by non-probabilistic uncertainty, vagueness, ambiguity and hesitation [...]

Computer-Aided Design for Identifying Anticancer Targets in Genome-Scale Metabolic Models of Colon Cancer

The efficient discovery of anticancer targets with minimal side effects is a major challenge in drug discovery and development. Early prediction of side effects is key for reducing development costs, increasing drug efficacy, and increasing drug safety. This study developed a fuzzy optimization framework for Identifying AntiCancer Targets (IACT) using constraint-based models. Four objectives were established to evaluate the mortality of treated cancer cells and to minimize side effects causing toxicity-induced tumorigenesis on normal cells and smaller metabolic perturbations. Fuzzy set theory was applied to evaluate potential side effects and investigate the magnitude of metabolic deviations in perturbed cells compared with their normal counterparts. The framework was applied to identify not only gene regulator targets but also metabolite- and reaction-centric targets. A nested hybrid differential evolution algorithm with a hierarchical fitness function was applied to solve multilevel IACT problems. The results show that the combination of a carbon metabolism target and any one-target gene that participates in the sphingolipid, glycerophospholipid, nucleotide, cholesterol biosynthesis, or pentose phosphate pathways is more effective for treatment than one-target inhibition is. A clinical antimetabolite drug 5-fluorouracil (5-FU) has been used to inhibit synthesis of deoxythymidine-5′-triphosphate for treatment of colorectal cancer. The computational results reveal that a two-target combination of 5-FU and a folate supplement can improve cell viability, reduce metabolic deviation, and reduce side effects of normal cells.