Resolution and simplification of Dombi-fuzzy relational equations and latticized optimization programming on Dombi FREs

In this paper, we introduce a type of latticized optimization problem whose objective function is the maximum component function and the feasible region is defined as a system of fuzzy relational equalities (FRE) defined by the Dombi t-norm. Dombi family of t-norms includes a parametric family of continuous strict t-norms, whose members are increasing functions of the parameter. This family of t-norms covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. Since the feasible solutions set of FREs is non-convex and the finding of all minimal solutions is an NP-hard problem, designing an efficient solution procedure for solving such problems is not a trivial job. Some necessary and sufficient conditions are derived to determine the feasibility of the problem. The feasible solution set is characterized in terms of a finite number of closed convex cells. An algorithm is presented for solving this nonlinear problem. It is proved that the algorithm can find the exact optimal solution and an example is presented to illustrate the proposed algorithm.Comment: arXiv admin note: text overlap with arXiv:2206.09716, arXiv:2207.0637

An exact algorithm for linear optimization problem subject to max-product fuzzy relational inequalities with fuzzy constraints

Fuzzy relational inequalities with fuzzy constraints (FRI-FC) are the generalized form of fuzzy relational inequalities (FRI) in which fuzzy inequality replaces ordinary inequality in the constraints. Fuzzy constraints enable us to attain optimal points (called super-optima) that are better solutions than those resulted from the resolution of the similar problems with ordinary inequality constraints. This paper considers the linear objective function optimization with respect to max-product FRI-FC problems. It is proved that there is a set of optimization problems equivalent to the primal problem. Based on the algebraic structure of the primal problem and its equivalent forms, some simplification operations are presented to convert the main problem into a more simplified one. Finally, by some appropriate mathematical manipulations, the main problem is transformed into an optimization model whose constraints are linear. The proposed linearization method not only provides a super-optimum (that is better solution than ordinary feasible optimal solutions) but also finds the best super-optimum for the main problem. The current approach is compared with our previous work and some well-known heuristic algorithms by applying them to random test problems in different sizes.Comment: 29 pages, 8 figures, 7 table

Interfacial bond strength of coloured SCC repair layers : an experimental and optimisation study

This study investigates experimentally and analytically the interfacial bond strength of coloured SCC repair layers. Ten SCC mixes with 5%, 10% and 15% of blue, green or red pigments were produced to examine their fresh properties. Subsequently, 60 coloured SCC specimens were tested to assess interfacial bond strength using pull-off and push-out tests. The results confirm that pigments reduce the mechanical properties of SCC and its bond strength to concrete substrates, with red pigment reducing (by up to 41%) interfacial bond strength. It is shown that the push-out test is effective to determine the interfacial shear bond strength between the SCC repair layers and substrates. A GNNC-Modified PSO algorithm is proposed to calculate accurately (R2 = 0.95) the interfacial bond strength of coloured SCC repair layers. This study contributes towards developing more effective test methods and more accurate models to calculate interfacial bond strength of the SCC repair layers used in this study