/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Mathematical programming

(1962). Management Models and Industrial Applications of Linear Programming. Journal of the Operational Research Society: Vol. 13, No. 3, pp. 274-275.

https://link.springer.com/content/pdf/10.1057%2Fjors.1962.42.pdf

Management Models and Industrial Applications of Linear Programming

https://cyberleninka.org/article/n/662470.pdf

Literature review of deteriorating inventory models by key topics from 2012 to 2015

The emergence of fuzzy sets makes job-shop scheduling problem (JSSP) become better aligned with the reality. This article addresses the JSSP with fuzzy execution time and fuzzy completion time (FJSSP). We choose the classic differential evolution (DE) algorithm as the basic optimization framework. The advantage of the DE algorithm is that it uses a special evolutionary strategy of difference vector sets to carry out mutation operation. However, DE is not very effective in solving some instances of FJSSP. Therefore, we propose a novel selection mechanism augmenting the generic DE algorithm (NSODE) to achieve better optimization results. The proposed selection operator adopted in this article aims at a temporary retention of all children generated by the parent generation, and then selecting N better solutions as the new individuals from N parents and N children. Various examples of fuzzy shop scheduling problems are experimented with to test the performance of the improved DE algorithm. The NSODE algorithm is compared with a variety of existing algorithms such as ant colony optimization, particle swarm optimization, and cuckoo search. Experimental results show that the NSODE can obtain superior feasible solutions compared with solutions produced by several algorithms reported in the literature.

Solving Fuzzy Job-Shop Scheduling Problem Using DE Algorithm Improved by a Selection Mechanism

A reliability-based consensus model and regret theory-based selection process for linguistic hesitant-Z multi-attribute group decision making

New approach for solving multi-objective transportation problem

Inventory model involving reworking of faulty products with three carbon policies under neutrosophic environment

Effect of sliding friction on torsional vibration of wind turbine drivetrain system under constant wind load

Many situations occur where exact solution cannot be found for real world problems and hence we solved these approximately. Probability theory, fuzzy set theory (FST), rough set theory (RST), soft set theory (SST) are novel mathematical tools to solve real world problems including uncertainty. All these theories more or less can help to understand and make dealt to imperfect knowledge. The basic philosophy of rough set is based on the assumption that human knowledge about a universe depends upon their capability to classify its objects. Every object of the universe there is associated a certain amount of information (data). Classifications of a universe and equivalence relations defined on the universe are known to be interchangeable notions. So, for mathematical point of view, equivalence relations are considered to define rough set. For every rough set, we associate two crisp sets, called lower and upper approximations and viewed as the sets of elements which certainly and possibly belong to the set. The advantage of rough set method is that it does not need any additional information about data, like probability in statistics, or membership in fuzzy set theory. Lattice is a simple algebraic structure since the basic concepts of the theory which include only orders, least upper bound and greatest lower bound. It is widely discussed and studied in classical algebraic theory. Lattice theory is used to formulate some types of generalised rough sets. Lattice theory extensively used in computer science and engineering. Based on the existing works about the algebraic structure of rough sets and soft sets we say that lattice structures of rough set and soft set have wide field of applications. Despite its novelty, the theory and its extensions have been widely applied to many problems, including decision analysis, data-mining, intelligent control and pattern recognition. In this thesis, we incorporate a detailed study on rough set in lattice. That is, we are trying to make an algebraic connection between the rough set and the lattice. We introduce rough modular lattice and rough distributive lattice in rough set environment by considering Pawlak’s approximation space. Beside this, concept of rough ideal and rough homomorphism are established in rough set environment. The equivalence classes are the basic building blocks for the construction of the lower and upper approximations. In real-life situation, it is difficult to find an equivalence relation. To over come this difficulty, many researchers approached to use tolerance relation, similarity relations, dominance relation to partition a universe and introduced generalized rough set. Soft set theory (SST) is introduced by Molodtsov (67), is a novel concept to deal with uncertainty. One main advantage of SST is that it has enough parameterization tools. It is well known that each equivalence relation on a set partitions the set into disjoint classes and each partition of the set provide us an equivalence relation on the set. In this thesis, we use a soft set instead of an equivalence relation to partition a set and then introduce the notion of soft approximation space. We attempt to study on lattice theory in the soft approximation space. In this thesis, we present the concepts of soft rough lattice and soft rough ideal in the soft rough approximation space. Soft rough set is presented by Feng et al. (32) which is a hybridization of soft set and rough set. Modified soft rough (MSR) set is an another approach to hybridization of soft set and rough set. Considering modified soft rough approximation space, we approximate a soft set and hereby introduce the notion of rough soft set. We discuss lattice theory in the frame-work of rough soft theory. In this research content, we introduce soft set relation in a new way. We incorporate lattice theory in soft set using this soft set relation. We consider the study of congruence relation on soft set. Considering lattice as universal set, we introduce soft congruence relation in soft set. The concepts of upper and lower approximations of a subset in a lattice are depicted based on this soft congruence relation. At last, we try to make a fusion between fuzzy set and rough soft set. Here we measure roughness of rough soft set and introduce the concept of fuzzy rough soft set in MSR-approximation space. Some properties of fuzzy rough soft set are derived. Moreover, lattice theory is studied on the fuzzy rough soft set. In the whole thesis, we are trying to incorporate lattice theory in uncertain environments. Lattice theory in different approximation spaces is studied. Finally, conclusion and direction of future works of the study are presented.

http://inet.vidyasagar.ac.in:8080/jspui/bitstream/123456789/2397/1/Susanta_Thesis.pdf

Sankar Kumar Roy

Papers

A reliability-based consensus model and regret theory-based selection process for linguistic hesitant-Z multi-attribute group decision making

New approach for solving multi-objective transportation problem

Inventory model involving reworking of faulty products with three carbon policies under neutrosophic environment

Effect of sliding friction on torsional vibration of wind turbine drivetrain system under constant wind load

A comprehensive study on lattice under uncertain environments