var tagData = [
    {
        id: 1,
        title: "Internal"
    },
    {
        id: 2,
        title: "Industry"
    },
    {
        id: 3,
        title: "Company"
    }
];

var articleData = [
    {
        id: 1,
        pagetitle: "Card title that wraps to a new line",
        image: "https://via.placeholder.com/500x250/171717/222222?text=500x250",
        tags: [
            "Internal",
            "Industry",
            "Company",
        ],
        content: "This is a longer card with supporting text below as a natural lead-in to additional content. This content is a little bit longer.",
        alias: "/news-article-1",
        published: 1672668835
    },
    {
        id: 2,
        pagetitle: "Card title",
        image: "https://via.placeholder.com/500x250/171717/222222?text=500x250",
        tags: [
            "Company",
        ],
        content: "This card has supporting text below as a natural lead-in to additional content.",
        alias: "/news-article-2",
        published: 1672668835
    },
    {
        id: 3,
        pagetitle: "Card with no image",
        image: "",
        tags: [
            "Internal",
            "Company",
        ],
        content: "This is another card with title and supporting text below. This card has some additional content to make it slightly taller overall.",
        alias: "/news-article-3",
        published: 1672668835
    },
    {
        id: 4,
        pagetitle: "Yet another article",
        image: "",
        tags: [
            "Industry"
        ],
        content: "Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.",
        alias: "/news-article-4",
        published: 1672668835
    },
];

var vm = new Vue({
    el: "#app",
    productionTip: false,
    data: {
        articles: articleData,
        search: '',
        tags: tagData,
        checkedTags: []
    },
    computed: {
        searchArticles: function searchArticles() {
            var result = this.articles.filter(function (article) {
                // articles can have more than one tag/category assigned
                //if any checkboxes have been checked...
                if(this.checkedTags.length) {
                    return this.checkedTags.every( tag => article.tags.includes(tag)) &&  (article.pagetitle.toLowerCase().match(this.search.toLowerCase()) || article.content.toLowerCase().match(this.search.toLowerCase()) )
                } else {
                    return article.pagetitle.toLowerCase().match(this.search.toLowerCase()) || article.content.toLowerCase().match(this.search.toLowerCase())   
                }
            }, this);
            return result;
        }
    }
});

.search {
  margin: 8px 4px 8px 4px;
}

<div id="app">
<div class="search">
<label>Search:</label> <input v-model="search" />&nbsp;
<label>Tags:</label> 
<span v-for="tag in tags">
<input type="checkbox" name="tags" :id="tag.id" :value="tag.title" v-model="checkedTags" /> 
<label for="tag.id">{{tag.title}}</label>&nbsp;
</span>
</div>
<table border=1>
<thead><tr><th>Id</th><th>Title</th><th>Tags</th></tr></thead>
<tbody>
<tr v-for="item in searchArticles">
  <td>{{item.id}}</td>
  <td>{{item.pagetitle}}</td>
  <td>{{item.tags}}</td>
</tr>  
</tbody>
</table>
</div>
<script src="https://cdnjs.cloudflare.com/ajax/libs/vue/2.5.17/vue.js"></script>